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Current Electricity Electric Current and Drift of Electrons The time rate of flow of charge through any cross section is called current i = q/t. Current is having direction but it is scalar. The conventional direction of current is taken to be the direction of flow of positive charge. If "n" particles each having a cha... |
How many homomorphisms $\Psi : S_3 \rightarrow S_3$ exist?
Attempt: I found $16$ homomorphisms in total.
$S_3 ={(1). (12),(13),(23), (123),(132)}$
There are three normal subgroups in $S_3 = \{(1),~ S_3 ~, ~A_3 = \langle (123)\rangle\}$
Let $\Psi : S_3 \rightarrow S_3$ be a homomorphism. then $Ker~ \Psi$ can be any of t... |
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Journal of High Energy Physics, ISSN 1126-6708, 12/2016, Volume 2016, Issue 12, pp. 1 - 59
A combination of measurements sensitive to the CKM angle gamma from LHCb is performed. The input... |
I try to do a little more spectacular that phrase ( Δελτιο Υλης) . Is the headline on a press material for my students. The fact is that I could accomplish this with gimp or a graphics program such as the inscape or similar programs.
But what I want is to make a somewhat
artistic distortion of letters through tikz to s... |
Answer
$\frac{8x}{9}$
Work Step by Step
$\frac{x}{3}\div\frac{3}{8}$ Invert the divisor and multiply. $\frac{x}{3}\times\frac{8}{3}$ Multiply numerator by numerator and denominator by denominator. $\frac{8x}{9}$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an an... |
Which metric is better to use in different scenarios while using decision trees?
Gini impurity and Information Gain Entropy are pretty much the same. And people do use the values interchangeably. Below are the formulae of both:
$\textit{Gini}: \mathit{Gini}(E) = 1 - \sum_{j=1}^{c}p_j^2$ $\textit{Entropy}: H(E) = -\sum_... |
For the other sciences it´s easy to point to the most important equations that ground the discipline. If I want to explain Economics to a physicist say, what are considered to be the most important equations that underly the subject which I should introduce and attempt to explain?
Instead of proposing specific equation... |
I noticed that the generator of the second stable stem b is the square of the generator of the first stable stem a, in the sense that if take two copies of a and smash product them together you get b out. I'm wondering if there are any ( many) other exmples of this. What are the elements in the stable homotopy of spher... |
Side of an equilateral triangle: \(a\)
Angle of an equilateral triangle: \(\alpha = 60^\circ\) Perimeter: \(P\) Altitude: \(h\)
Angle of an equilateral triangle: \(\alpha = 60^\circ\)
Perimeter: \(P\)
Altitude: \(h\)
Radius of the circumscribed circle: \(R\)
Radius of the inscribed circle: \(r\) Area: \(S\)
Radius of t... |
Side of a rhombus: \(a\)
Diagonals of a rhombus: \({d_1}\), \({d_2}\) Consecutive angles: \(\alpha\), \(\beta\) Altitude: \(h\)
Diagonals of a rhombus: \({d_1}\), \({d_2}\)
Consecutive angles: \(\alpha\), \(\beta\)
Altitude: \(h\)
Radius of the inscribed circle: \(r\)
Perimeter: \(P\) Area: \(S\)
Perimeter: \(P\)
Area:... |
Let $A$ be a commutative ring and $I$ a (finitely generated) ideal in $A$. We denote by $\hat{A}$ the $I$-adic completion of $A$, i.e. $\hat{A} = \varprojlim(A/I \leftarrow A/I^2 \leftarrow \ldots)$.
When do we have $I \otimes_A \hat{A} \cong I\hat{A}$?
It is well known that this is true when $A$ is noetherian (e.g. se... |
We consider a connection-level model of Internet congestion control, introduced by Massouli\'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows present in a network. Here, bandwidth is shared fairly among elastic document transfers according to a weighte... |
Numerical Approximation of Gradient and Gradient Checking
How to make sure the implementation of Backpropagation is correct?
Solution: Implement gradient checking
Representation: Let f($\theta$) be a function of $\theta$ and it is required to calculate the derivate f’($\theta$).
Without using calculus: Let $\epsilon$ b... |
The main goal of the
on-line characterization is the determination of thicknesses of already deposited layers. On-line characterization functions of OptiReOpt DLL can be also used for monitoring deposition processes by generating a command for the termination of current layer deposition.
The on-line characterization of... |
Augmented Dickey-Fuller Test
Performs the Augmented Dickey-Fuller test for the null hypothesisof a unit root of a univarate time series
x (equivalently,
x is anon-stationary time series).
Usage
adf.test(x, nlag = NULL, output = TRUE)
Arguments x a numeric vector or univariate time series. nlag the lag order with defaul... |
For baseband real signals the frequency spectrum is conjugate symmetric; i.e., $$X(f) = X(-f)^*$$ This translates to an even magnitude spectrum; i.e., $$|X(f)| = |X(-f)|$$ and an odd phase spectrum.
Because of the symmetry it's also called as the
double side band spectrum in commnnications terminology. For the real bas... |
Let $(X,F,\mu)$ be a probability space. Let $f:X\rightarrow [0,\infty)$ be a random variable (so measurable). The integral $$E=\int_X f \, d\mu$$ is the expectation value of $f$ and $$V=\int_X (f-E)^2 \, d\mu$$ is the variance of $f$.
Show that, if the variance of $f$ is small, $f$ deviates from its expectation value w... |
"If $a \equiv b \pmod m$ and $a \equiv b \pmod n$ and $\gcd(m,n)=1$, then $a \equiv b \pmod {mn}$ "
Is that a true theorem? I can't find it in my textbook!
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign u... |
I'm dealing with a doubly charged scalar singlet that interacts only with theright-handed muon as follows,$$\mathcal{L} = \lambda \psi_{R}C\psi_{R} \phi^{++},$$where $\lambda$ is the coupling, $\...
How do I find the Feynman rules for a general Lagrangian density?For example the Lagrangian $$L = \partial_\mu \psi \part... |
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Now showing items 1-10 of 18
J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
Optimization Algorithms - RMSprop and Adam
Gradient Descent is widely used as an optimization algorithm for optimizing the cost functions. There are various improved version of these algorithms like StochasticGradientDescent, Gradient Descent with Momentum, RMSprop and Adam.
RMSprop : Root Mean Square Prop
Intuition: S... |
What is the difference between a $\pi/4$-QPSK modulation and a QPSK differential modulation (DQPSK)?
Are these modulations identical?
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It only takes a minute to sign up.Sign up t... |
A t-test is a family of statistical hypothesis tests in which the test statistic follows a Student's t-distribution under the null hypothesis. The most widely used t-tests include the one-sample t-test, t-test for paired samples and independent two-sample t-test.
The one-sample t-test is used to test the null hypothesi... |
I am modeling a lime slaker which is basically a stirred tank reactor with two separate feeds:
1. CaO feed screw (powder) 2. H2O binary valve (liquid)
These react according to the reaction:
$\ce{CaO(s) + H2O(l) -> Ca(OH)2(s)}$
The slaker is operated on a semibatch fashion where water and lime are fed until the desired ... |
In the clamped case, things get a lot easier! Some modifications to the previous post:
Let: [u(x,t) = X(x)T(t)] in [u_{tt}(x,t) + K u_{xxxx} = 0, K > 0, u(0,t) = u_{xx}(0,t)=u(l,t)=u_{xx}(l,t)=0]
Then: [u_{tt}(x,t) = X(x)T''(t), u_{xxxx}(x,t) = X''''(x)T(t)]
[u_{tt}(x,t) + K u_{xxxx} = X(x)T''(t) + K X''''(x)T(t) = 0]
... |
The following fact, which I've heard being called "soft version of Moschovakis's lemma" (see top answer here) is the following:
Under AD, if there is a surjection $\Bbb R\rightarrow\alpha$, then there is a surjection $\Bbb R\rightarrow\mathcal{P}(\alpha)$.
I remember few days ago I have seen a really nice proof of this... |
An electron is confined to a finite square well whose “walls” are $8.0$ eV high. If the ground-state energy is $0.5$ eV, estimate the width of the well.
My solution:
$E_1=0.5 \ eV=8\times10^{-20} \ J$
Electron mass: $m=9.11\times10^{-31} \ Kg$
$\hbar=1.055\times 10^{-34} \ Js$
$E_1=\frac{\pi^2 \hbar}{2mL^2} \ \Rightarr... |
Tagged: invertible matrix Problem 583
Consider the $2\times 2$ complex matrix
\[A=\begin{bmatrix} a & b-a\\ 0& b \end{bmatrix}.\] (a) Find the eigenvalues of $A$. (b) For each eigenvalue of $A$, determine the eigenvectors. (c) Diagonalize the matrix $A$.
Add to solve later
(d) Using the result of the diagonalization, c... |
Take $n = 12$
$12$'s prime factorization is $2^1\times2^1\times3^1$
So then, the number of factors by UFT is $(1+1)(1+1)(1+1) = 8$
But there's only $1,2,3,4,6,12 = 6$ factors!!
Where are the other two?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in re... |
Differential and Integral Equations Differential Integral Equations Volume 22, Number 7/8 (2009), 669-678. Multiple positive solutions for a class of $p - q$-Laplacian systems with multiple parameters and combined nonlinear effects Abstract
In this work, we prove a multiplicity result for a class of quasilinear ellipti... |
A two-dimensional figure where all points are at a fixed equal distance from a center point. Center of a circle having all points on the line circumference are at equal distance from the center point. Chord of a circle is line segment on the interior of a circle. Diameter of a circle is any straight line segment that p... |
I have often seen a statement that we can model only a short rate process $r(t)$ and then use it to derive a term structure $R(t,T)$ for every $t$. Could someone please elaborate? Say, I’ve simulated $r(t)$ up to time $t$, what would I use to derive $R(t,T)$?
This is indeed a standard result. You can convince yourself ... |
I'm programming an orbital simulator and need some help modeling hyperbolic orbits (or trajectories, whatever you want to call them). So far I can model elliptical orbits with the standard orbital elements (perigee, eccentricity, semi-major axis, mean anomaly, etc); I can calculate the mean anomaly in a few seconds fro... |
Products are omnipresent in physics – and even in less quantitative sciences – from Day One. The product $A=XY$ of two numbers may be visualized as the area $A$ of the rectangle whose sides are the two factors $X$ and $Y$. When embedded in physics, this simple formula $A=XY$ already includes units: the sides are in met... |
Introduction: General Formalism
We look at a Hamiltonian with \(V(t)\) some time-dependent perturbation
\[H=H^0+V(t) \label{eq1}\]
so now the wavefunction will have perturbation-induced time dependence. Our starting point is the set of eigenstates \(|n\rangle\) of the unperturbed Hamiltonian \(H^0|n\rangle =E_n|n\rangl... |
I am reviewing some concepts in statistical mechanics and am becoming confused with how to calculate probabilities when a system has $N$ non-interacting particles.
For instance, let's say we have $N$ electrons with magnetic moment $\vec{\mu} = (g e/2 m)\vec{S}$. If we apply a strong magnetic field parallel to $\vec{S}$... |
This is a bordism problem, and as such can be answered using algebraic topology. I'll answer in the unoriented setting, then indicate how to modify things if $M$ and $W$ are required to be oriented.
Complex line bundles $\mathcal{L}$ over $W$ are classified by maps $f:W\to BU(1)\simeq \mathbb{C}P^{\infty}$. We want to ... |
In this paper http://arxiv.org/abs/hep-th/9705122 Section 2
We have $$S_A = \frac{1}{4g^2} \int{d^4x F_{\mu\nu}(A)F^{\mu\nu}(A)}$$
where $F_{\mu\nu}(A) = \partial_{[\mu A\nu]}$. Its Bianchi Identity is $\partial_\mu *F^{\mu\nu}$ (Note that $*$ represents hodge dual)
Great. Now the author went to parent action:
$$S_{F,\... |
PRIMA-PARC-PIMS meeting on PDEs Start Date: 12/07/2010 End Date: 12/08/2010
Sun Sig Byun, Seoul National University
Alessio Figalli, University of Texas - Austin (lecturer for two expository talks)
Stephen Gustafson, University of British Columbia
Lami Kim, Seoul National University
Seick Kim, Yonsei University
Ki-Ahm ... |
Tagged: group Problem 343
Let $G$ be a finite group and let $N$ be a normal abelian subgroup of $G$.
Let $\Aut(N)$ be the group of automorphisms of $G$.
Suppose that the orders of groups $G/N$ and $\Aut(N)$ are relatively prime.
Then prove that $N$ is contained in the center of $G$. Problem 332
Let $G=\GL(n, \R)$ be th... |
there are n derivative filters: $f_i$, and denote $f_i^r$ as $f_i$'s reverse filter such that$$f_i(x,y)=f_i^r(-x, -y)$$$r_i, f_i$ given, to find $r$ from the equations:$$f_i * r = r_i, (1 \leq i \...
This article here talks about a room impulse response generator which takes the source and destination coordinates, soun... |
Hello one and all! Is anyone here familiar with planar prolate spheroidal coordinates? I am reading a book on dynamics and the author states If we introduce planar prolate spheroidal coordinates $(R, \sigma)$ based on the distance parameter $b$, then, in terms of the Cartesian coordinates $(x, z)$ and also of the plane... |
Inequality constraints in an SDP can be turned into equality constraints by introducing non-negative slack variables. If your original problem is
$\max \Sigma_{i=1}^{n} z_{i}$
subject to
$\mbox{tr}(P_{i}X) \geq z_{i}\;\;$ $i=1, 2, \ldots, n$
$ X \succeq 0$
You can rewrite the constraints as
$\mbox{tr}(P_{i}X) - z_{i} \... |
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Now showing items 1-10 of 108
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 ... |
In the book Schutz on general relativity, I have come across the dot product between vectors, the action of a dual vector on a vector (or also a tensor on vectors) and the tensor product between dual vectors and vectors. I am not able to understand the difference between the three distinctively. Kindly help. Try to kee... |
Well, these are very fundamental questions, and I think they are written in any good book. But maybe it's hard to extract the exact information from them, which you ask for. So, let me briefly answer:
In wireless, the channel is usually modelled as a FIR filter with impulse response $h(\tau)$. But, this channel might c... |
Determine truth value of following:
$(1)\;\forall x P(x)$
$(2)\;\exists x Q(x)$
$(3)\;\forall x\, \exists y\;R(x,y)$
$(4)\;\exists x \,\forall y\;R(x, y)$
$(5)\;\forall x\,(\lnot Q(x))$
For $x, y \in \mathbb Z^+$, (meaning $x, y$ are positive integers):
Let $P(x): x$ is even; $\quad\;Q(x): x$ is a prime number; $\quad ... |
I have a doubt as to in which frame of reference the Schrödinger equation is written? I think it is inertial but can't reason it out.
I'd like to add to Michael Brown's comment that "You can write Schrödinger's equation in any frame you like": it is quite literally true and Schrödinger's equation has a meaning that is ... |
s -Block Elements Preparation and properties of sodium carbonate, sodium hydroxide and sodium hydrogen carbonate Preparation of sodium hydroxide : Nelson's cell Castner–Kellner process
Nelson cell method : It is a 'U' shaped perforated steel vessel Cathode : steel vessel Anode : graphite rod At anode : 2Cl − → Cl 2 + 2... |
The idea of the argument is this: an integrable function that does not tend to zero may have thinner and thinner pikes, and the integral on each pike needs to tend to zero. If the function is uniformly continuous, these pikes can't get thinner and thinner, and the function can't be integrable, as the integral on pikes ... |
Problem 115
Express the vector $\mathbf{b}=\begin{bmatrix}
2 \\ 13 \\ 6 \end{bmatrix}$ as a linear combination of the vectors \[\mathbf{v}_1=\begin{bmatrix} 1 \\ 5 \\ -1 \end{bmatrix}, \mathbf{v}_2= \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix}, \mathbf{v}_3= \begin{bmatrix} 1 \\ 4 \\ 3 \end{bmatrix}.\] ( The Ohio State Un... |
Circle
The functions \(\sin (\theta)\) and \(\cos (\theta)\) are defined such that, if you drew a circle of radius \(r\) with a triangle inset like the one below, the lengths of the sides will have the listed values:
As the picture suggests, \(\sin \theta\) and \(\cos \theta\) have values that repeat when you increase ... |
We can use a qubit as a particle detector that doesn't change the particle's energy. This can be implemented as follows. We start out with a qubit initialized in the state $\left|0\right>$ and we apply the Hadamard gate $U$ that acts as follows:
$$\begin{split}U\left|0\right> &= \frac{1}{\sqrt{2}}\left[\left|0\right\ra... |
Yes, nucleus is composed of subatomic particles that have probability cloud. Protons and neutrons fill orbitals in the nucleus just like electrons in the atom do. What's more, every proton or neutron is a complex particle itself and the quarks inside have their very own probability cloud. (Quarks are simple objects tha... |
How to solve the optimization problem written below?
$$\begin{align} &\operatorname{argmax}\limits_{a}\; a^T b - \frac{1}{2} a^T X a\\ &\text{subject to } \sum_i |a_i|=4,\; \sum_i a_i = 0 \end{align}$$
where $a$, $b$ are $n$-vectors and $X$ is a $n\times n$ matrix. Also, $b$ and $X$ are constants.
My main issue is abou... |
31
(a)Determine all critical points of the given system of equations.
(b) Find the corresponding linear system near each critical point.
(c)Find the eigenvalues of each linear system. What conclusions can you then draw about the nonlinear system? (d)Draw a phase portrait of the nonlinear system to confirm your conclusi... |
Event detail Topology Seminar (Main Talk): Computational complexity and 3-manifolds and zombies
Seminar | January 25 | 4:10-5 p.m. | 3 Evans Hall
Eric Samperton, UC Davis
We consider the computational complexity of counting homomorphisms from 3-manifold groups to fixed finite groups $G$. Let $G$ either be non-abelian s... |
\(\text{FIGURE V.2A}\)
Consider a disc of surface density (mass per unit area) \(σ\), radius \(a\), and a point \(\text{P}\) on its axis at a distance \(z\) from the disc. The contribution to the field from an elemental annulus, radii \(r\), \(r + δr\), mass \(2πσ \ r \ δr\) is (from equation 5.4.1)
\[δg = 2 \pi G σ \f... |
Relay selection based on social relationship prediction and information leakage reduction for mobile social networks
1.
School of Computer Science and Engineering, Changshu Institute of Technology, Changshu, China
2.
Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, Suzhou, C... |
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Now showing items 1-2 of 2
Search for new resonances in $W\gamma$ and $Z\gamma$ Final States in $pp$ Collisions at $\sqrt{s}=8\,\mathrm{TeV}$ with the ATLAS Detector
(Elsevier, 2014-11-10)
This letter presents a search for new resonances decaying to final states with a vector boson produced in association with a... |
By the “equator” of a magnet I mean a plane normal to its magnetic moment vector, passing through the mid-point of the magnet.
The magnetic field at a point at a distance
r on the equator of a magnet may be expressed as a series of terms of successively higher powers of \(1/r\) (the first term in the series being a ter... |
If we rotate the set of axes in counter-clockwise through 3 Euler's angles to get the transformation matrix, then what about the direction of rotation to get direct transformation instead of the previously performed 3 transformations? Is the direction of rotation of set of axis in direct transformation clockwise or cou... |
Instead of updating my previous answer, I've decided to add a new answer in order to keep it short(ish).
In the comments following his original question, TonyS added the extra assumption that $R$ is finitely generated over $A$. This is a strong condition, since it makes $R$ very close to being commutative. Moreover $R$... |
In the clamped case, things get a lot easier! Some modifications to the previous post:
Let: [u(x,t) = X(x)T(t)] in [u_{tt}(x,t) + K u_{xxxx} = 0, K > 0, u(0,t) = u_{xx}(0,t)=u(l,t)=u_{xx}(l,t)=0]
Then: [u_{tt}(x,t) = X(x)T''(t), u_{xxxx}(x,t) = X''''(x)T(t)]
[u_{tt}(x,t) + K u_{xxxx} = X(x)T''(t) + K X''''(x)T(t) = 0]
... |
Wave Optics Interference of Light Waves and Young’s Experiment Fringe width is the distance between any two consecutive maxima or minima Fringe width \tt \beta=\frac{\lambda D}{d} Fringe width is independent of the order of fringe. Fringe width depends on wave length (λ) of light used. Fringe width Depends upon distanc... |
I just started self-studying measure theory and had a question about the "generalised density" (as it appears on Wikipedia):
A random variable X with values in a measurable space $({\mathcal{X}},{\mathcal {A}})$ (usually $\mathbb {R} ^{n}$ with the Borel sets as measurable subsets) has as probability distribution the m... |
What are the Christoffel symbols for the Schwarzschild spacetime, expressed in the Kruskal-Szekeres coordinates?
closed as off-topic by AccidentalFourierTransform, ZeroTheHero, Emilio Pisanty, Prahar, Jon Custer Jun 4 '18 at 20:42
This question appears to be off-topic. The users who voted to close gave this specific re... |
If I have two balls with masses and charges $m_1, q_1^{+}$, $m_2, q_2^{+}$, initially held at distance $d$, and then released, how can I know the kinetic energies of each of the balls at infinite distance between them? I'm quite stuck on that, because they both have the same potential energy at the beginning, and it de... |
Answer
$S_6=\dfrac{1365}{256} \approx 5.332$
Work Step by Step
Here, we have $\sum_{i=1}^6 4(1/4)^{i-1}$ We know that $S_{n}=a_1(\dfrac{1-r^{n}}{1-r})$ Now, $S_6=4[\dfrac{1-(1/4)^{6}}{1-(1/4)}]$ or, $=4 \times (\dfrac{4096/4096-1/4096}{3/4})$ or, $=4 \times \dfrac{1365}{1024}$ Hence, $S_6=\dfrac{1365}{256} \approx 5.33... |
Background
The use of block (displayed) equations (
$$...$$) in question titles has been disallowed on Mathematics Stack Exchange. Titles are meant to be short descriptions of the question, and using block equations generally causes your equations to be larger: compare
$$\lim_{n \to \infty} \frac{1}{n}$$ to
$\lim_{n \t... |
What is the correct series expansion for the $U(1)$ Faddeev-Popov ghosts?
I know that the $U(1)$ ghosts are only a phase such that they can be neglected in most cases but it turns out that this is not true in curved spaces even for $U(1)$ theories so please don't answer this...
In this thread Faddeev-Popov ghost propag... |
What is the sum total of all individual digits from 1 to 10^100? In other words: 1+2+3+4+5+6+7+8+9+[1+0]+[1+1]+[1+2]+[1+3].......and so on to 10^100? Any help or hint would be greatly appreciated. thank you.
HINT:
1 through 9 is obviously 45.
So look from 10 to 99
the tens digit it 1 through 9 = 45
but the ones digit i... |
Difference between revisions of "SageMath"
Line 46: Line 46:
For a more comprehensive tutorial on the Sage Notebook see the [http://www.sagemath.org/doc/reference/notebook.html Sage documentation]. For more information on the {{ic|notebook()}} command see [http://www.sagemath.org/doc/reference/sagenb/notebook/notebook_... |
So, under this generality, it seems to me that we can choose $A$ in a clever way: if we make $A$ smaller, then it gets "easier" to satisfy the condition. So why not take $A$ to be the scalar multiples of the identity-- then $D$ commutes with all of $A$ on the nose.
Now let $H=\ell^2$ and let $D$ be multiplication by a ... |
The Context-Free tree grammar has rules of the form:
$A\rightarrow t$ or $A(x_1,\dots,x_n)\rightarrow t_x$,
where $A\in N$, $t\in T(N\cup T)$, $t_x\in T(N\cup T\cup \{x_1,\dots,x_n\})$, $T(Z)$ means a set of all possible trees with labels from $Z$.
where $N$ is a finite unranked set of non-terminals and $T$ is a finite... |
Motivating the classical momentum $\mathbf{p} = m\mathbf{v}$ is quite easy: it is meant to represent the quantity of motion of the particle, and since the mass is one measure of quantity of matter it should be proportional to mass (how much thing is moving) and should be proportional to velocity (how fast and to where ... |
In my previous article “Better Insight into DSP: Learning about Convolution”, I discussed convolution and its two important applications in signal processing field. There, the signals were presumably considered to be one-dimensional in the spatial domain. However, the process of convolution can be carried-on on multi-d... |
Category: Group Theory
Group Theory Problems and Solutions.
Popular posts in Group Theory are:
Problem 625
Let $G$ be a group and let $H_1, H_2$ be subgroups of $G$ such that $H_1 \not \subset H_2$ and $H_2 \not \subset H_1$.
(a) Prove that the union $H_1 \cup H_2$ is never a subgroup in $G$.
Add to solve later
(b) Pro... |
Communication Systems Amplitude Modulation, Production and Detection of Amplitude Modulated Wave During PHASE MODULATION, the phase of the CW (carrier wave) is changed in accordance with the amplitude variations of the signal. The extent to which the modulation is to be taken up is called the modulation factor (m a) \t... |
1IntroductionIn the theory of ordinary differential equations and in particular in the theory of Hamiltonian systems the existence of first integrals is important, because they allow to lower the dimension where the Hamiltonian system is defined. Furthermore, if we know a sufficient number of first integrals, these all... |
It is obvious that a question which is too short will almost certainly lack context, and that a question which is too long may run the risk of readers never finding out what the question actually is (Some may not want to read the full question).
Therefore, I was wondering:
What is the optimal length in characters for a... |
This is a three-dimensional problem and the wave equation is
\[c^2 \nabla^2 \Psi = \ddot \Psi. \label{7.6.1}\]
The wave-function here, \(\Psi\), which is a function of the coordinates and the time, can be thought of as the density of the sphere; it describes how the density of the sphere is varying in space and with ti... |
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Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
Denote by $i \in \{1, \ldots, n\}$ an economic agent. Let $\mathbf x \in \mathbb R^n$ denote a vector of actions and $x_i \in \mathbf x$ a typical element. Let further $f_i : \mathbb R^n \to \mathbb R$ denote the objective function. The vector $\mathbf x^*$ constitutes a Nash equilibrium if the following holds \begin{a... |
Without knowing the mass of the Earth, calculating the gravitational constant is impossible from $g$ and the acceleration of the Moon. The best you can do is calculate the product of the gravitational constant and the Earth's mass (GM). This is why Cavendish's experiments with the gravity of lead weights was important,... |
I thought this result was a bit interesting. Mahlon M. Day in the paper [1] showed that the amenable groups are precisely the groups where there Markov-Kakutani theorem holds.
If $(X,\mathcal{M})$ is an algebra of sets, then a function $\mu:\mathcal{M}\rightarrow[0,1]$ is said to be a finitely additive probability meas... |
I am trying to estimate required shielding masses to maintain a radiation level at or below earths average radiation of 3 mSv per year at different earth orbits (LEO, MEO, GEO and 50000 km+).
Initially I reverse engineered the radiation estimation method used to compute the estimated received radiation for the apollo m... |
Properties of the algorithm: Sequential complexity: [math]O(n^3)[/math] Height of the parallel form: [math]O(n)[/math] Width of the parallel form: [math]O(n^2)[/math] Amount of input data: [math]\frac{n (n + 1)}{2}[/math] Amount of output data: [math]\frac{n (n + 1)}{2}[/math] 1 Properties and structure of the algorith... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
Structure of Atom Heisenberg uncertainty principle Heisenberg's Uncertainty Principle :
\triangle x.\triangle p \geq \frac{h}{4\pi}
Δx = uncertainty in the position Δp = uncertainty in momentum Δp = Δ(mv) = mΔv \triangle x.\triangle v \geq \frac{h}{4\pi m} View the Topic in this Video from 0:40 to 11:55
Disclaimer: Com... |
Considering the top answer to the question “If xor-ing a one way function with different input, is it still a one way function?”…
The function is no longer one-way.
we build a counter example in the following way. Assume $g$ is a one-way function that preserves size, and define $f$ on input $w=bx_1x_2$ in the following... |
Question
Four fair six-sided dice are rolled. The probability that the sum of the results being $22$ is $$\frac{X}{1296}.$$ What is the value of $X$?
My Approach
I simplified it to the equation of the form:
$x_{1}+x_{2}+x_{3}+x_{4}=22, 1\,\,\leq x_{i} \,\,\leq 6,\,\,1\,\,\leq i \,\,\leq 4 $
Solving this equation result... |
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Note by Rishabh Jain 4 years, 12 months ago
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than ... |
I am looking for a formula (Fourier series) to generate an impulse train waveform - a spike-wave with amplitude and period both $1$ – so that $f(x)$ has value $1$ at $x = 1,2,3,4...$ and $f(x)$ has value $0$ at all non-integer values of $x$.
Someone very helpfully gave me:
$$S = \frac 1 N \sum_{k=0}^{N-1} e ^{j2\pi\fra... |
Introduction
Let’s begin with the
definition of gravitational field: The gravitational field at any point P in space is defined as the gravitational force felt by a tiny unit mass placed at P.
So, to visualize the gravitational field, in this room or on a bigger scale such as the whole Solar System, imagine drawing a v... |
I am trying to make my first LaTeX file and have been reading syntax for a bit and have not been able to figure one thing out yet and don't seem to find anything about it online so I thought I might just ask:)
How is it possible to place an image next to an equation?
I tried to do it by wrapping it around, putting it i... |
This is an exercise from Apostol (p.285) that I'm having trouble with (in fact, I'm having trouble with the whole section):
Prove that $\displaystyle{\int_0^1 \frac{1+x^{30}}{1+x^{60}} = 1 + \frac{c}{31}}, \qquad \text{where } 0 < c < 1.$
This comes from the section of Exercises following Taylor expansions, and Taylor'... |
A problem in section 1.3 of Hatcher's
Algebraic Topology is
Let $\tilde{X}$ and $\tilde{Y}$ be simply-connected covering spaces of the path-connected, locally path-connected spaces $X$ and $Y$. Show that if $X \simeq Y$ then $\tilde{X} \simeq \tilde{Y}$. [Exercise 11 in Chapter 0 may be helpful.]
Exercise 11 in chapter... |
It seems as if $$\lim_{x\to 0^+} \sqrt{x+\sqrt[3]{x+\sqrt[4]{\cdots}}}=1$$
I really am at a loss at a proof here. This doesn't come from anywhere, but just out of curiosity. Graphing proves this result fairly well.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and profes... |
Consider a body attached to a horizontal spring and resting on a surface, inclined at an angle $\theta$ from the ground.
The spring constant is $k$. Initially the spring was kept in its natural length while the body was held still by some external agent. When the external agent was removed, the body slid $x$ units down... |
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