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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 ... |
The second virial coefficient describes the contribution of the pair-wise potential to the pressure of the gas. The third virial coefficient depends on interactions between three molecules, and so on and so forth.
Introduction
As the density is increased the interactions between gas molecules become non-negligible. Dev... |
Geometric series is very important in analysis. It denition is
\( \sum _{n=0}^{\infty}(z)^n \) Calculate this infinite sum is easier as seems if we note following \( S_{n} = \sum _{n=0}^{\infty}(z)^n = 1 + z + z^2 + ... + z^n \Rightarrow zS_{n}= z + z^2 + ... + z^{n+1} \) this implies \( S_{n}(1-z) = 1 + z + z^2 + ... ... |
I have to solve a set of nonlinear optimization problems in the subspace defined as the orthogonal space to a given vector.
More precisely, $$ \arg\min f(\vec x) \qquad \text{with} \qquad \vec x \cdot \vec n =0 $$
I am thinking of applying the nonlinear conjugate gradient method projecting the direction of descent but ... |
Oct 12th 2018, 01:48 AM
# 1
Junior Member
Join Date: Sep 2018
Posts: 2
Problem with different reference frames - special relativity
I have the following conditions: A plane with length L in its own rest frame moves with constant velocity with respect
to the inertial system S. The inertial system of the plane is called ... |
Question
How does BayesiaLab calculate the Means and Values in the
Monitors? What is the difference? Answer
For each node that has values associated with its states, an Expected Value $v$ is computed by using the associated values and the marginal probability distribution of the node $$v = \sum_{s \in S} p_s \times V_s... |
For exercises 1-10, consider points \(P(−1,3), Q(1,5),\) and \(R(−3,7)\). Determine the requested vectors and express each of them \(a.\) in component form and \(b.\) by using standard unit vectors.
1) \( {\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{PQ}}} \)
Answer: \(a. \vec{PQ}=⟨2,2⟩ \quad b. \vec{PQ}=2\hat{\m... |
One of the earliest models I looked at with the information equilibrium (IE) framework was the relationship $P : N \rightleftarrows L$ where $P$ is the price level, $N$ is nominal output, and $L$ is the level of employment. The relationship effectively captures Okun's law (i.e. changes in real GDP are related to change... |
Definition:Total Ordering Definition
$\mathcal R$ is a
total ordering on $S$ if and only if: $\forall x, y \in S: x \mathop {\mathcal R} y \lor y \mathop {\mathcal R} x$
$\mathcal R$ is a
total ordering on $S$ if and only if: $(1): \quad \mathcal R \circ \mathcal R = \mathcal R$ $(2): \quad \mathcal R \cap \mathcal R^{... |
Fermat spiral
A planar transcendental curve the equation of which in polar coordinates has the form
$$\rho=a\sqrt\phi.$$
To each value of $\phi$ correspond two values of $\rho$ — a positive and a negative one. The Fermat spiral is centrally symmetric relative to the pole, which is a point of inflection. It belongs to t... |
"Off-Policy Evaluation for Slate Recommendation" by Swaminathan et al. 2017 Off-policy evaluation for slate recommendation. Swaminathan, Adith, Akshay Krishnamurthy, Alekh Agarwal, Miro Dudik, John Langford, Damien Jose, and Imed Zitouni. In Advances in Neural Information Processing Systems, pp. 3635-3645. 2017. Summar... |
Birthday Paradox Contents Paradox
Let there be $23$ or more people in a room.
The probability that at least $2$ of them have the same birthday is greater than $50 \%$.
Proof
Let there be $n$ people in the room.
Let $\map p n$ be the probability that no two people in the room have the same birthday.
Let the birthday of ... |
This was really driving me nuts. The so-called "barometric formula". Here's what it is all about: an ideal gas in a container of a given volume would fill that volume at constant pressure $p$ and temperature $T$ so that the
ideal gas law applies:
\[pV=RnT,\]
where $T$ is the temperature, $n$ is the number of gas molecu... |
Fitting models to large datasets and/or models involving a large number of random effects (for the
rma.mv() function) can be time consuming. Admittedly, some routines in the metafor package are not optimized for speed and efficient memory usage by default. However, there are various ways for speeding up the model fitti... |
A blog of Python-related topics and code.
To produce a children's sticker chart from a provided image, the following code divides it into squares (which can be cut out) and produces further images with matching labels for the reverse side of the printed image and a piece of card onto which the squares can be stuck (you... |
A note on cohomological dimension over Cohen-Macaulay rings
Bull. Korean Math. Soc. Published online August 20, 2019
Iraj Bagheriyeh, Kamal Bahmanpour, and Ghader GhasemiUniversity of Mohaghegh Ardabili
Abstract : Let $(R,\m)$ be a Noetherian local Cohen-Macaulay ring and $I$ be a proper ideal of $R$.Assume that $\beta... |
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. ... |
This question already has an answer here:
I know that diminishing marginal returns even to all factors of production doesn't imply decreasing returns to scale. But could you please give me just an example of such production function?
Economics Stack Exchange is a question and answer site for those who study, teach, res... |
Consider $A =\left( \begin{array}{ccc} -1 & 2 & 2\\ 2 & 2 & -1\\ 2 & -1 & 2\\ \end{array} \right)$. Find the eigenvalues of $A$.
So I know the characteristic polynomial is:
$$f_A(\lambda) = (-\lambda)^n+(trA)(-\lambda)^{n-1}+...+\det A$$
I found the $\det A = 27$, so the characteristic polynomial of $A$ is:
$$-\lambda^... |
Let $x_1,...,x_n $ are distinct real numbers.
Is it a formula for the Vandermonde type determinant $V(x_1, \cdots,x_n)$ whose last column is $x_1^k,\ \cdots,\ x_n^k$, where $k \geq n$, instead of $x_1^{n-1},\ \cdots,\ x_n^{n-1}$?
Thanks
Mathematics Stack Exchange is a question and answer site for people studying math a... |
I’ll post what I have so far, as requested and because someone might pick up a way forward from the end result. It is also too long for a comment but should not be considered a solution to the problem. I feel that there might actually be a closed from worth chasing.
Firstly the function of interest has the integral rep... |
I have read the following theorem:
If $p_1,p_2,\dots,p_n$ are distinct prime numbers, then$$\left(\mathbb Q\left[\sqrt p_1,\dots,\sqrt p_n\right]:\mathbb Q\right)=2^n.$$
I have tried to prove a more general statement but I have a problem at one point. (I still don't know how to prove the theorem above, too, because I d... |
2018-09-11 04:29
Proprieties of FBK UFSDs after neutron and proton irradiation up to $6*10^{15}$ neq/cm$^2$ / Mazza, S.M. (UC, Santa Cruz, Inst. Part. Phys.) ; Estrada, E. (UC, Santa Cruz, Inst. Part. Phys.) ; Galloway, Z. (UC, Santa Cruz, Inst. Part. Phys.) ; Gee, C. (UC, Santa Cruz, Inst. Part. Phys.) ; Goto, A. (UC,... |
Electronic Communications in Probability Electron. Commun. Probab. Volume 18 (2013), paper no. 72, 10 pp. The impact of selection in the $\Lambda$-Wright-Fisher model Abstract
The purpose of this article is to study some asymptotic properties of the $\Lambda$-Wright-Fisher process with selection. This process represent... |
In the last set of notes we talked about how to
differentiate \(k\)-forms using the exterior derivative \(d\). We’d also like some way to integrate forms. Actually, there’s surprisingly little to say about integration given the setup we already have. Suppose we want to compute the total area \(A_\Omega\) of a region \(... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$
Is $~\pi^2\approx g~$ a coincidence ?
Some have answered
, others said yes , and no yet others considered $(!)$ as perfectly viable options. Personally, I cannot help but chuckle, as this question reminds me of both Newton’s famous disc, which can be said to be both white an... |
Nov 10th 2008, 04:58 AM
# 2
Member
Join Date: Jul 2008
Posts: 60
Ok, I know what the problem is, I made a mistake in the moment of inertia...
I do have another question due.
First of all, when they say this is the angular acceleration of the poll, does it mean the angular acceleration of the center of mass?
In the next... |
Textbook solution
The first thing to do is to define the center of mass and relative coordinates:
$$ R(t) = {m_1 r_1 + m_2 r_2 \over m_1 + m_2} $$
$$ r(t) = r_2 - r_1 $$
You invert this to find
$$ r_1= R - {m_2\over M} r$$$$r_2=R+ {m_1\over M} r$$
The equation of motion for R is trivial, since center of mass is a conse... |
I was doing a couple of problems for homework:
Calculate $K_\mathrm{sp}$ of $\ce{AgI}$ at $55.0\ \mathrm{^\circ C}$
Calculate $K_\mathrm{b}$ of $\ce{NH3}$ at $36.0\ \mathrm{^\circ C}$
I have to use $\Delta G^\circ= -RT\ln K$ and $\Delta G= \Delta H-T\,\Delta S$
When I did this $\Delta G^\circ$ is positive ($89.59\ \mat... |
On phaseless compressed sensing with partially known support
School of Mathematics, Tianjin University, Tianjin 300072, China
We establish a theoretical framework for the problem of phaseless compressed sensing with partially known signal support, which aims at generalizing the Null Space Property and the Strong Restri... |
Difference between revisions of "Inertia"
(→Normalised Inertia Constants)
Line 54: Line 54:
:: <math>S_{b}</math> is the rated power of the machine (VA)
:: <math>S_{b}</math> is the rated power of the machine (VA)
−
Based on actual
+ + + + + + + + + + + + + + + +
Based on actual data, the normalised inertia constants f... |
ISSN:
1534-0392
eISSN:
1553-5258
All Issues
Communications on Pure & Applied Analysis
March 2009 , Volume 8 , Issue 2
Select all articles
Export/Reference:
Abstract:
We study the long-time behavior of non-negative solutions to the Cauchy problem
(
P)
$\qquad \rho(x) \partial_t u= \Delta u^m\qquad$
in $Q$:$=\mathbb R^n\... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
I came across John Duffield Quantum Computing SE via this hot question. I was curious to see an account with 1 reputation and a question with hundreds of upvotes.It turned out that the reason why he has so little reputation despite a massively popular question is that he was suspended.May I ...
@Nelimee Do we need to m... |
The aim of the following is to address the intuition side of the question - I doubt that I have more experience than anybody else, and the following is certainly not rigorous - still... One way to the answer - at least in this case! - is to use calculus, i.e., assume everything in sight is differentiable, and perhaps t... |
Why set of real numbers not a set of ordered pairs ?
We write $\mathbb{R}^2 = \mathbb{R} \times \mathbb{R}$, then we define addition and multiplication on this new set. Together with those definitions we call $\mathbb{R}^2$ as the set of complex numbers $\mathbb{C}$.
This is the gist of what I know from my book.
(I don... |
This is something I've been trying to figure out for a long time, and all I have is vague numerical results. I'm trying to answer the following question analytically:
Suppose I have a time dependent system:
$u_t = L(x, u, u_x, u_{xx}) , u(t=0,x) = u_0 $
I approximate differences with some finite difference scheme, for ... |
The idea behind the information transfer model is that what is called "demand" in economics is essentially a source of information that is being transmitted to the "supply", a receiver, and the thing measuring the information transfer is what we call the "price".
Choosing constant information sources (i.e. keeping dema... |
According to Kolmogorov, the energy spectrum function of a turbulent fluid is given as,
$E(k)=C\epsilon^{\frac{2}{3}}k^{\frac{-5}{3}}$
where $\epsilon$ is the energy flux and $k=\frac{2\pi}{r}$ where $r$ is the length scale.
The normal explanation I see in most physics texts and articles is that the -5/3 exponent is fo... |
No, the damping coefficient will not vary with mass.
Based on the back in forth in the comments, you are confusing a few concepts here.
The damping coefficient (subscript $c$) is a measure of applied force compared to velocity. In terms of the equations of simple harmonic motion, this is a constant which has no terms d... |
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. ... |
This is a continuation of my previous question.
I have two classes, $C_1$ and $C_2$.
$C_1$ is a bivariate Gaussian with mean $\mu = (0,0)$ and covariance $\Sigma = I$
$C_2$ is a bivariate Gaussian with mean $\mu = (1,3)$ and covariance $\Sigma = 2I$, where $I$ is the identity matrix.
I am trying to calculate $P(x|C_1)$... |
Although we will have practically no occasion to use the quantum microcanonical ensemble (we relied on it more heavily in classical statistical mechanics), for completeness, we define it here. The function \(f\), for this ensemble, is
\[f(E_i)\delta E = \theta(E_i-(E+\delta E))-\theta(E_i-E)\]
where \(\theta (x) \) is ... |
Search
Now showing items 1-1 of 1
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 ... |
Castellón, 12/12/2017
Take an isolated surface singularity.
By Milnor fibration theorem, the germ is the topological cone over the link.
Let \(\pi: M \rightarrow \Sigma\) be a \(\mathbb{S}^1\) bundle
Given two \(\mathbb{S}^1\) bundles \(\pi_1: M_1 \rightarrow \Sigma_1\), \(\pi_2: M_2 \rightarrow \Sigma_2\)
Are obtained... |
Let $\pi:A\longrightarrow M$ be a vector bundle and $E\subseteq A$ a vector sub-bundle. Recall, a $k$-form on $A$ is a section of $\Lambda^k A^*$. Let us write $\Omega^k(A):=\Gamma(\Lambda^k A^*)$.
The inclusion $\jmath: E\longrightarrow A$ is a vector bundle map and therefore induces $\jmath^*:\Omega^k(A)\longrightarr... |
In most type systems, the type rules work together to define judgements of the form:
$$\Gamma\vdash e:\tau$$
This states that in context $\Gamma$ the expression $e$ has type $\tau$.
$\Gamma$ is a mapping of the free variables of $e$ to their types.
A type system will consist of a set of axioms and rules (a formal syste... |
I am trying to calculate an integral involving multiple indicator functions, such as:
$$ h(u,v,w) = -\int_0^1 J^{\prime\prime}(s) (I_{(0,s]}(u) - s)(I_{(0,s]}(v) - s)(I_{(0,s]}(w) - s)\, dF^{-1}(s)$$
where $0 < u, v, w < 1$ and
$$\begin{align} J(s) &= 6s(1-s)\\ F(s) &= 1/[1 + \exp[-s]]\\ F^{-1}(s) &= -\log[-1 + 1/s]\\ ... |
We will call a complementary set of $$A$$, and denote it as $$A^c$$, the set difference $$(U - A)$$, $$U$$ being the universal set. This is: $$$A^c=\{x: \ x\in U \ and \ x\notin A\}$$$
The complementary set of $$A$$ is the set of the elements $$x$$ that satisfy $$x$$ belongs to $$U$$, and $$x$$ does not belong to $$A$$... |
Let $\{p_n\}$ denote a sequence such that: $$ S_n = {1\over p_1} + {1\over p_2} + \cdots + {1\over p_n} $$ converges. Prove that: $$ \sigma_n = \left(1+{1\over p_1}\right)\left(1+{1\over p_2}\right)\cdots\left(1+{1\over p_n}\right) $$ converges, where $n, p_n \in \Bbb N$.
Consider each bracket from $\sigma_n$. By ${1\o... |
The presentation of the homology version of Cauchy's theorem in Ahlfors is slick, but sweeps a lot of the topology under the rug using clever arguments. This question is an attempt to reconcile Ahlfors' analytic notion of a curve being homologous to zero (presented in his book
Complex Analysis and originally due to E. ... |
As others have pointed out, it is important to justify that $6 \mid q^2 \Rightarrow 6\mid q$. And it isn't totally clear from your proof.
I suggest the following.
First show that $\sqrt{6}$ is not an integer. It's not difficult to do that. Since $4<6<9$, it follows that $2<\sqrt{6}<3$ and that means that $\sqrt{6}$ is ... |
$\def\d{\mathrm{d}}$There was a hint in the book, use intregation by parts in this way: $$\lim_{x\to 0^+} \frac{1}{x} \int_0^{x} \sin\frac{1}{t} \,\d t = \lim_{x\to 0^+} \frac{1}{x} \int_0^{x} t^2 \left(\frac{1}{t^2} \sin\frac{1}{t}\right)\,\d t.$$
When we integrate by parts we find this integral:
$$\int_0^{x} t\cos\fr... |
The dodecahedron is a regular polyhedron of $$12$$ faces. If the mentioned faces are regular pentagons we call it a regular dodecahedron:
To find the area of edge a of a dodecahedron $$a=10 \ m$$.
To calculate the area of edge $$a$$ of the regular dodecahedron it will be necessary to first find the area of side $$a$$ o... |
Latex distinguishes between three different enumeration/itemization environments. Each of them provide four levels, which means you can have nested lists of up to four levels.
Enumerate: \begin{enumerate} \item ... \end{enumerate}
The enumerate-environment is used to create numbered lists.
If you like to change the app... |
You are asking all the right questions!
Let me give you an extreme example. Then I'll answer you question.
Let $f(x)$ then the function that.
If $x$ is irrational then $f(x) = 2+x$.
If $x = \frac ab$ where $\frac ab$ is a rational number in "lowest terms", then $f(x) = 2 + \frac 1{b}$. (We'll assume the denominator is ... |
Assume, we have an $m\times n$ block matrix $M=\left[\begin{array}{c c}A&C\\B&D \end{array}\right]$, where
$A$ is an $m_1 \times n_1$ matrix of rank $k_A$. $B$ is an $m_2 \times n_1$ matrix of rank $k_B$. $C$ is an $m_1 \times n_2$ matrix of rank $k_C$. $D$ is an $m_2 \times n_2$ matrix of rank $k_D$.
Obviously, $m_1+m... |
Let's start considering the following example:
A screw factory has two machines, the $$M1$$, which is old, and does $$75\%$$ of all the screws, and the $$M2$$, newer but small, that does $$25\%$$ of the screws. The $$M1$$ does $$4\%$$ of defective screws, while the $$M2$$ just does $$2\%$$ of defective screws. If we ch... |
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Now showing items 1-3 of 3
Azimuthally differential pion femtoscopy relative to the second and thrid harmonic in Pb-Pb 2.76 TeV collisions from ALICE
(Elsevier, 2017-11)
Azimuthally differential femtoscopic measurements, being sensitive to spatio-temporal characteristics of the source as well as to the collectiv... |
Yesterday I asked about $\lim_\limits{\sigma_A, \sigma_B \to \infty }e^{-\sigma_A-\sigma_B} \sum_{k=0}^{\infty} \frac{{\sigma_A}^k}{k!}\cdot\frac{{\sigma_B}^k}{k!}$, and some fellow users helped me understand that this expression goes to zero. I hoped that I could use the logic of this proof to also understand this, sl... |
I understand that using a unit vector (of a vector say $\vec{a}$ ) and computing the directional derivative gives the slope (or rate of change of the function) in the direction of the vector.
I have three questions :
If I use the vector itself rather than it's unit vector what will I getwhen I compute it's dot product ... |
Let $S$ be a vector space of functions from $\mathbb{R}^n$ to $\mathbb{R}$, say $S := \{ f:\mathbb{R}^n \rightarrow \mathbb{R} \}$.
I am looking for some examples in which the dimension of $S$ is known.
For instance, trivial examples are the following.
Linear functions $f(x) := a^\top x$ implies that $\text{dim}(S) = n... |
The other answers are nice, but none address the question: what numeric base(s) might quantum computers use? I will answer in two parts: first, the question is a little subtle, and second, you may use any numeric base, and then you work with qutrits or in general with qudits, which lead to qualitatively new intuitions!... |
Let $X$ be a topological space, and let $\{K_\alpha\}_{\alpha\in A}$ be a family of closed compact subsets of $X$. Show that $\bigcap_{\alpha\in A} K_\alpha$ is compact.
Proof:
Let $\mathcal{T}$ be the given topology on $X$. And let $\mathcal{T}_\alpha$ be the corresponding subspace topology on $K_\alpha$.
Let $K=\bigc... |
This post will be more speculative than the derivation of supply and demand -- it will give one possible take of how sticky prices appear in the model (which are key to at least some schools of modern macroeconomic theory). If we return to non-ideal information transfer $I_{Q^s} \leq I_{Q^d}$ such that Equations (4) an... |
Q. Let $X$ be a random variable with the probability density function
$ f_{X}(x) = \begin{cases} 1 &\text{ if} \quad 0 < x < 1 \\ 0 &\text{ otherwise} \end{cases} $
Let $Y$ be a random variable with the conditional probability density function
$ f_{Y|X}(y|x) = \begin{cases} 1/x &\text{ if} \quad 0 < y < x \\ 0 &\text{ ... |
I've got cumulative distribution function given: $F_X(t) = 0 $ for $t<0$, $\frac{1}{3} $ for $t=0$ , $\frac{1}{3} + \frac{t}{90} $ for $ t\in (0,60)$ and $1$ for $t \ge 60$. I am to find expexted value ($EX$). So, what to do? I wanted to find a density function, but I can't, because cumulative distribution function is ... |
I have a list of data existing as {{{x, y, z}, f},...} from which I construct a 3D interpolation function using Interpolation[ ]. I am able to construct a vector field from the gradient of this scalar field, I have verified this looks correct by plotting it.
I wish to find the 'attractors' of this vector field.
By 'att... |
T Singh
Articles written in Pramana – Journal of Physics
Volume 63 Issue 5 November 2004 pp 937-945
We have studied five-dimensional homogeneous cosmological models with variable
Volume 68 Issue 5 May 2007 pp 721-734 Research Articles
We have studied the evolution of a homogeneous, anisotropic universe given by a Bianc... |
I came across a problem thatwhile doing some review that states:
Consider the transformation $\textit{T}$:$\mathbb{R}^2\rightarrow\mathbb{R}^2$ defined by the matrix $$ \begin{pmatrix} 2 & 0 \\ 1 & 3 \\ \end{pmatrix} $$ Prove that the transformation is linear, state the kernel of T and find the image of the vector (1, ... |
I don't know if this is research level or math se level so I try posting here first.
The problem is to prove that the left hand side equals the right hand side for $t>0$ when leaving out singularities such as the points $t$ equal to the imaginary part of a Riemann zeta zero:
$$\left\lfloor \frac{t \log \left(\frac{t}{2... |
Let $\pi:X\to X/\!\!\!\sim\;$ denote the projection map associated with $\sim$. (That is, for any $x\in X$, $\pi(x)$ is the $\sim$-equivalence class that $x$ belongs to.) Let $\nsim\; \subseteq X \times X$ be shorthand for the complement of $\;\;\sim\;\;$ in $X \times X\;$, i.e. $\nsim\;\;=\;(X \times X\;) \;\;-\; \sim... |
Here, I mostly referred to the Cobb-Douglas production function piece, not the piece of the Solow model responsible for creating the equilibrium level of capital. That part is relatively straight-forward. Here we go ...
Let's assume two additional information equilibrium relationships with capital $K$ being the informa... |
Simulating a Classical Computer Using a Quantum Computer An easier way to think of quantum computers
I was very fortunate my last quarter as a graduate student at UCSD to have helped organize a quantum computing seminar. I was strongly influenced by Aaronson’s excellent book Quantum Computing Since Democritus where Aar... |
An RLC circuit is a simple electric circuit with a resistor, inductor and capacitor in it -- with resistance
R, inductance Land capacitance C, respectively. It's one of the simplest circuits that displays non-trivial behavior.
You can derive an equation for the behavior by using Kirchhoff's laws (conservation of the st... |
I'm solving the 3D Diffusion equation $$u_t=k(u_{xx}+u_{yy}+u_{zz})$$
in MATLAB using Fourier techniques. I assume a 3D Fourier expansion $(e^{-ipx},e^{-imy},e^{-imz})$of the solution.
Physical space: $u(x,y,z,t)$. Fourier Space: $c(m,n,p,t)$.
Substitution and differentiation result in: $$c(m,n,p)^{N+1}-c(m,n,p)^{N} = ... |
doi: 10.1685/journal.caim.531
Stochastic processes related to time-fractional diffusion-wave equation Abstract
It is known that the solution to the Cauchy problem:
$$ D^\beta_* u(x,t)= R^\alpha u(x,t) \,, \quad u(x,0)=\delta(x) \,, \quad \frac{\partial}{\partial x}u(x,t=0) \equiv 0 \,, \quad -\infty < x < \infty \,, \q... |
Given that $n>2$. Prove that if $2^n-1$ is prime then $2^n+1$ is composite or vice versa. I looked on wikipedia on Fermat number and Mersenne prime, but I still don't know how they work.
Hint $\ a\mid (a\!-\!1)^n\!\pm 1\ $ since $ $ mod $\ a\!:\ (a\!-\!1)^n \equiv (-1)^n\equiv \pm 1$
e.g. $\,\ 10\mid 9^n\pm1\, $ is a w... |
Difference between revisions of "Droop Control"
Line 3: Line 3:
== Background ==
== Background ==
−
Recall that the [[AC_Power_Transmission#Lossless_Line_.28Classical_Approach.29|active and reactive power transmitted across a lossless line]] are:
+ + + + + + +
Recall that the [[AC_Power_Transmission#Lossless_Line_.28Cl... |
2018-09-11 04:29
Proprieties of FBK UFSDs after neutron and proton irradiation up to $6*10^{15}$ neq/cm$^2$ / Mazza, S.M. (UC, Santa Cruz, Inst. Part. Phys.) ; Estrada, E. (UC, Santa Cruz, Inst. Part. Phys.) ; Galloway, Z. (UC, Santa Cruz, Inst. Part. Phys.) ; Gee, C. (UC, Santa Cruz, Inst. Part. Phys.) ; Goto, A. (UC,... |
ISSN:
1937-1632
eISSN:
1937-1179
All Issues
Discrete & Continuous Dynamical Systems - S
June 2009 , Volume 2 , Issue 2
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Abstract:
In October, 2007 the AMS Central Sectional Meeting was held at DePaul University in Chicago, IL. At that time, the guest editors of this issue of DCDS-S ... |
Given two linear functions $f(x)$ and $g(x)$ defined on real values, let's say that I want to show that $f(x) > g(x)$ for all real $x > t > 0$. According to the order-1 Taylor expansion at the origin, these two functions can be written as \begin{equation*} f(x) = f(0) + (x-0)f'(0)\quad \text{and}\quad g(x) = g(0) + (x-... |
Consider for large integers $n$ the expression $\sin \left(\pi \sqrt{4 n^2+n}\right)$.
Since
$\sqrt{4 n^2+n}=2 n \sqrt{1 + \frac{1}{4 n}}$
we can use the standard series for the square root and next the standard series for $sin$ to find a series expansion of this expression around $\infty$. That is a simple first year ... |
ISSN:
1937-1632
eISSN:
1937-1179
All Issues
Discrete & Continuous Dynamical Systems - S
December 2009 , Volume 2 , Issue 4
A special issue on Bifurcation Delay
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Abstract:
The theory of slow-fast systems is a challenging field both from the viewpoint of theory and applications. Advan... |
Suppose that there is an algorithm which sorts a sequence of $n$ elements
$$a_1, a_2, ..., a_n$$
Each of the $a_i$ is chosen with probability $1/k$ from a set of $k$ distinct integer numbers.
Is it true, given that $k \to \infty$, that:
The probability that any two of incoming sequence elements are equal, tends to $0$?... |
Condition on Connectedness by Clopen Sets Theorem
Let $T = \left({S, \tau}\right)$ be a topological space.
Then: $T$ admits no separation the only clopen sets of $T$ are $S$ and $\varnothing$. Thus both conditions can be used to define a connected topological space. Proof Necessary Condition
Then by definition $T$ admi... |
I saw the following claim in some book without a proof and couldn't prove it myself.
$\dfrac{d}{dp}\mathbb{P}\left(\text{Bin}\left(n,\,p\right)\leq d\right)=-n\cdot\mathbb{P}\left(\text{Bin}\left(n-1,\,p\right)=d\right)$
So far I got:
$\begin{array}{l} \dfrac{d}{dp}\mathbb{P}\left(\text{Bin}\left(n,\,p\right)\leq d\rig... |
I'm reading quantum chemistry. The book says that the orbital angular momentum of a $\pi$ electron along the symmetry axis of a molecule made up of two atoms is $\pm 1$. I think this is a primary question, but I do not konw why.
I currently have a preliminary understanding of this:
In a molecule inculding two atoms, po... |
I have a system of ODEs which is (at least moderately) stiff.
Consider the class of spectral collocation methods https://en.wikipedia.org/wiki/Spectral_method or the related class of weighted residual methods.
Basically, take a system of ODEs like $$ y'(t) = f(t, y(t)) $$ where $f(\cdot,\cdot)$ is nonlinear in my case ... |
Most people start out by calculating the volume of liquid. As with many mathematical tasks some thought in advance may save a lot of work . Failing that, if you review your method you may find a neater and more efficient way to do it. Try to evaluate your own work, think about it and ask yourself questions like: "what ... |
Minkowski space is a real
affine space of dimension $4$ whose space of translations is equipped with a metric of Lorentzian type.
A (real)
affine space is a triple $(\mathbb A, V, \vec{})$, where $\mathbb A$ is a set whose elements are said points, $V$ is a (real) vector space and $\vec{}$ is a map $\vec{} : \mathbb A ... |
The definition you are given is equivalent to
$$\lim_{x \to a} \frac{f(x)-g(x)}{(x-a)^n}=0 $$
We are given $g$ defined as the sum
$$g(x) = \sum_{i=0}^n \frac{f^{(i)}(a)}{i!}(x-a)^i$$
so we want to check wether or not
$$\lim_{x \to a} \frac{f(x)-\sum_{i=0}^n \frac{f^{(i)}(a)}{i!}(x-a)^i}{(x-a)^n}=0 $$
Since the last ter... |
I'm answering my own question. It is related to the answers given by both AJMansfield and Tony J., but slightly different, needing the inclusion of a vectorization transpose reordering operator, which is more involved than a simple transpose.
Long story short, the answer is that the desired matrix is given by,$$(B^T \o... |
I want to find an example of Polish space which is not locally compact. I am thinking about the space of all continuous function from $[0,1]$ to $R$, endowed with the metric $d(f,g) = \sup_{x\in [0,1]}|f(x)-g(x)|$.
I know this space is complete. And by Weierstrass Approximation Theorem, all the polynomials with rationa... |
@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... |
Nehari Manifold and Multiplicity Results for a Class of Fractional Boundary Value Problems with $p$-Laplacian
Bull. Korean Math. Soc. Published online August 6, 2019
Abdeljabbar Ghanmi and Ziheng ZhangUniversity of Jeddah, Tianjin Polytechnic University
Abstract : In this work, we investigate the following fractional b... |
Could someone explain the correspondence between lines in twistor space and minkowski space-time points? a basic derivation would suffice
The ordinary twistor space is parameterized by $(\lambda^\alpha,\mu_{\dot\alpha})$. Here, the $\alpha$ is a 2-valued $SL(2,C)$ spinor index of one chirality and the dotted index is i... |
Suppose I have a 2D mesh consisting of nonoverlapping triangles $\{T_k\}_{k=1}^N$, and a set of points $\{p_i\}_{i=1}^M \subset \cup_{k=1}^N T_K$. What is the best way to determine which triangle each of the points lies in?
For example, in the following image we have $p_1 \in T_2$, $p_2 \in T_4$, $p_3 \in T_2$, so I wo... |
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