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Show that the first excited state of 8-Be nucleus fits the experimental value of the rotational band $E(2^+) = 92 keV$ (this is the first excited state, which is 92 keV above the ground state). To do so model 8-Be to be made of 2 alpha particles $4.5 fm$ apart rotating about their center of mass.
The method I used is:
... |
I am reading a paper Lie superbialgebras and poisson-lie supergroups and trying to figure out how to compute a super Poisson bracket from a super $r$-matrix.
Let $G$ be a Lie supergroup and $\mathfrak{g}$ its Lie superalgebra. The formula (3) on page 158 of the paper Lie superbialgebras and poisson-lie supergroups is \... |
Ex.7.2 Q5 Coordinate Geometry Solution - NCERT Maths Class 10 Question
Find the ratio in which the line segment joining \(A\; (1, -5)\) and \(B\; (-4, 5)\) is divided by the \(x\)-axis. Also find the coordinates of the point of division.
Text Solution Reasoning:
The coordinates of the point \(P(x, y)\) which divides th... |
Because the slab extends infinitely in the xy plane, the electric field lies only along the z direction. The differential form of Gauss' Law for such a one-dimensional electric field is $$\frac{dE}{dz}=\frac{\rho(z)}{\epsilon_0}$$ This can be integrated, using the boundary condition that the electric field must be zero... |
No. The most basic way to see this is to use the fact that ACF$_0$ (the theory of algebraically closed fields of characteristic $0$, of which $\overline{\mathbb{Q}}$ is a model) has quantifier elimination. So every formula $\varphi(x,\overline{a})$ (with parameters $\overline{a}$, in one free variable $x$) is equivalen... |
@mickep I'm pretty sure that malicious actors knew about this long before I checked it. My own server gets scanned by about 200 different people for vulnerabilities every day and I'm not even running anything with a lot of traffic.
@JosephWright @barbarabeeton @PauloCereda I thought we could create a golfing TeX extens... |
Let $\mathfrak{g}$ be a sub-Lie-algebra of $\mathfrak{gl}_n(\mathbb{C})$, the Lie algebra of complex $n\times n$ square matrices.
Let us call $(H)$ the hypothesis: for all $x, y\in\mathbb{C}^n$, whenever $x$ and $y$ are linearly independent, we have $\langle \mathfrak{g}(x)\cup \mathfrak{g}(y)\rangle=\mathbb{C}^n$. Her... |
I am trying to understand the logic behind chi-squared test.
The Chi-squared test is $\chi ^2 = \sum \frac{(obs-exp)^2}{exp}$. $\chi ^2$ is then compared to a Chi-squared distribution to find out a p.value in order to reject or not the null hypothesis. $H_0$: the observations come from the distribution we used to creat... |
Fit Cluster or Cox Point Process Model
Fit a homogeneous or inhomogeneous cluster process or Cox point process model to a point pattern.
Usage
kppm(X, …)
# S3 method for formulakppm(X, clusters = c("Thomas","MatClust","Cauchy","VarGamma","LGCP"), …, data=NULL)
# S3 method for pppkppm(X, trend = ~1, clusters = c("Thomas... |
Let $\mathcal{P}:=\mathcal{P}(\mathcal{X})$ be the $n$-dimensional manifold of all (strictly positive) probability vectors (distributions) on $\mathcal{X}=\{x_0,\dots,x_n\}$,
i.e., each $p=(p(x_0),\dots,p(x_n))\in \mathcal{P}$ is such that $p(x_i)>0$ for all $i$ and $\sum_{i}p(x_i)=1$ and can be thought of a point in $... |
Imagine I was a hypothetical ant man the size of an atom, and I position myself at the exact, down to the atom, center of mass of the earth. A move in any direction will move me out of the center. Would I experience gravity pulling outward on my body in all directions?
There's actually a very useful way to solve this u... |
Abbreviation:
DLOS
A
is a structure $\mathbf{A}=\langle A,\vee,\wedge,\cdot\rangle$ of type $\langle 2,2,2\rangle$ such that distributive lattice ordered semigroup
$\langle A,\vee,\wedge\rangle$ is a distributive lattice
$\langle A,\cdot\rangle$ is a semigroup
$\cdot$ distributes over $\vee$: $x\cdot(y\vee z)=(x\cdot y... |
I am learning Fourier analysis and without any teacher, just trying to read books on my own. I think I have made some decent progress but they are a couple of points which are still very unclear to me and that I can't find explained in any of the books I have.
One of the sources that I found in this document, which is ... |
Let $A$ be an $m \times n$ matrix, and define: \begin{align*} U &= {\rm diag} \{ \frac{1}{\beta_j} \}, \beta_j = \sum_{k=1}^m |a_{kj}|, j = 1 \dots n \\ V &= {\rm diag} \{ \frac{1}{\alpha_i} \}, \alpha_i = \sum_{k=1}^n |a_{ik}|, i = 1 \dots m. \end{align*}
i.e. $\beta_j$ is the 1-norm of the $j$th column of $A$, and $\... |
The $x$ component of vector $A$ is 25.0 m and the $y$ component is 40.0 m.
(a) What is the magnitude of $A$?
(b) What is the angle between the direction of $A$ and the positive direction of x?
For (b) I tried using the formula $\tan \theta = \frac{a_y}{a_x} = \frac{40}{-25} = -1.6$, thus $\arctan(-1.6)=58$ degrees whic... |
Here are a couple of ways to go about making some informed decisions in estimating a line integral given a picture:
We note the path is a simple path, it is a semi-circle of radius $r=1$ and total arc length of $\pi$, this can help in the estimation step. We also note that $f$ is approximately monotone decreasing along... |
I'm looking at algorithms to construct short paths in a particular Cayley graph defined in terms of quadratic residues. This has led me to consider a variant on Lagrange's four-squares theorem.
The Four Squares Theorem is simply that for any $n \in \mathbb N$, there exist $w,x,y,z \in \mathbb N$ such that $$ n = w^2 + ... |
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Journal of High Energy Physics, ISSN 1126-6708, 3/2018, Volume 2018, Issue 3, pp. 1 - 23
The ratios of the branching fractions of the decays Λ c + → pπ − π +, Λ c + → pK ... |
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Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
If you know the gradient and Hessian of the log-likelihood, you can write quick functions in R similar to the one you need for the LL itself. If you pass the gradient, you can use (L)BFGS in R as opposed to Nelder-Mead, which should converge a bit faster. Regardless, once you have the point of convergence, you can plug... |
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Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
Wind-Driven Gyres: Quasi-Geostrophic Limit¶
Contributed by Christine Kaufhold and Francis Poulin.
Building on the previous two demos that used the Quasi-Geostrophic (QG) model for the time-stepping and eigenvalue problem, we now consider how to determine a wind-driven gyre solution that includes bottom drag and nonline... |
The number of Dyck paths in a square is well-known to equal the catalan numbers: http://mathworld.wolfram.com/DyckPath.html But what if, instead of a square, we ask the same question with a rectangle? If one of its sides is a multiple of the other, then again there is a nice formula for the number of paths below the di... |
Bernoulli Bernoulli Volume 25, Number 4A (2019), 2793-2823. Self-normalized Cramér type moderate deviations for martingales Abstract
Let $(X_{i},\mathcal{F}_{i})_{i\geq 1}$ be a sequence of martingale differences. Set $S_{n}=\sum_{i=1}^{n}X_{i}$ and $[S]_{n}=\sum_{i=1}^{n}X_{i}^{2}$. We prove a Cramér type moderate dev... |
In LCAO, it is the set of atomic orbitals (AOs) that is the basis, and the coefficients are the basis expansion coefficients. For example, take the hydrogen molecule, with 1 atomic orbital on each atom:
The lower energy MO, the bonding one, will be (excluding normalization):
$$\psi_{\mathrm{1s}} = \phi_{\text{left}} + ... |
Quasi-Geostrophic Model¶
The Quasi-Geostrophic (QG) model is very important in geophysical fluid dynamics as it describes some aspects of large-scale flows in the oceans and atmosphere very well. The interested reader can find derivations in [Ped92] and [Val06].
In these notes we present the nonlinear equations for the... |
Preamble for clarity:
The many worlds interpretation is usually used to explain the measurement of a 2 level system ($|0\rangle$ or $|1\rangle$) as:
$$\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)|\text{device ready}\rangle|\text{env}_a\rangle\to\frac{1}{\sqrt{2}}(|0\rangle|\text{device says 0}\rangle|\text{env}_b\rangle+|1\... |
Last edited: March 15th 2018
Newton's law of gravitation states that the force between two point masses is proportional to the product of their masses and inversely proportional to the square of the distance between them. This can be written as\begin{equation} F= G\frac{m_1m_2}{r^2}, \label{eq:newton_grav} \end{equatio... |
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Multiplicity dependence of the average transverse momentum in pp, p-Pb, and Pb-Pb collisions at the LHC
(Elsevier, 2013-12)
The average transverse momentum <$p_T$> versus the charged-particle multiplicity $N_{ch}$ was measured in p-Pb collisions at a collision energy per nucleon-nu... |
Lecture: HGX208, F 9:55-11:35
Section: HGX208, T 18:30-20:10
Lecture: H5116, F 8:00-9:40
Section: HGW2403, F(e) 18:30-20:10
Textbook: https://doi.org/10.1017/CBO9781107050884
Lecture: HGW2403, T 18:30-21 Section: HGW2403, R 18:30-20 Instruction for the final paper
You can choose one of the following topics.
An introduc... |
It's a long time since I learned about point groups. But I'll have a go.
I believe that we are talking about the matrix representation in the basis $(x,y,z)$, in which case they are the familiar looking $3\times 3$ rotation matrices. But not the set of
all $3\times 3$ rotation matrices! There are (as you said) 8 symmet... |
I'm trying to understand the answer here to the question of finding the induced maps of coordinate rings corresponding to explicit isomorphisms between $\mathcal Z(xy-z)$ and $\mathbb A^2$.
A morphism $\pi\colon \mathcal Z(xy-z) \to \mathbb A^2$ is given by $\pi(a_1,a_2,a_3) = (a_1,a_2)$, and its inverse is the morphis... |
Your alternative method uses the non-relativistic approximation twice : first when you insert a value for $v/c$ in the numerator, second when you insert a value for $v$ in the denominator. Because of this your error is compounded, so you get a result which is less accurate than if you inserted the approximation only on... |
[1003.0299] The local B-polarization of the CMB: a very sensitive probe of cosmic defects
Authors: Juan Garcia-Bellido, Ruth Durrer, Elisa Fenu, Daniel G. Figueroa, Martin Kunz Abstract: We present a new and especially powerful signature of cosmic strings and other topological or non-topological defects in the polariza... |
Given a graph $G = (V,E,w)$, we define $G'=(V,E,w')$ with $w'(e) = aw(e) + 1$ where $a = |E| + \varepsilon$ for some $\varepsilon \geq 0$ as proposed in the comments of the question.
Lemma
Let $P$ a path in $G$ with cost $C$, i.e. $w(P)=C$. Then, $P$ has cost $aC + |P|$ in $G'$, i.e. $w'(P) = aC + |P|$.
The lemma follo... |
That's the continuous (differential) entropy; not the entropy of the discrete random variable that your ADC output is!
You could (and seeing your profile page, you'll probably have a lot of fun doing that) look into what is called
rate distortion in the field that concerns itself with information entropy, information t... |
In short:
wavelets and relatives are pretty good at compacting a sufficiently large class of regular-enough and useful signals and images. What follows are signal properties (and corresponding wavelet features) that make wavelets good (not best) candidates for lossy compression: piecewise-smooth ( vanishing moments, or... |
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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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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... |
Is it possible to construct a Lorentz invariant, three rank Levi-Civita tensor in Minkowski Spacetime? If not, why so? I am talking about something like this $\epsilon_{\alpha\beta\gamma}$ or $\epsilon^{\alpha\beta\gamma}$, where each indices run from $0$ to $3$. As in this answer here, which proves the Lorentz co-vari... |
It is an illusion that the computation rules "define" or "construct" the objects they speak about. You correctly observed that the equation for $\mathrm{ind}_{=_A}$ does not "define" it, but failed to observe that the same is true in other cases as well. Let us consider the induction principle for the unit type $1$, wh... |
Complex networks is a young and active area of scientific research inspired largely by the empirical study of real-world networks such as computer networks, social networks, biological networks, ecological networks, telecommunication networks etc. A lot of interesting and important properties of complex networks were f... |
This vignette illustrates the basic usage of the
knockoff package with Model-X knockoffs. In this scenario we assume that the distribution of the predictors is known (or that it can be well approximated), but we make no assumptions on the conditional distribution of the response. For simplicity, we will use synthetic d... |
Let's say I have a normal, space-suited human who, for various reasons, must climb a very long, indestructible ladder in space. Air, heat, food, water and waste are already accounted for. What I want to know is what their rate of progress up the ladder will be ? How many kilometers a day can they travel ? How much rest... |
This question already has an answer here:
Show using the Poisson distribution that
$$\lim_{n \to +\infty} e^{-n} \sum_{k=1}^{n}\frac{n^k}{k!} = \frac {1}{2}$$
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sig... |
First I have defined the exterior algebra of a module $M$ as the quotient $T(M)/A(M)$ where $T(M)$ is the tensor algebra of $M$ and $A(M)$ is the ideal generated by all elements of the form $m\otimes m$ for $m\in M$.
The exterior algebra is graded, with k'th homogeneous component $\bigwedge ^k(M)=T^k(M)/A^k(M)$ where $... |
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Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
Difference between revisions of "De Bruijn-Newman constant"
Line 9: Line 9:
It is known that <math>\Phi</math> is even, and that <math>H_t</math> is even, real on the real axis, and obeys the functional equation <math>H_t(\overline{z}) = \overline{H_t(z)}</math>. In particular, the zeroes of <math>H_t</math> are symmet... |
Let $f(x)$ be a function which is differentiable on $[0,1]$ with $f(0)=0$ and $f(1)=1$. Show that for every $n\in \Bbb N$ there exists numbers $x_1,x_2,\ldots,x_n\in [0,1]$ such as $$ \sum_{k = 1}^n \frac{1}{f' (x_k)} = n $$ I think the mean value theorem should be applied. So there exists $x_1$ in $[0,1]$ such that $f... |
$ \newcommand{\ra}[1]{\kern-1.5ex\xrightarrow{\ \ #1\ \ }\phantom{}\kern-1.5ex} \newcommand{\ras}[1]{\kern-1.5ex\xrightarrow{\ \ \smash{#1}\ \ }\phantom{}\kern-1.5ex} \newcommand{\da}[1]{\bigg\downarrow\raise.5ex\rlap{\scriptstyle#1}}$ Suppose we have $CW$-complex $X$. All the self-homotopy equivalences form a monoid, ... |
Here I have some confusing points about the definition of
flux in the projective construction. For example, consider the same mean-field Hamiltonian in my previous question, and assume the $2\times 2$ complex matrix $\chi_{ij}$ has the form $\begin{pmatrix} t_{ij}& \Delta_{ij}\\ \Delta_{ij}^* & -t_{ij}^*\end{pmatrix}$.... |
(Bug?) HP48 Equation Library
02-14-2017, 03:36 AM (This post was last modified: 02-14-2017 04:15 AM by Han.)
Post: #21
RE: (Bug?) HP48 Equation Library
Thank you all -- Brad Barton, SlideRule, and rprosperi -- for your insights. It has helped me understand the formulas much better. So from what I gathered,
\[ \text{if}... |
Algebraic Geometry Seminar Fall 2016
The seminar meets on Fridays at 2:25 pm in Van Vleck B305.
Contents Algebraic Geometry Mailing List Please join the AGS Mailing List to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department compu... |
De Bruijn-Newman constant
For each real number [math]t[/math], define the entire function [math]H_t: {\mathbf C} \to {\mathbf C}[/math] by the formula
[math]\displaystyle H_t(z) := \int_0^\infty e^{tu^2} \Phi(u) \cos(zu)\ du[/math]
where [math]\Phi[/math] is the super-exponentially decaying function
[math]\displaystyle... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
I'm interested in numerical analysis but I don't have experience on it. I was wondering how one can solve integral equations numerically like $\int_0^x e^{t^3}dt=4$? I was thinking whether there is some numerical differential equation solution method faster that finding some range $a\leq x\leq b$ and then splitting tha... |
I am carefully following all the new preprints by ATLAS and CMS that are currently being presented at the Moriond 2013 conference so that you don't have to. So far, everything is compatible with the Standard Model including the \(126\GeV\) Higgs boson and the latter beast is still behaving as obediently as the Standard... |
DBSCAN Engine
Given the graph, we extract the alarms from all the vertices and use these as points as input to the DBSCAN algorithm.
DBSCAN requires a constant \(\epsilon\) and a distance function, which we define as follows:
where:
\(a_{1}\) and \(a_{2}\) are the points representing the alarms
\(\alpha \in (0, \infty)... |
What is the energy limit for fibre optics? For a dual-pulsed nd:yag laser firing at 10Hz with energy roughly 2x 400mJ, and pulse width ~5-10ns. My gut says that this is far too high to pass through fiber optics, but I have no experience in this matter.
It depends. The first challenge is damage at the surface. Is your f... |
Ex.5.3 Q7 Arithmetic Progressions Solution - NCERT Maths Class 10 Question
Find the sum of first \(22\) terms of an AP in which \(d = 7\) and \(22\rm{nd}\) term is \(149.\)
Text Solution What is Known?
\(d\) and \({a_{22}}\)
What is Unknown?
\({S_{22}}\)
Reasoning:
Sum of the first \(n\) terms of an AP is given by \({S... |
EDIT: The following is (mostly) for $\alpha < 2$; scroll to the bottom for more on general $\alpha$. Kudos to Abdelmalek Abdesselam (again).
As for $\mathbb{R}^d$, this is classical: the solution is given by the "fractional heat kernel": $$u(t,x) = u_0 * p_t(x),$$ where $p_t(x)$ is the inverse Fourier transform of $\ex... |
The energy loss in a hydraulic jump is still calculated with the old equation of Bresse from year 1860; (I.e., equation 7 in this paper from 2017)
$$ \frac{\Delta E}{E_1} = \frac{(\sqrt{1+8Fr^2}-3)^3}{16(\sqrt{1+8Fr^2}-1)(1+\frac{1}{2}Fr^2)} $$
There is no measured energy loss when $Fr<\sqrt3$, though this equation pre... |
Votes cast (58)
all time by type 58 up 15 question 0 down 43 answer
3
Find all random variables $X$ such that if $Y$ is $N(0,1)$ and independent from $X$, then $X+Y$ and $\frac{1}{3}X+2Y-1$ have the same distribution
3
Find $\lim_{n \rightarrow \infty} \int_0^n (1+ \frac{x}{n})^{n+1} \exp(-2x) \, dx$
3
Existence of som... |
In the book "Statistical Physics, Part I ($3^{{\rm rd}}$ edition)" by Landau and Lifshitz, at $\S59$ when he treats the diamagnetic part of the magnetisation of a degenerate electron gas for weak fields ($\mu_BH\ll\varepsilon_F$, where $\varepsilon_F$ is the Fermi energy), he says that the energy levels of the orbital ... |
What is the simplest fermionic normalized quantum many-particle wavefunction, expressed in the first-quantized position representation, that you can think of? The normal single-particle examples don't seem to be that simple: Slater determinant of Gaussians times Hermite polynomials for harmonic oscillator, the free par... |
Osaka Journal of Mathematics Osaka J. Math. Volume 54, Number 3 (2017), 499-516. Feller evolution families and parabolic equations with form-bounded vector fields Abstract
We show that the weak solutions of parabolic equation $\partial_t u - \Delta u + b(t,x) \cdot \nabla u=0$, $(t,x) \in (0,\infty) \times \mathbb R^d$... |
The following is probably one of the weirdest unexpected bridges between abstract mathematics and theoretical physics I know of; the two weirdest features being that it's pretty simple to explain, and that the area of math it connects to is number theory. While the latter thing
can occur occasionally, especially in the... |
A limit point of a set $S$ in a metric space $X$ can be either in $S$ or in $X$.
So you have this point, call it $x$. Now think of an arbitrary distance (using your distance metric, $d(x,y)$). Call it $r$. If $x$ is a limit point, then it means that for
ANY $r>0$, you will be able to find some other point $y \in S$ suc... |
In categorical literature, the notation $f: X \rightarrow Y$ only means "$f$ is a function from $X$ to $Y$" in the case where the category you are working in is Set, that is the category of sets and functions. In the category of sets and relations, the same notation means $f$ is a relation from $X$ to $Y$. To answer (p... |
Answer
$sin~C = 1$ $C = 90^{\circ}$ Triangle ABC is a $30^{\circ},60^{\circ},90^{\circ}$ triangle.
Work Step by Step
We can use the law of sines to find the angle $C$: $\frac{a}{sin~A} = \frac{c}{sin~C}$ $sin~C = \frac{c~sin~A}{a}$ $sin~C = \frac{(2\sqrt{5})~sin~(30^{\circ})}{\sqrt{5}}$ $sin~C = 1$ $C = arcsin(1)$ $C =... |
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Now showing items 1-5 of 5
Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
In a paper by Joos and Zeh, Z Phys B 59 (1985) 223, they say:This 'coming into being of classical properties' appears related to what Heisenberg may have meant by his famous remark [7]: 'Die "Bahn" entsteht erst dadurch, dass wir sie beobachten.'Google Translate says this means something ...
@EmilioPisanty Tough call. ... |
The hint by Yuval in his comment is the right one. An approach to writing context-sensitive grammars is to design them like a machine. Send messages over the string. This is very close to writing a linear bounded automaton (or linear space Turing machine). In such a machine the reading/writing head scans over the tape ... |
This exercise is inspired by exercises 83 and 100 of Chapter 10 in Giancoli's book
A uniform disk ($R = 0.85 m$; $M =21.0 kg$) has a rope wrapped around it. You apply a constant force $F = 35 N$ to unwrap it (at the point of contact ground-disk) while walking 5.5 m. Ignore friction.
a) How much has the center of mass o... |
I have a signal, $f(t)$. I know a function that can be used to generate this signal, such that I can determine its Fourier series. I want to express this Fourier series in simpler terms so that the waveform can be rendered by a GPU in parallel, with the added ability to change the lowpass cutoff frequency of the signal... |
Practical and theoretical implementation discussion.
Post Reply
8 posts • Page
1of 1
Hi,
I have a simple question as in the title. Why is volumetric emission proportional to absorption coefficient? I often see the volumetric emission term is written as I can also see another representation, volumetric emittance functio... |
Hello,
I've a problem to calculate the Position of a pendulum as a function of theta.
For example: $\theta (t)$ is a function of time which returns the angle made by the pendulum at a particular instant wrt it's equilibrium Position.
So,
$$ T = \dfrac 12 m l^2 \dot \theta^2 $$$$ U = - mgl \cos \theta $$ $$ L(\theta, \d... |
Young's Modules is defined as,
$Y = \frac{\sigma}{\epsilon}$
where $\sigma$ is the strain defined as $\sigma = F/A$ and $\epsilon$ is the stress defined as $\epsilon = \frac{\Delta L}{L_0}$.
In this case we require the stress, thus re-arranging the first equation gives,
$\sigma = \epsilon Y$
After plugging in the defin... |
In a paper by Joos and Zeh, Z Phys B 59 (1985) 223, they say:This 'coming into being of classical properties' appears related to what Heisenberg may have meant by his famous remark [7]: 'Die "Bahn" entsteht erst dadurch, dass wir sie beobachten.'Google Translate says this means something ...
@EmilioPisanty Tough call. ... |
I'm convinced that radians are, at the very least, the most convenient unit for angles in mathematics and physics. In addition to this I
suspect that they are the most fundamentally natural unit for angles. What I want to know is why this is so (or why not).
I understand that using radians is useful in calculus involvi... |
First of all, your transfer function has a pole at $z=-3$, which means your filter is unstable and you will probably see your output going to infinity if your process anything with it.
However, in general, you can process an impulse with your difference equation and do an FFT (or freqz) of the resulting impulse respons... |
What is Electronics Introduction
One answer to the question posed by the title might be: "The understanding that allows a designer to interconnect electrical components to perform electrical tasks." These tasks can involve measurement, amplification, moving and storing digital data, dissipating energy, operating motors... |
I've heard rumors of covert acoustic room impulse response measurement being done during concerts. You would need the people in the room if you want to use the impulse response for artificial reverberation and you don't want the room to sound overly echoey like there's no-one in it. As received at the microphone, the
s... |
I was reading the following notes on tensor products: http://www.math.uconn.edu/~kconrad/blurbs/linmultialg/tensorprod.pdf
At some point (p. 39) there is the following example
In the last paragraph, he says that using exterior powers it can be proved that if $I\oplus I\simeq S^2$ as $S$-module, then $I\otimes_S I\simeq... |
If $M$ is a Riemannian manifold and $f:M\to \mathbb{R}$ a Morse-Smale function (which is just a rigorous way to say "generic smooth function"), then Morse theory essentially recovers the manifold itself from relatively basic information about the gradient flow diffeomorphisms of $f$. To sketch briefly: for each pair of... |
Calculating analytically solutions to differential equations can be hard and sometimes even impossible. Methods exist for special types of ODEs. One method is to solve the ODE by separation of variables. The idea of substitution is to replace some variable so that the resulting equation has the form of such a special t... |
I am basically very new to this image processing field. I am presently working on edge detection on colour images. While learning the basics of edges and edge detection in images, I encountered image derivatives and spatial masks for the corresponding operations. It's where I happened to learn about Prewitt operator an... |
If you need to insert cross-references to numbered elements in the document, (like equations, sections and figures) there are commands to automate it in LaTeX. This article explains how.
Contents
Below you can see a simple example of images cross referenced:
\section{Introduction} \label{introduction} This is an introd... |
A (weak) composition of a positive integer $n$ into $k$ parts is an ordered sequence of nonnegative integers $(a_1, a_2, \ldots, a_k)$ such that $ \sum_{i=1}^k a_i = n $. I am interested in the case when the parts are bounded: $a_i\in\{0, 1, \ldots, j-1\}$. The number of such compositions satisfies the two-variable rec... |
Quantitative Modeling for Algorithmic Traders – Primer Quantitative Modeling techniques enable traders to mathematically identify, what makes data “tick” – no pun intended 🙂 .
They rely heavily on the following core attributes of any sample data under study:
Expectation– The mean or average value of the sample Varianc... |
This is notation from Distribution Theory in Functional Analysis. The theory of distributions is meant to make things like the Dirac Delta rigorous.
In this context, just to give you one overview, a distribution is a functional on the space of test functions. We define the space of test functions over $\mathbb{R}$ as $... |
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Let $p$ be an odd prime. Prove that $\frac{p-1}{2}$ is a primitive root modulo $p$ if and only if $2(-1)^{(p-1)/2}$ is a primitive root modulo $p$.
I was thinking that since $\frac{p-1}{2}$ is a primitive root modulo $p$ that its order is $p-1$.
Mathematics Stack Exchange is a question and answer site for people studyi... |
Let V be the universe (the class of all sets), let W(0)=V, W(1) be the class of all singletons whose unique member element is a member set of W(0), and for n>0 let W(n+1) be the class of all singletons whose unique member element is a member set of W(n). Let, for every n>=0 S(n)=W(n+1)/W(n) be the class that is the dif... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
In a nut-shell:
exchange integrals are two-electron integrals, and two-electron integrals yield positive values. Note that the "kind" or "meaning" of the input functions is irrelevant, because in practice, you will always have linear combinations of primitives, and in most cases gaussians. For the proof of the claim ab... |
Practical and theoretical implementation discussion.
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I've had a question that I couldn't answer myself and haven't found any formal derivation on the topic. If one has a point light with position \(\vec{c}\) and intensity \(I\), then the irradiance at point \(\vec{p}\) at some surface c... |
Suppose we have the derived category $\mathcal{D}(A)$ of some algebra $A$ over some commutative ring $R$.
I would like an example of two objects $X,Y$ in $\mathcal{D}(A)$ such that for all $n \in \mathbb{Z}$, $H^n(X) \cong H^n(Y)$, but they are not isomorphic in $\mathcal{D}(A)$.
Though I am not sure such an example ex... |
This question is from Abstract Algebra book by Pierre Grillet (2nd edition).
Let $\phi:R\to S$ be a homomorphism of rings with identity and let $A$ be a unital left $S$-module. Make $A$ a unital left $R$-module.
Aim is to find a map $g:R \times A \to A$ that satisfies module conditions.
We have $\phi(1_R)=1_S$ and sinc... |
I'm reading this book about electrical properties of materials where the electron is introduced as a wave. Using the equation of a wave, they bring about the "envelope" of a wave. So here is how the derivation goes:
Consider the equation of a wave traveling in one dimension: $ u = ae^{-i(\omega t - kz)} $ where $\omega... |
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