text stringlengths 256 16.4k |
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The proton to electron mass ratio: $$\mu={m_p\over m_e}= {\alpha^2\over \pi r_pR_H}=1836.15267\;\;\leftarrow\;significant!!!$$
& the Planck mass to electron mass ratio:$${m_{\ell}\over m_e}={\alpha^2\over{4\pi\ell R_H}}=2.3893048e+22$$
using $$m_pr_p=4\ell m_{\ell}=r_em_e\;where\;r_e={\alpha^2\over\pi R_H}$$
$\alpha=$ ... |
Background: The arena is fixed particle number nonrelativistic quantum mechanics. The state space is $$ \mathbf{H}(1)=\mathcal H\otimes\mathcal S, $$ where $\mathcal H$ is an "orbital" state space ($L^2(\mathbb R^3)$ if one'd like), and $\mathcal S$ is the spin space, which for a particle of spin $s$ is identifiable wi... |
Difference between revisions of "Inertia"
(→Derivation)
Line 42: Line 42:
where <math>J = mr^{2}</math> is called the '''[https://en.wikipedia.org/wiki/Moment_of_inertia moment of inertia]''' (kg.m<sup>2</sup>).
where <math>J = mr^{2}</math> is called the '''[https://en.wikipedia.org/wiki/Moment_of_inertia moment of in... |
What’s in a name? that which we call a rose
By any other name would smell as sweet…
—William Shakespeare
In our daily lives, we are accustomed to giving multiple names to a single object. My wife calls me Xander, while my brothers and sisters call me Alex, and my students call me Mr. H. The titles, honorifics, and dimi... |
While this reaction is highly regioselective, it is not 100% regioselective. Consider the nearly identical reactions:
$$\begin{align}\ce{CCl4 + H2C=CH-(CH2)5CH3 ->[(PhCO2)2][90\text{-}105ºC] Cl3C-CH2-CHCl-(CH2)5CH3} \hspace{.63cm} \text{75%}^{[1]}\\ \ce{CCl4 + H2C=CH-COH-(CH3)2 ->[(PhCO2)2][80ºC] Cl3C-CH2-CHCl-CH(OH)-(... |
I am new to differential geometry and I am trying to understand Gaussian curvature. The definitions found at Wikipedia and Wolfram sites are too mathematical. Is there any intuitive way to understand Gaussian curvature?
For a
intuitive understanding, imagine a flat sheet of paper (or just grab one in your hand). It has... |
$\dfrac{d}{dx}{\, (\cos{x})} \,=\, -\sin{x}$
The differentiation or derivative of cos function with respect to a variable is equal to negative sine. This formula is read as the derivative of $\cos{x}$ with respect to $x$ is equal to negative $\sin{x}$.
If $x$ is used to represent a variable, then the cosine function is... |
I'm trying to calculate the properties of the combustion process using propane and nitrous oxide. When I tried to nail down the combustion temperature, the result looks just off to me. I went through several times with the process but since the reaction should produce less enthalpy change than using pure oxygen gas and... |
Quadratic programming (QP) involves minimizing or maximizing an objective function subject to bounds, linear equality, and inequality constraints. Example problems include portfolio optimization in finance, power generation optimization for electrical utilities, and design optimization in engineering.
Quadratic program... |
Shinichi Mochizuki of Kyoto divided the steps needed to prove the 1985 conjecture by Oesterlé and Masser into four papers listed at the bottom of the Nature article above.
Up to a few exceptions to be proved separately, a strengthening of Fermat's Last Theorem Four days ago, Nature described a potentially exciting deve... |
1. Definition & Example
A
permutationof size$n$ is a bijection of $\{1,\ldots,n\}$. $\mathfrak{S}_n$ denotes the set of all such permutations.
There are two standard ways to denote $\pi \in \mathfrak{S}_n$.
The
one-line notationis given by $\pi = [\pi(1),\ldots,\pi(n)]$. E.g., $\pi = [5,4,2,3,1]$ says that
$$\pi(1)=5,\... |
This example shows how to add text to a chart, control the text position and size, and create multiline text.
Add text next to a particular data point using the
text function. In this case, add text to the point . The first two input arguments to the
text function specify the position. The third argument specifies the ... |
Just skimmed over the links:
Highview:
Using ambient heat to warm it, the process
recovers around 50 per cent of the electricity that is fed in, says Highview's chief executive Gareth Brett. The efficiency rises to around 70 per cent if you harness waste heat from a nearby industrial or power plant to heat the cryogen ... |
Prove that $\operatorname{trace}(ABC) = \operatorname{trace}(BCA) = \operatorname{trace}(CAB)$ if $A,B,C$ matrices have the same size.
closed as off-topic by user26857, mrp, John B, Daniel W. Farlow, Nick Peterson Mar 3 '17 at 23:25
This question appears to be off-topic. The users who voted to close gave this specific ... |
Difference between revisions of "Inertia"
(→Normalised Inertia Constants)
(→Normalised Inertia Constants)
Line 50: Line 50:
: <math>H = \frac{1}{2} \frac{J \omega_0^{2}}{S_{b}}</math>
: <math>H = \frac{1}{2} \frac{J \omega_0^{2}}{S_{b}}</math>
−
where <math>\omega_{0} = 2 \pi \times \frac{n}{60}</math> is the nominal m... |
Huge cardinal
Huge cardinals (and their variants) were introduced by Kenneth Kunen in 1972 as a very large cardinal axiom. Kenneth Kunen first used them to prove that the consistency of the existence of a huge cardinal implies the consistency of $ZFC+$"there is a $\aleph_2$-saturated ideal over $\omega_1$". [1]
Content... |
Optimal control of the coefficient for the regional fractional $p$-Laplace equation: Approximation and convergence
1.
Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA
2.
University of Puerto Rico, Rio Piedras Campus, Department of Mathematics, College of Natural Sciences, 17 Universi... |
Search
Now showing items 1-5 of 5
Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c wit... |
Can a doable experiment prove that the objective reality doesn't exist?
Here's a rare example of the media hype that leads the reader to a basically correct conclusion about quantum mechanics.
As I have often argued, quantum mechanics fundamentally requires the description of the phenomena to be observer-dependent. An ... |
It's hard to say just from the sheet music; not having an actual keyboard here. The first line seems difficult, I would guess that second and third are playable. But you would have to ask somebody more experienced.
Having a few experienced users here, do you think that limsup could be an useful tag? I think there are a... |
Equidistribution of zeros of Random orthogonal polynomials
Speaker
Dr. Koushik Ramachandran Oklahoma State University, USA
When Mar 08, 2018
from 04:00 PM to 05:00 PM
Where LH 006 Add event to calendar vCal
iCal
Abstract: We study the asymptotic distribution of zeros for the random polynomials \(Pn(z)\) = \(\sum^n_{k=0... |
The exact value of secant of $45$ degrees is derived in geometry and it can also be derived in trigonometry by a trigonometric identity. In geometry, the $\sec{(45^°)}$ value can be derived in theoretical and practical approaches. Now, let’s learn the ways of deriving the $\sec{\Big(\dfrac{\pi}{4}\Big)}$ value in mathe... |
Trichotomy (mathematics)
In mathematics, the Law of
Trichotomy states that every real number is either positive, negative, or zero. [1] More generally, trichotomy is the property of an order relation < on a set X that for any x and y, exactly one of the following holds: x
In mathematical notation, this is
\forall x \in... |
(The society is limited to people with PhDs after 1990, occasioning the title of this post, a reference to a song about a bar limited to people under 21, a reference you will not get unless your PhD was granted well before 1990.)
I can't blog all the great papers and discussions, so I'll pick one of particular interest... |
There are four important things to remember here.
The first is that you can factor numbers and here we have $84 = 12\cdot 7$
The second is that $\log_x(y\cdot z) = \log_x(y) + \log_x(z)$
The third is that $\log_x(y) = \dfrac{\log_z(y)}{\log_z(x)}$
Finally, remember that $\log_x(x)=1$
These are true for all positive rea... |
The Basel problem can be solved by simple integration!
Recall that the Basel problem is to determine the value of $\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \ldots$.
Consider $f(x) = \ldots + e^{-3x} + e^{-2x} + e^{-1x} + e^{0x} + e^{1x} + e^{2x} + e^{3x} + \ldots$. By double integrating $f$, we get $h(x) = \ldot... |
Author: Subhransu Maji
Background
In the improved B-CNN paper published at BMVC 2017 we showed that the matrix square root is an effective way to normalize covariance matrices used for classification tasks. While the square root and its gradient can be computed via a SVD decomposition, this is not efficienly implemente... |
This is slightly contrived, but consider a situation where you have two balls, of mass $M$ and $m$, where $M=16\times100^N\times m$ for some integer $N$. The balls are placed against a wall as shown:
We push the heavy ball towards the lighter one and the wall. The balls are assumed to collide elastically with the wall ... |
@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... |
Searching for just a few words should be enough to get started. If you need to make more complex queries, use the tips below to guide you.
Purchase individual online access for 1 year to this journal.
Impact Factor 2019: 0.808
The journal
Asymptotic Analysis fulfills a twofold function. It aims at publishing original m... |
This question already has an answer here:
With this given information I am able to calculate $\phi$ limits for $P$ portion over $T$ using the following method:
$$ \begin{split} \tan \beta = z/y,\\ z=R\cos\theta, \end{split}\quad \iff \quad y={R\cos\theta\over\tan\beta} $$
$$ \begin{split} R\sin\theta\sin\phi={R\cos\the... |
I am quite confused about the objective function of the bayesian model averaging in the paper "Bayesian Averaging of Classifiers and the overfitting Problem".1
On the section 2, here is the first equation:
Let $n$ be the training set size, $\mathbf{x}$ examples in the training set, $\mathbf{c}$ the corresponding class ... |
Division Ring Norm is Continuous on Induced Metric Space
Jump to navigation Jump to search
Theorem
Let $\struct {R, \norm {\,\cdot\,}}$ be a normed division ring.
Proof
Let $x_0 \in R$.
Let $\epsilon \in \R_{\gt 0}$.
Let $x \in R: \norm {x - x_0} \lt \epsilon$.
Then:
\(\displaystyle \size {\norm {x} - \norm {x_0} }\) \... |
The set of integers $\Bbb Z$ under ordinary addition is cyclic. Both $1$ and $-1$ are generators. But I am a bit confused how can $1$ generate $0$ and how $-1$ generates $0$? What is the order of $1$ and $-1$ on this group of integers?
The subgroup generated by a set of elements of a group is the smallest subgroup that... |
Ian Miller's answer is the nicest and most efficient solution to the problem.
Just for your curiosity, I shall give you another one using Taylor series since you will use them a lot during your studies.
First, changing variable $x=\frac \pi 2+y$ $$\frac{\sqrt[4]{ \sin (x)} - \sqrt[3]{ \sin (x)}}{\cos^2(x)}=\frac{\sqrt[... |
If $f \in R(\alpha)$ on $[a,b]$ and if for every monotonic function $f : $
$$\int_a ^b f~ d \alpha = 0 $$
then, prove that $\alpha$ must be constant on $[a,b]$
Proof:
By integration by parts :
$\int_a ^b f~ d \alpha + \int_a ^b \alpha~ df = f(b) \alpha (b) -f(a) \alpha (a) $ . Substituting $\int_a ^b f~ d \alpha = 0 $ ... |
Erin Carmody successfully defended her dissertation under my supervision at the CUNY Graduate Center on April 24, 2015, and she earned her Ph.D. degree in May, 2015. Her dissertation follows the theme of
killing them softly, proving many theorems of the form: given $\kappa$ with large cardinal property $A$, there is a ... |
$\{s_n\}$ is defined by $$s_1 = 0; s_{2m}=\frac{s_{2m-1}}{2}; s_{2m+1}= {1\over 2} + s_{2m}$$
The following is what I tried to do.
The sequence is $$\{0,0,\frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{3}{8},\frac{7}{8},\frac{7}{16},\cdots \}$$
So the even terms $\{E_i\} = 1 - 2^{-i}$ and the odd terms $\{O_k\} = \frac{1}{2... |
$\cot{(A+B)}$ $\,=\,$ $\dfrac{\cot{B}\cot{A}\,–\,1}{\cot{B}+\cot{A}}$
$\dfrac{\cot{B}\cot{A}\,–\,1}{\cot{B}+\cot{A}}$ $\,=\,$ $\cot{(A+B)}$
The cot of angle sum identity is called as cot of sum of two angles identity or cot of compound angle identity. It is usually used in two cases in mathematics.
The cot of angle sum... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
Ok, suppose $M,N$ are Riemannian manifolds and $F:M\to N$ is a smooth map between them. In a book I have here they consider that $\dim M=m \geq \dim N=n$ and that $x\in M$ is a regular point such that the derivative $DF(x):T_x M\to T_{F(x)}N$ is surjective. With this conditions, note that $\ker DF(X)^\perp$ is isomorph... |
Answer: The three denominations are $65$, $72$ and $97$.How did I detect this answer?I searched the list of primitive Pythagorean triples at [link to triple list], while using the Frobenius applet available at [applet link].Based on my search I know that the answer to the puzzle is unique; still, I would like to see a ... |
Difference between revisions of "Inertia"
(→Derivation)
(→Derivation)
Line 46: Line 46:
:* In physics, the moment of inertia <math>J</math> is normally denoted as <math>I</math>. In electrical engineering, the convention is for the letter "i" to always be reserved for current, and is therefore often replaced by the let... |
OpenCV 3.1.0
Open Source Computer Vision
In this tutorial you will learn how to:
Principal Component Analysis (PCA) is a statistical procedure that extracts the most important features of a dataset.
Consider that you have a set of 2D points as it is shown in the figure above. Each dimension corresponds to a feature you... |
I'm using
chemfig (perhaps improperly) for relational algebra graphs. Here, for example, is a simple one:
\documentclass{article}\usepackage[italian]{babel}\usepackage[utf8]{inputenc}\usepackage[T1]{fontenc}\usepackage{chemfig}\usepackage{amsmath}\usepackage{amssymb}\usepackage{relsize}\newcommand{\select}{\sigma}\newc... |
Suppose we have IID random variables $X_1,\dots,X_n$ with distribution $\mathrm{Ber}(\theta)$. We are going to observe a sample of the $X_i$'s in the following way: let $Y_1,\dots,Y_n$ be independent $\mathrm{Ber}(1/2)$ random variables, suppose that all the $X_i$'s and $Y_i$'s are independent, and define the sample si... |
A mathematical operation of dividing an algebraic term by its unlike term is called the division of unlike algebraic terms.
The division of any two unlike algebraic terms is written by displaying a division sign between them for calculating their quotient. The quotient of the unlike terms is actually calculated by elim... |
Moduli interpretations for noncongruence modular curves (2017, published in Mathematische Annalen)
Let $G$ be a finite 2-generated group. In this paper I study Teichmuller structures of level $G$ (or just $G$-structures) on elliptic curves $E$, which roughly correspond to a $G$-torsor on $E$, etale away from the origin... |
My inorganic lab had us do an XRD measurement, but I've never been explained how to interpret the data.
Question:
Calculate the unit cell dimensions $a$, $b$, and $c$, for $\ce{YBa2Cu3O7}$ from the indexed X-ray powder pattern provided in [the textbook]. Explain why the crystals are nearly tetragonal in terms of the at... |
The policy issue is this: we're in a recession. Interest rates are zero, and can't go lower. The Fed is desperately trying to goose the economy. Lots of people (most of the recent Jackson Hole Fed conclave) are advising "open-mouth operations," and "managing expectations," that the key to current prosperity is for the ... |
In my course I often see questions that ask me to calculate the limit of sequences such as: $$\lim\limits_{n \to \infty}{\sqrt [n]{a_n}} $$
How do I handle these questions?
A related question is to show that as ${a_n\to\infty}$
then$${\sqrt [n]{a_n}} > \left(1+\frac {1}{n}\right)$$
for almost every $n$.
I don't know th... |
I am doing IGCSE Maths, and am having a few problems with function notation. I understand the form
f(x).
What does the form
f: x ↦ y mean? Could you also give one or two examples?
And, if possible, state your source. Thank you.
Mathematics Stack Exchange is a question and answer site for people studying math at any lev... |
So I found out about the gamma function yesterday and I spent a bunch of time trying to evaluate certain values like $0.5!=\Gamma \left(1.5\right)$. I used multiple integration by parts, and in the end I always get $0=0$. How can someone compute gamma function values for all real numbers manually? I want to evaluate th... |
I have been going back through some Kleppner problems and have a doubt concerning problem 6.18. It states:
Find the period of a pendulum consisting of a disk of mass $M$ and radius $R$ fixed to the end of a rod of length $l$ and mass $m$. How does the period change if the disk is mounted to the rod by a frictionless be... |
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1. Measurement of the ratio of the production cross sections times branching fractions of B c ± → J/ψπ ± and B± → J/ψK ± and ℬ B c ± → J / ψ π ± π ± π ∓ / ℬ B c ± → J / ψ π ± $$ \mathrm{\... |
This is an exercise from my calculus class. The function is defined as $x\sin (1/y)+y\sin (1/x)$ if $x\neq0 $ and $y\neq0 $, and $0$ if $x=0 $ or $y=0$.
I'm pretty confident the limit exists and should be $0$, because: $$\lim_{(x,y)\to(0,0)}[x\sin (1/y)+y\sin (1/x)]=\lim_{(x,y)\to(0,0)}[x\sin (1/y)]+\lim_{(x,y)\to(0,0)... |
The
large cash bag is a rare item won from Treasure Hunter. When opened, it will give the player coins based on the player's total level. During the weekend of 1 February 2013, the gold received from the bag was doubled.
The coins received from a large cash bag is a random number between $ 90X $ and $ 110X $, where $ X... |
Searching for just a few words should be enough to get started. If you need to make more complex queries, use the tips below to guide you.
Purchase individual online access for 1 year to this journal.
Impact Factor 2019: 0.808
The journal
Asymptotic Analysis fulfills a twofold function. It aims at publishing original m... |
A new Higgs tadpole cancellation condition reformulating the hierarchy problem Strings 2013 [talks] is underway.The first hep-ph paper today probably got to that exclusive place because the authors were excited and wanted to grab the spot. Andre de Gouvea, Jennifer Kile, and Roberto Vega-Morales of Illinois chose the t... |
The Gaussian Plane Waves method (GPW) solves the DFT Kohn-Sham equations efficiently. It uses gaussians as basisset, and planewaves as auxiliary basis. This is similar at the Resolution of Identity (RI) methods but with a different basisset.
In GPW the whole density is transferred to plane waves, and one has the densit... |
Question is to solve for Galois Group of $x^4-2x^2-2$ over $\mathbb{Q}$.
I know the roots of this polynomial are $\sqrt{1+\sqrt{3}},-\sqrt{1+\sqrt{3}},\sqrt{1-\sqrt{3}},-\sqrt{1-\sqrt{3}}$.
But, $\sqrt{2}i=\sqrt{1+\sqrt{3}}.\sqrt{1-\sqrt{3}}$. So, I concluded that splitting field would be $\mathbb{Q}(\sqrt{1+\sqrt{3}},... |
Homoclinic orbits for a class of asymptotically quadratic Hamiltonian systems
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
$ \ddot{q}(t)-\lambda q(t)+\nabla W(t,q(t)) = 0 $
$ \lambda>0 $
$ \frac{|\nabla W(t,x)|}{|x|} $
$ |x|\rightarrow\infty $
$ |t|\rightarrow\infty $ Keywords:Hom... |
Just a question for personal comprehension. Consider the following statement:
It is NP-hard to approximate Set-Cover within a $(1 - \epsilon) \log n$ factor for any $0 < \epsilon < 1$.
Now, NP-hardness refers to decision problems.So what is NP-Hard exactly here ?
My guess is that the statement is equivalent to saying t... |
How many positive integer values of n are there such that $2^n + 7^n$ is a perfect square?
I am not sure how to approach this question given that there are two different bases 2 and 7
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It o... |
Tool to calculate Double Integral. The calculation of two consecutive integral makes it possible to compute areas for functions with two variables to integrate over a given interval.
Double Integral - dCode
Tag(s) : Functions, Symbolic Computation
dCode is free and its tools are a valuable help in games, maths, geocach... |
Difference between revisions of "Lower attic"
From Cantor's Attic
Line 1: Line 1: −
{{DISPLAYTITLE:The
+
{{DISPLAYTITLE: The }}
[[File:SagradaSpiralByDavidNikonvscanon.jpg | right | Sagrada Spiral photo by David Nikonvscanon]]
[[File:SagradaSpiralByDavidNikonvscanon.jpg | right | Sagrada Spiral photo by David Nikonvsca... |
Wave energy converters in coastal structures: verschil tussen versies
(→Application for wave energy converters)
(→Application for wave energy converters)
Regel 80: Regel 80:
where <math>m_n</math>
where <math>m_n</math>
−
represents the spectral moment of order n. An equation similar to that describing the power of reg... |
So I was recently discussing the transitions in Egyptian Blue ($\ce{CaCu[Si4O10]}$) with some of my students, who had to prepare this compound. What I like in particular in this case is how, at least in a simplified view you can show, that the blue is not simply due to one single transition with the complementary color... |
There are six power rules in exponentiation and here is the list of the formulas in algebraic form.
$\large {(b^m)}^n \,=\, b^{mn}$
$b^0 \,=\, 1$
$\large b^{-m} \,=\, \dfrac{1}{b^m}$
$\large b^{\frac{1}{n}} \,=\, \sqrt[\displaystyle n]{b}$
$\large b^{\frac{m}{n}} \,=\, \sqrt[\displaystyle n]{b^m}$
$\large b^1 \,=\, b$
... |
Let $c \in \mathbb{R}$ be such that $\{f,f_c\}$ is a basis for $V$, where $f_c(x)=f(x+c)$. Then by definition there are unique functions $a,b\colon \mathbb{R} \to \mathbb{R}$ such that $f_t=a(t)f+b(t)f_c$ for all $t \in \mathbb{R}$. Now for any $x_1, x_2 \in \mathbb{R}$, let $$M(x_1,x_2)=\left[\begin{matrix} f(x_1) & f... |
Defining parameters
Level: \( N \) = \( 12 = 2^{2} \cdot 3 \) Weight: \( k \) = \( 6 \) Character orbit: \([\chi]\) = 12.a (trivial) Character field: \(\Q\) Newforms: \( 0 \) Sturm bound: \(12\) Trace bound: \(0\) Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(12))\).
Total... |
Assume two identical solid blocks of copper with molar heat capacity at constant volume $C_{V,m}=24.5 \text{ J$\cdot$K$^{-1}$mol$^{-1}$}$ . Assume the heat capacity to be constant in the temperature range of the experiment. Block 1 has a temperature $T_1$ and block 2 has a temperature $T_2=4T_1$. The copper blocks are ... |
What is Induction?
Induction is also known as inductance and is defined for a conductor such that the magnetic field is proportional to the rate of change of the magnetic field. L is used to represent the inductance and Henry is the SI unit of inductance.
1 Henry is defined as the amount of inductance required to produ... |
Equivalence of Definitions of Local Basis/Neighborhood Basis of Open Sets Implies Local Basis for Open Sets Theorem
Let $T = \struct {S, \tau}$ be a topological space.
Let $x$ be an element of $S$.
every neighborhood of $x$ contains a set in $\mathcal B$. Then $\mathcal B$ satisfies: $\forall U \in \tau: x \in U \impli... |
Example of Converting from Slope Intercept to Standard Form
Multiply by the least common denominator of the fractions (if any)
The only fraction is $$ \frac { 5}{ \red 4} $$ so you can multiply everything by 4.
$ \red 4 \cdot y = \red 4 \cdot \big( \frac { 5}{ \red 4}x +5 \big) \\ 4y = 5x + 20 $ Use our Calculator
You ... |
The value of secant function when angle of right triangle equals to $45^°$ is called secant of angle $45$ degrees. It is written as $\sec{(45^°)}$ as per sexagesimal system in mathematics.
$\sec{(45^°)} \,=\, \sqrt{2}$
The value of sec of angle $45$ degrees in fraction is $\sqrt{2}$ exactly. It is an irrational number ... |
There are three basic notable properties in a right triangle when its angle equals to $30$ degrees.
$\Delta POQ$ is a right triangle and its angle is $30^°$. Assume, the length of hypotenuse is equal to $d$.
Then, the length of opposite side is exactly equal to half of the length of the hypotenuse.
$Length \, of \, Opp... |
Risk and Return
Risk-averse investors attempt to maximize the return they earn per unit of risk. Ratios such as Sharpe ratio, Treynor’s ratio, Sortino ratio, etc. and coefficient of variation measure return per unit of investment risk.
It is important to analyze and attempt to quantify the relationship between risk and... |
How do we add a matrix to a LaTeX document?
Ash's answer typesets the matrix inline with the text. A (perhaps) nicer way to do this is to use the
smallmatrix environment in the
amsmath package. Add to the document preamble:
\usepackage{amsmath}
And then you can do:
$M = \begin{smallmatrix} a&b\\ c&d \end{smallmatrix}$
... |
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Now showing items 1-10 of 24
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 ... |
I'll preface the examples I am trying to understand with the definitions of weak and weak-* convergence in a Banach space $X$:
"A sequence $(x_n)_{n=1}^\infty$ converges weakly to $x$ in $X$ if for all $f\in X'$, $f(x_n)\to f(x)$ in $\mathbb F$ as $n\to\infty.$ A sequence $(f_n)_{n=1}^\infty\subset X'$ converges weak-*... |
@Tsemo Aristide is absolutely correct, you can follow that link and also The Proof for your specific case here. However, this is a different kind of explanation for what you have, which is not a proof but I think it might help you better grasp the concept.
At the first glance, this looks very similar to the Vandermonde... |
Quadratic Formula Calculator and Solver
The Discriminant
The Work
The Actual Solutions
The Graph
The calculator uses the quadratic formula to find solutions to any quadratic equation.
The formula is: $ \frac{ -b \pm \sqrt{b^2 -4ac}}{2a } $
The quadratic formula calculator below will solve any quadratic equation that yo... |
A fundamental question about mathematics
This answer was reorganized after the OP gave more precisions as tothe meaning and intent of his question. I also comment other answershere, as it is awkward to do so in the usual comment format. Commenting them also gives extra insight into the relevant issues. In a nutshell
Yo... |
I am trying to figure out where I went wrong on the following problem:
The two batteries are identical, and each has an open-circuit voltage of 1.5V. The lamp has a resistance of 5\$\Omega\$ when lit. With the switch closed, 2.5V is measured across the lamp. What is the internal resistance of each battery?
(Problem 2.1... |
If you want coefficients of your expression, you'd better use Coefficient.Here are the functions for which you want to determine the coefficients:functions = Cases[{exp1, exp2, exp3},Exp[x_]|Sin[x_]|Cos[x_], Infinity] // Union$\{ e^{-\frac{t}{x^2+y^2}}\,, \, \cos\Big[\frac{2\pi t}{T}\Big]\,,\, \sin\Big[\frac{2\pi t}{T}... |
Return to Glossary.
Formal Definition
Let $H$ be a subgroup of a group $G$. The number of left cosets of $H$ in $G$ is the
index $(G:H)$ of $H$ in $G$. Informal Definition
The index is the number of cosets which can be enumerated by dividing the number of elements in the group by the number of elements in the subgroup.... |
Consider the CFT that corresponds to a gauge-fixed closed bosonic string.
Ground level string states are described by vertex operators such as $$V(p) = :\exp(i p_{\mu} X^{\mu}(z, \bar{z})):$$ which are conformal primaries with weight $$ h = \bar{h} = \frac{\alpha'}{4} p^2. $$
The physical states of the strings must hav... |
There is a normality assumption when it comes to consider OLS models and that is that the errors be normally distributed. I have been browsing through Cross Validated and it sounds like Y and X don't have to be normal in-order for errors to be normal. My question is why when we have non-normally distributed errors is t... |
Travelling Wave Line Model Contents Introduction
A travelling wave on a transmission line is a transient disturbance that that moves along the line at a constant speed yet maintains its shape (see Figure 1). Examples include lightning surges, switching transients, faults, etc.
In this article, we will derive various ti... |
I'm a physics student starting grad school, and I figured I'd read up on manifolds since they pop up so much. However, one thing that continues to elude me is why tangent spaces have such involved definitions. Given that the tangent space of an $n$ dimensional manifold at any point is diffeomorphic to $\mathbb{R}^n$, w... |
I read some proofs that show that the outer measure $m^*(I)$ of an interval is equal to its length $l(I)$, i.e. $m^*(I)=l(I)$, where for an interval $I=[a,b]$, we have $l(I)=b-a=m^*(I)$.
I understand the part that $m^*(I) \leq l(I)$, but for the other direction $m^*(I) \geq l(I)$, I could not see why the proofs really ... |
In this calculus problem, the limit of the quotient of $\cos{x}$ by $\dfrac{\pi}{2}-x$ should have to evaluate as $x$ approaches $\dfrac{\pi}{2}$. In this problem, the $x$ represents a variable and also represents an angle of a right triangle.
$\displaystyle \large \lim_{x \,\to\, \Large \frac{\pi}{2}}{\normalsize \dfr... |
Let $S_4$ denote the group of permutations of $\{1,2,3,4\}$ and let $H$ be a sub group of $S_4$ of order $6$ . Show that $\exists~ i \in \{1,2,3,4\}$ which is fixed by each element of $H$.
Attempt: As per the given question, $H$ is a sub group of $S_4$ of order $6$ .
We have to prove that $\exists~ i \in \{1,2,3,4\} ~ ... |
Usage is fairly complex but there is a nice tutorial here:
http://www.forkosh.c...extutorial.html
Use the following syntax:
[math]f(x)=\int_{-\infty}^x e^{-t^2}dt[/math]
...which yields
[math]f(x)=\int_{-\infty}^x e^{-t^2}dt[/math]
Jump to content
Posted 04 May 2006 - 03:12 AM
[math]f(x)=\int_{-\infty}^x e^{-t^2}dt[/ma... |
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Purchase individual online access for 1 year to this journal.
Impact Factor 2019: 0.808
The journal
Asymptotic Analysis fulfills a twofold function. It aims at publishing original m... |
Tool for Second Derivative calculation f''. The second derivative is the application of the derivation tool to the (first) derivative of a function, a double derivation on the same variable.
Second Derivative - dCode
Tag(s) : Functions
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles... |
Not sure if this approach has any gotcha's.
\documentclass{article}
\usepackage[nomessages]{fp}
\newcommand\FPuse[1]{\FPeval{\result}{#1}{\result}}
\begin{document}
$\cos(\pi)=\FPuse{clip(cos(pi))}$\
$\sin(\pi/3)=\FPuse{sin(pi/3)}$
$\sin(\pi/3)=\FPuse{round(sin(pi/3),3)}$
\end{document}
In the comments below, jfbu and ... |
As I mentioned in other blogs, we can still use a classically derived test known as the generalized log-likelihood ratio as a way of simply ranking different A-B combinations against each other according to how interesting they are. Even without being able to interpret the statistical score as a statistical test, we ge... |
Mentor: Bjoern Muetzel
If you are an undergraduate interested in a reading course, independent study or working on a research project, feel free to contact me. I am particularly interested in the following topics.
The hyperbolic plane is a space of constant negative curvature minus one, where different rules than in Eu... |
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