text stringlengths 256 16.4k |
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Okay, so I'm having real problems distinguishing between the Steady State concept and the balanced growth path in this model:
$$ Y = K^\beta (AL)^{1-\beta} $$
I have been asked to derive the steady state values for capital per effective worker:
$$ k^*=\left(\frac{s}{n+g+ \delta }\right)^{\frac{1}{1-\beta }} $$
As well ... |
Define a Bayesian game as follows: $$G = \left\langle I, \left(A_i,T_i,(p_{t_i})_{t_i \in T_i}, u_i \right)_{i \in I} \right\rangle$$
$I$ is the set of players $A_i$ is the action set for player $i$, $T_i$ is the set of possible types for player $i$, $p_{t_i} \in \Delta(T_{-i})$ is player $i$'s beliefs regarding the ty... |
This section addresses the graphing of the Tangent, Cosecant, Secant, and Cotangent curves.
Verbal
1) Explain how the graph of the sine function can be used to graph \(y=\csc x\).
Answer
Since \(y=\csc x\) is the reciprocal function of \(y=\sin x\)you can plot the reciprocal of the coordinates on the graph of \(y=\sin ... |
So the quantity I would like to understand is:
$$\sum_{x \in \{ 0,1,\dots,m \}^n : \sum_{i=1}^n x_i=m} \exp \left ( -\beta \sum_{i=1}^n |x_{i+1}-x_i| \right )$$
where $m$ is a positive integer, $\beta=\frac{1}{k_B T}>0$, and we define $x_{n+1}=x_1$ (periodic boundary conditions). This is the partition function of a cer... |
I've had several Computer Science courses and, from what I recall, I've never been given a rigorous definition of
suitable encoding. Definitions always tend to use effective method or some synonym to define a suitable encoding, even though the reason we are defining suitable encodings is to formalize what an effective ... |
Assume $X_t$ is a multivariate Ornstein-Uhlenbeck process, i.e. $$dX_t=\sigma dB_t-AX_tdt$$ and the spot interest rate evolves by the following equation: $$r_t=a+b\cdot X_t.$$ After solving for $X_t$ using $e^{tA}X_t$ and Ito and looking at $\int_0^T{r_s\;ds}$, it turns out that $$\int_0^T{r_s\;ds} \sim \mathcal{N}(aT+... |
So far, we have learned how to differentiate a variety of functions, including trigonometric, inverse, and implicit functions. In this section, we explore derivatives of logarithmic functions. Logarithmic functions can help rescale large quantities and are particularly helpful for rewriting complicated expressions.
Der... |
I have successfully solved the multi-species diffusion-reaction equation \begin{equation} \frac{\partial c_i}{\partial t} = \nabla \cdot (d_i(x)\nabla c_i) + s_i(x,t), \quad \quad (1) \end{equation} with dicontinuous source term \begin{equation} s(x,t) = \left\{ \begin{array}{rcl} s_1(x,t) & \text{for} & 0<x\le x' , \\... |
I've been trying to find some resources that would help me figure out how to numerically solve a coupled system of ODEs which is also an eigenvalue problem.
The system is something like:
$ \tag{1} \kappa h_2(r) +\kappa r h'_2(r)+ (1+\kappa) W_3(r) + (1+ \kappa) r W'_3(r)+ (1 + \kappa) r^2 W''_3(r) = 0 $
$ \tag{2} W_3 +... |
Condition for Cartesian Product Equivalent to Associated Cardinal Number Theorem
Let $\left|{S}\right|$ denote the cardinal number of $S$.
Then: $S \times T \sim \left|{S \times T}\right| \iff S \sim \left|{S}\right| \land T \sim \left|{T}\right|$
where $S \times T$ denotes the cartesian product of $S$ and $T$.
Proof N... |
Complete Linearly Ordered Space is Compact Theorem
Let $\left({X, \preceq, \tau}\right)$ be a linearly ordered space.
Let $\left({X, \preceq}\right)$ be a complete lattice.
Then $\left({X, \tau}\right)$ is compact. Proof
By Compactness from Basis, it is sufficient to prove that an open cover of $X$ consisting of open i... |
This section explores the use of symmetry to determine selection rules. Here we derive an analytical expression for the transition dipole moment integral for the particle-in-a-box model. The result that the magnitude of this integral increases as the length of the box increases explains why the absorption coefficients ... |
1) Determine whether the function \(y=156(0.825)^t\) represents exponential growth, exponential decay, or neither. Explain.
Answer
exponential decay; The growth factor, \(0.825\) is between \(0\) and \(1\)
2) The population of a herd of deer is represented by the function \(A(t)=205(1.13)^t\)where \(t\) is given in yea... |
Terms and Concepts
1. The strategy for establishing bounds for triple integrals is "from ________ to ________, then from ________ to ________ and then from ________ to ________."
Answer: We integrate from to surface , then from surface to curve and then from curve to point . point
2. Give an informal interpretation of ... |
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... |
Let's look at your original three equations.
$$x+2y+z=2$$$$3x+8y+z=12$$$$4y+z=2$$
Now let's multiply by $\frac{2}{5}$, $\frac{1}{5}$, and $\frac{-3}{5}$ respectively. We get
$$\frac{2x}{5}+\frac{4y}{5}+\frac{2z}{5}=\frac{4}{5}$$$$\frac{3x}{5}+\frac{8y}{5}+\frac{z}{5}=\frac{12}{5}$$$$\frac{-12y}{5}+\frac{-3z}{5}=\frac{-... |
I am trying to solve a bunch of equations for the zeros of the derivative of an analytic function, and I would like to know if there exist methods that exploit this structure to provide better performance than the standard algorithms.
At the moment I am using Mathematica's
FindRoot function, which I understand relies o... |
Hello, I've never ventured into char before but cfr suggested that I ask in here about a better name for the quiz package that I am getting ready to submit to ctan (tex.stackexchange.com/questions/393309/…). Is something like latex2quiz too audacious?
Also, is anyone able to answer my questions about submitting to ctan... |
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... |
my assignment has this question, given a topological space X with finite many connected components, a function $f:X\rightarrow Y$ is continuous if and only if it is continuous on each components. Is it still true if X has infinitely many components. The first is okay but the reverse makes me confused, so how can I prov... |
In page $36$ of "Partial Differential Equation," Evan define $v(z) = \Phi(z-x) - \phi^x(z)$, where $\phi^x(z)$ is a corrector function, satisfying the following identities,
$$ \Delta \phi^x = 0 \ in \ U \tag{1}$$ $$ \phi^x = \Phi(y-x) \ in \ \partial U \tag{2}$$
$$\lim_{\epsilon \rightarrow 0} \int_{\partial B(x,\epsil... |
Euler's Equation for Vanishing Variation is Invariant under Coordinate Transformations Theorem
Euler's Equation for Vanishing Variation is invariant under coordinate transformations.
Proof
Let $J\sqbrk y$ be an integral functional:
$\displaystyle J\sqbrk y=\int_a^b \map F{x,y,y'}\rd x$.
Suppose, we introduce new curvil... |
pre-calculus-trigonometry-calculator
\sin \left(x\right)+\sin \left(\frac{x}{2}\right)=0, 0\le x\le 2\pi
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We have had several questions about the relation of Cook and Karp reductions. It's clear that Cook reductions (polynomial-time Turing reductions) do not define the same notion of NP-completeness as Karp reductions (polynomial-time many-one reductions), which are usually used. In particular, Cook reductions can not sepa... |
Definition:Characteristic Polynomial
Jump to navigation Jump to search
Definition
Let $K$ be a field.
Let $L / K$ be a finite field extension of $K$.
Let $\alpha \in L$, and $\theta_\alpha$ be the linear operator:
$\theta_\alpha: L \to L : \beta \mapsto \alpha \beta$ The characteristic polynomial of $\alpha$ with respe... |
Current browse context:
math-ph
Change to browse by: Bookmark(what is this?) Mathematics > Differential Geometry Title: Spectral sections, twisted rho invariants and positive scalar curvature
(Submitted on 23 Sep 2013 (v1), last revised 25 Apr 2014 (this version, v3))
Abstract: We had previously defined the rho invaria... |
In this post I showed how the information flows in a simple market for apples, but here I'm going to show what I hinted at in the earlier post:
money is a tool to transfer information from the demand to the supply.
Let's start with a simple system of $d$ buyers (green) and two suppliers of gray bundles of something. Ea... |
This is my attempt at an exercise from Folland's
Real Analysis. Could someone evaluate it (particularly the second claim)?
Let $\mathcal M$ be an infinite $\sigma$-algebra.
Claim: $\mathcal M$ contains an infinite sequence of disjoint sets. Proof: Since $\mathcal M$ is infinite, it must contain a sequence $\left\{E_j\r... |
Well you just check the definitions. $T:V\to W$ is a linear transformation if, for all $v,w\in V$ and $a\in\mathbb{R}$ (works for general base fields), we have $$T(av+w)=aT(v)+T(w)$$Let's look at (a): Pick $(0,1,0)$ and $(0,-1,0)$. Then $T(0,0,0)=0$ but $T(0,1,0)+T(0,-1,0)=(4,-1,0)+(4,1,0)=(8,0,0)\not=(0,0,0)=T((0,1,0)... |
Let $Y$ be the random variable counting how many successes you have in $N$ trials. If $X_i$ is the Bernoulli random variable giving $1$ if the $i$th draw is a successs and $0$ otherwise, then $Y = \sum\limits_{i=1}^N X_i$.
Thus, $Y$ is a sum of presumably-independent Bernoulli random variables, hence a binomial random ... |
Alright, I have this group $\langle x_i, i\in\mathbb{Z}\mid x_i^2=x_{i-1}x_{i+1}\rangle$ and I'm trying to determine whether $x_ix_j=x_jx_i$ or not. I'm unsure there is enough information to decide this, to be honest.
Nah, I have a pretty garbage question. Let me spell it out.
I have a fiber bundle $p : E \to M$ where ... |
2018-09-11 04:29
Proprieties of FBK UFSDs after neutron and proton irradiation up to $6*10^{15}$ neq/cm$^2$ / Mazza, S.M. (UC, Santa Cruz, Inst. Part. Phys.) ; Estrada, E. (UC, Santa Cruz, Inst. Part. Phys.) ; Galloway, Z. (UC, Santa Cruz, Inst. Part. Phys.) ; Gee, C. (UC, Santa Cruz, Inst. Part. Phys.) ; Goto, A. (UC,... |
In about half an hour, UK #ISS pass, starting at 21:58:57, duration 54 secs, visible, Magnitude -1.3
In about half an hour, UK #ISS pass, starting at 20:23:08, duration 228 secs, bright, Magnitude -2.5
In about half an hour, UK #ISS pass, starting at 21:11:12, duration 120 secs, bright, Magnitude -2.4
In about half an ... |
An RLC circuit is a simple electric circuit with a resistor, inductor and capacitor in it -- with resistance
R, inductance Land capacitance C, respectively. It's one of the simplest circuits that displays non-trivial behavior.
You can derive an equation for the behavior by using Kirchhoff's laws (conservation of the st... |
I'd suggest to try it on your own. Do an expansion of your wavefunction in terms of spherical harmonics,
$$\psi(\mathbf r) \ = \ \sum_{\ell} R_\ell(r,t) \, Y_{\ell 0} (\theta,\phi)\,.$$
Note that I've set the index $m$ in $Y_{\ell m}$ to zero, in order to account for the symmetry of your Hamiltonian with respect to rot... |
This is eybrow-raisingly tricky to answer. The short answer is: you can define them, in a complicated way that's not really useful, but why would you want such a thing?
There's two main reasons why this is complicated, which hold for integer and non-integer powers respectively.
For one, the two operators will behave qu... |
OpenCV 4.1.2-pre
Open Source Computer Vision
This tutorial will demonstrate the basic concepts of the homography with some codes. For detailed explanations about the theory, please refer to a computer vision course or a computer vision book, e.g.:
Briefly, the planar homography relates the transformation between two pl... |
In 1923 a French physics graduate student named Prince Louis-Victor de Broglie (1892–1987) made a radical proposal based on the hope that nature is symmetric. If EM radiation has both particle and wave properties, then nature would be symmetric if matter also had both particle and wave properties. If what we once thoug... |
From the commutation relations for the conformal Lie algebra, we may infer that the dilation operator plays the same role as the Hamiltonian in CFTs. The appropriate commutation relations are
$[D,P_{\mu}] = iP_{\mu}$ and $[D,K_{\mu}] = -iK_{\mu}$,
so that $P_{\mu}$ and $K_{\mu}$ are raising and lowering operators, resp... |
The Annals of Probability Ann. Probab. Volume 19, Number 4 (1991), 1737-1755. Strong Limit Theorems of Empirical Functionals for Large Exceedances of Partial Sums of I.I.D. Variables Abstract
Let $(X_i,U_i)$ be pairs of i.i.d. bounded real-valued random variables ($X_i$ and $U_i$ are generally mutually dependent). Assu... |
The conditional probability measures the probability of a certain event while knowing previous information about another event.
For example, if we want to calculate the probability that, after having thrown a dice, a $$6$$ comes out, we already know, by the rule of Laplace, that the probability is $$\dfrac{1}{6}$$.
Nev... |
Let A be reducible to B, i.e., $A \leq B$. Hence, the Turing machine accepting $A$ has access to an oracle for $B$. Let the Turing machine accepting $A$ be $M_{A}$ and the oracle for $B$ be $O_{B}$. The types of reductions:
Turing reduction: $M_{A}$ can make multiple queries to $O_{B}$.
Karp reduction: Also called "pol... |
This question already has an answer here:
How does one go about calculating :
$$\int_0^{\infty}\frac{\ln x}{1+x^2}dx$$
I've tried Integration by parts, and failed over and over again
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It on... |
I am viewing an example of finding the Fisher information for a single sampling from an exponential distribution where: $$P(x|\theta) = \frac{1}{\theta}e^{-\frac{x}{\theta}}$$ The score $S$ is $S(x|\theta) = \frac{\partial}{\partial\theta}logP(x|\theta) = -\frac{1}{\theta} + \frac{x}{\theta^2}$. Fisher information is t... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
I've seen a lot couple of questions regarding the pumping lemma that are pretty similar to each other and this one is unfortunately not the exception. Most likely will be this question marked as a duplicate. But I guess there's no harm in asking.
I was trying to show using the pumping lemma that this language is not re... |
In an atom, the electron is not just spread out evenly and motionless around the nucleus. The electron is still moving, however, it is moving in a very special way such that the wave that it forms around the nucleus keeps the shape of the orbital. In some sense, the orbital is constantly rotating.
To understand precise... |
Here is the proposed theory:
Definition: Let $M$ be a nonempty set with a binary operation $+$ satisfying the following properties:
P-0: The operation $+: M \times M \to M$ is both associative and commutative.
P-1: $\text{For every } x,y,z \in M \text{, if } z + x = z + y \, \text{ then } \, x = y$.
P-2: $\text{For eve... |
Mathematics - Functional Analysis and Mathematics - Metric Geometry
Abstract
The following strengthening of the Elton-Odell theorem on the existence of a $(1+\epsilon)-$separated sequences in the unit sphere $S_X$ of an infinite dimensional Banach space $X$ is proved: There exists an infinite subset $S\subseteq S_X$ an... |
Permanent link: https://www.ias.ac.in/article/fulltext/pram/087/06/0086
The parameters of radio frequency helium discharge under atmospheric pressure were studied by electrical and optical measurements using high voltage probe, current probe and optical emission spectroscopy. Two discharge modes $\alpha$ and $\gamma$ w... |
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,... |
(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... |
Mulliken populations (R.S. Mulliken, J. Chem. Phys. 23, 1833, 1841, 23389, 2343 (1955)) can be used to characterize the electronic charge distribution in a molecule and the bonding, antibonding, or nonbonding nature of the molecular orbitals for particular pairs of atoms. To develop the idea of these populations, consi... |
.
Let $X \in \mathbb{Z}^n$. I need to find the number of pairs $ (i, j)$ with $ 0 < i < j \le n$ such that $ X_i>X_j$ as well as the number of pairs $ (i, j),\ 0 < i < j \le n$, such that $ X_i=X_j$.
I know how to calculate in $O(n \log(n))$ time complexity.How to prove that a comparison-based algorithm with better com... |
Conveners Flavor Violation David Hitlin (Caltech) Flavor Violation Alex Cerri (University of Sussex (GB)) Flavor Violation Yury Kolomensky (UC Berkeley/LBNL) Flavor Violation Alex Cerri (University of Sussex (GB)) Flavor Violation Hideki Okawa (University of Tsukuba (JP)) Flavor Violation Brando Bellazzini (CEA-Saclay)... |
I've been looking at
$$\int\limits_0^\infty {\frac{{{x^n}}}{{1 + {x^m}}}dx }$$
It seems that it always evaluates in terms of $\sin X$ and $\pi$, where $X$ is to be determined. For example:
$$\displaystyle \int\limits_0^\infty {\frac{{{x^1}}}{{1 + {x^3}}}dx = } \frac{\pi }{3}\frac{1}{{\sin \frac{\pi }{3}}} = \frac{{2\pi... |
Originally Posted by
philipishin
Blackhole formula
$\displaystyle E = mc^2$ is not the "black hole formula". It's Einstein's famous equation for the book-keeping associated with conversions between mass and energy. What makes it special is the fact that if 1 Joule of energy is converted to mass, we can find out precise... |
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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 ... |
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... |
In using CES production functions of the form $f(x_1,x_2)=(x_1^\rho+x_2^\rho)^{1/\rho} $, we always assume that $\rho\leq1$. Why do we make that assumption? I understand that if $\rho>1$, the production function won't be concave anymore (and hence production set will not be convex), but what does that imply about profi... |
I'm right now learning about Monodromy from self-studying Rick Miranda's fantastic book "Algebraic Curves and Riemann surfaces". Today, I read about monodromy, and the monodromy representation of a holomorphic map between compact Riemann surfaces. I understand that we start by having a holomorphic map $F:X \rightarrow ... |
Definition:LAST Contents Definition LAST stands for LAnguage of Set Theory. Formal Language
This is the formal language of
LAST: The Alphabet
The alphabet of
LAST is as follows: The Letters
The letters of
LAST come in two varieties: Names of sets: $w_0, w_1, w_2, \ldots, w_n, \ldots$
These are used to refer to
specific... |
CryptoDB Marco Streng Publications Year Venue Title
2008
EPRINT
Abelian varieties with prescribed embedding degree
We present an algorithm that, on input of a CM-field $K$, an integer $k \ge 1$, and a prime $r \equiv 1 \bmod k$, constructs a $q$-Weil number $\pi \in \O_K$ corresponding to an ordinary, simple abelian va... |
On Wielandt-Mirsky's conjecture for matrix polynomials
Bull. Korean Math. Soc. Published online March 14, 2019
Công-Trình LÊQuy Nhon University
Abstract : In matrix analysis, the \textit{Wielandt-Mirsky's conjecture} states that$$ dist(\sigma(A), \sigma(B)) \leq \|A-B\|, $$for any normal matrices $ A, B \in \mathbb C^{... |
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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... |
Based on the values you provide, here is what I think is happening. Your $\lambda$ value is incredibly high and your $\beta$s are very small. In essence, you are overfitting the data and modeling the noise. Not sure how many observations you have, but 15000 features is a lot and hopefully your ratio of $p/n$ is not ast... |
In this section, we shall discuss a few technical results about \(\gcd(a,b)\).
Theorem \(\PageIndex{1}\label{thm:EA}\)
Let \(d=\gcd(a,b)\), where \(a,b\in\mathbb{N}\). Then \[\{ as+bt \mid s,t\in\mathbb{Z} \} = \{ nd \mid n\in\mathbb{Z} \}.\] Hence, every linear combination of \(a\) and \(b\) is a multiple of \(\gcd(a,... |
Set of Words Generates Group Theorem
Let $S \subseteq G$ where $G$ is a group.
Let $\hat S$ be defined as $S \cup S^{-1}$, where $S^{-1}$ is the set of all the inverses of all the elements of $S$.
Then $\gen S = \map W {\hat S}$, where $\map W {\hat S}$ is the set of words of $\hat S$. Proof
Let $H = \gen S$ where $S \... |
This question already has an answer here:
I was reading Schutz, A First Course in General Relativity. On page 9, he argued that the metric tensor is symmetric:
$$ ds^2~=~\sum_{\alpha,\beta}\eta_{\alpha\beta} ~dx^{\alpha}~dx^{\beta} $$ $\text{Note that we can suppose}$ $\eta_{\alpha\beta}=\eta_{\beta\alpha}$ $\text{for ... |
The capillary action formula is given as: $$h=2T/ρgR$$ where h is the capillary rise, R is the radius of curvature of miniscus, ρ is density, g is force of gravity and T is the surface tension. Now consider a capillary with a large base which gets narrower as we move along the top, such that the radius of miniscus at t... |
I saw a flock of birds flying around today, and noticed that they didn't cast any shadows on the ground. I thought this to be rather strange, so I tried to resolve this mystery.
My first idea was that the sun might actually be wide enough such that both 'ends' of the sun might cut underneath the birds, as the ground wo... |
Linear Recurrences
A linear recurrence is a linear equation that recursively defines a sequence. An example is the Fibonacci sequence, that is defined as
\[F_0 = 0\] \[F_1 = 1\] \[F_n = F_{n-1} + F_{n-2}\]
In general, a linear recurrence is a sequence \(\{a_n\}_n\) given by base cases and equations
\[a_1 = x_1\] \[a_2 ... |
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The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
Analytic Function Visualization
This webapp is a somewhat-naive tool to visualize complex, and, in particular, complex-analytic functions. You can enter a function in the very top left; the left half shows $\mathbb C$ and the right half shows the image of $\mathbb C$ under the given function.
But what's with those two ... |
To answer your immediate question, $\gamma = 2$. You’re scaling the translated rectangle so that it has the same shape as the desheared parallelogram. Since you’ll be shearing parallel to the $x$-axis, you want the width of the scaled rectangle to equal the length of the paralellogram’s base, and the rectangle’s height... |
Let $x_n$ be a sequence of independent random variables such that $P(x_n = 0) = 1 - \frac{1}{n}$
1) Does $x_n$ converge to $0$ almost surely
2) Does $x_n$ converge to $0$ in probability
3) Does $x_n$ converge to $0$ in $L_p$
It is clear for me that answer for 2) is yes: $P(|x_n| > \epsilon) \leq P(x_n \neq 0)$. Since t... |
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EUROPEAN TRANSPORT RESEARCH REVIEW, ISSN 1867-0717, 07/2019, Volume 11, Issue 1, pp. 1 - 16
PurposeIn terms of freight transportation it is essential to pick the most con... |
Almost regular | θ-normal | β-normal | α-normal | κ-normal | Almost normal | Almost β-normal | Normal | Weakly θ normal | MATHEMATICS | MATHEMATICS, APPLIED | kappa-normal | theta-normal | weakly theta normal | NORMAL SPACES | almost normal | alpha-normal | beta-normal | almost regular | almost beta-normal
Nutrition po... |
ARUNAVA MUKHERJEA
Articles written in Proceedings – Mathematical Sciences
Volume 119 Issue 5 November 2009 pp 669-677
This article gives sufficient conditions for the limit distribution of products of i.i.d. $2\times 2$ stochastic matrices to be continuous singular, when the support of the distribution of the individua... |
A neural network is a non-linear classifier (separator is not a linear function). It can also be used for regression.
A Shallow neural network is a one hidden layer neural network.
A Vanilla neural network is a regular neural network having layers that do not form cycles.
TensorFlow Playground is an interactive web int... |
For this assignment, we were told to go forth and create a linear motion axis built from scrap and then measure its precision. I had some leftover 8mm steel rod from what used to be 3D-printer materials, so I decided to make a small linear rail out of that. These rods were only 30cm long and rather thin for desk materi... |
Taghavi, A., Rohi, H., Darvish, V. (2015). Additivity of maps preserving Jordan $\eta_{\ast}$-products on $C^{*}$-algebras. Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), 107-116.
A. Taghavi; H. Rohi; V. Darvish. "Additivity of maps preserving Jordan $\eta_{\ast}$-products on $C^{*}$-algebra... |
Talk:Absolute continuity
From Encyclopedia of Mathematics
Revision as of 14:08, 30 July 2012 by Camillo.delellis
Could I suggest using $\lambda$ rather than $\mathcal L$ for Lebesgue measure since
it is very commonly used, almost standard it would be consistent with the notation for a general measure, $\mu$ calligraphi... |
[OS X TeX] Missing $ inserted in a "variations" environment ewan.Delanoy at math.unicaen.fr ewan.Delanoy at math.unicaen.fr Sun Mar 15 15:09:53 CET 2009 Hello all,
I've just encountered the following problem with TeXShop :
1) Compilation stops with the error message "Missing $ inserted".
2) If I insist and press "Enter... |
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Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
The size of the band is defined by the
bandwidth NBW. This defined as the smallest
number for which: K_{i,j}=0 for all i,j satisfying |i-j| > {NBW} .
If K is symmetric, we will store the lower half of the band, i.e. all entries K_{i,j}
for which i gt;= j . The halfbandwidth NHBW is defined by NBW = 2*NHBW + 1.
Since we... |
Let $M$ be a smooth compact $n$-manifold without boundary, $g$ some choice of Riemannian metric on $M$, and $\omega_g$ the volume form gotten from $g$. Say you're interested in finding extrema for quantities determined by a choice of Riemannian metric on $M$ . . . perhaps $\lambda_1(\int_M \omega_g)^{2/n}$, where $\lam... |
Proper time
The proper time \(τ\) is the time measured by an observer \(O\) (which can just be a particle) who “stands still” in space relative to a coordinate system. For example, if I am standing still on the surface of the Earth one meter away from a tree (where I am standing still and not moving away from the tree)... |
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Now showing items 1-9 of 9
Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
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Let \(G\) be a graph, and let \(\textbf{Free}(G)\) be the corresponding free category.Somebody tells you that the only isomorphisms in \(\textbf{Free}(G)\) are the identity morphisms.
Is that person correct?
Why or why not?
Previous... |
this is a mystery to me, despite having changed computers several times, despite the website rejecting the application, the very first sequence of numbers I entered into it's search window which returned the same prompt to submit them for publication appear every time, I mean ive got hundreds of them now, and it's stil... |
I'm doing some research into the RSA cryptosystem but I just need some clarity on how it worked when it was published in the 70s. Now I know that it works with public keys but did it also work with private keys back then or did it use a shared public key first and then private keys were introduced later?
RSA never was ... |
We need some definitions to state the problem.
Let $B$ be a commutative ring, $A$ its subring. We denote by $(A : B)$ the set $\{x \in B | xB \subset A\}$. $(A : B)$ is an ideal of $B$. It is contained $A$, hence it is also an ideal of $A$. It is called the conductor of the ring extention $B/A$.
Let $K$ be an algebraic... |
$$\lim_{x\to\infty} \sqrt{4x^2 + 3x} - 2x$$
I thought I could multiply both numerator and denominator by $\frac{1}{x}$, giving
$$\lim_{x\to\infty}\frac{\sqrt{4 + \frac{3}{x}} -2}{\frac{1}{x}}$$
then as x approaches infinity, $\frac{3}{x}$ essentially becomes zero, so we're left with 2-2 in the numerator and $\frac{1}{x... |
H L LUO
Articles written in Bulletin of Materials Science
Volume 39 Issue 2 April 2016 pp 519-523
The effect of plating temperatures between 60 and 90$^{\circ}$C on structure and corrosion resistance for electroless NiWP coatings on AZ91D magnesium alloy substrate was investigated. Results show that temperature has a s... |
The news reports from Jackson Hole are very interesting. Fed officials are grappling with a tough question: what will happen to inflation? Why is there so little inflation now? How will a rate rise affect inflation? How can we trust models of the latter that are so wrong on the former?
Well, why don't we turn to the mo... |
Article
Keywords: Baire class one function; set of points of discontinuity; oscillation of a function
Summary: A characterization of functions in the first Baire class in terms of their sets of discontinuity is given. More precisely, a function $f\colon \mathbb {R}\rightarrow \mathbb {R}$ is of the first Baire class if... |
Last time we gave a quick intro to the chemistry and thermodynamics we'll use to understand 'coupling'. Now let's really get started!
Suppose that we are in a setting in which some reaction
$$ \mathrm{X} + \mathrm{Y} \mathrel{\substack{\alpha_{\rightarrow} \\\longleftrightarrow\\ \alpha_{\leftarrow}}} \mathrm{XY} $$
ta... |
We start our consideration of rotational motion with a system consisting of two atoms connected by a rigid bond, shown in Figure \(\PageIndex{1}\). Translational motion can be separated from rotational motion if we specify the position of the center of mass by a vector \(R\), and the positions of each atom relative to ... |
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