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I just started self-studying
Mathematical Logic by Ebbinghaus. I already knew something about formal languages, but nothing about model theory. There is something I don't understand:
Exercise 3.3, page 33, states:
Let $P$ be a unary relation symbol and $f$ be a binary function symbol. For each of the formulas: $$\foral... |
$$3\times 4=8$$ $$4\times 5=50$$ $$5\times 6=30$$ $$6\times 7=49$$ $$7\times 8=?$$
We have not managed to solve it so far, all we know is the solution (which was given
after we had given up) :
$224$
How do we find this solution ?
Mathematics Stack Exchange is a question and answer site for people studying math at any l... |
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Now showing items 1-2 of 2
Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
Let $\mathcal{A}$ be a commutative unital Banach algebra, $\mathcal{B} \subset \mathcal{A}$ a closed unital subalgebra, $\mathcal{I} \subset \mathcal{B}$ a closed ideal.
Is there in general a way to "identify" (soft question, perhaps) the maximal ideal spaces $\Sigma(\mathcal{B})$ and $\Sigma(\mathcal{A}/\mathcal{I})$,... |
Basically, I want to know how one can see the $SL(2,\mathbb{R})\times SL(2,\mathbb{R})$ symmetry of AdS$_3$ explicitly.
AdS$_3$ can be defined as hyperboloid in $\mathbb{R}^{2,2}$ as$$X_{-1}^2+X_0^2-X_1^2-X_2^2=L^2$$where $L$ is the AdS radius. Since the metric of $\mathbb{R}^{2,2}$,$$ds^2=-dX_{-1}^2-dX_0^2+dX_1^2+dX_2... |
I really don't know how to tackle this proof because it has mod in it. There's 3 parts to the question. You don't have to answer all three parts (would be cool to check answer with though), I just need a starting point so get this proof rolling.
Question:
Relatively Prime: Means if two numbers' greatest common divisor ... |
The $\delta$ function is not continuous, so it's a priori not differentiable. In fact, it's not even well-defined as an ordinary real-valued function, but can be made so in terms of distributions - linear maps on a space of test functions given by $f\mapsto\int\delta f=f(a)$.
It's possible to sensibly
define derivative... |
Addendum.
After re-considering the form of your question (
e.g. the M †M in the denominator --- as opposed for instance to a single operator M, which suffices for projectors) and reconsulting my copy of Nielsen and Chaung, here are some supplementary details not covered by my previous answer. (I'm posting this as a sep... |
8.1.2.1.3 - Example: Ice Cream Research Question: Is the percentage of Creamery customers who prefer chocolate ice cream over vanilla less than 80%?
In a sample of 50 customers 60% preferred chocolate over vanilla.
\(np_0 = 50(0.80) = 40\)
\(n(1-p_0)=50(1-0.80) = 10\)
Both \(np_0\) and \(n(1-p_0)\) are at least 10. We ... |
Let be the unitary evolution operator of a quantum system be $U(t)=\exp(itH)$ for $t >0$.
Then what is the meaning of the equation
$$\det\bigl(I-U(t)e^{itE}\bigr)=0$$
where $E$ is a real variable?
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only tak... |
For part $(i)$ you're on the right track, but note that we are concerned with $x_n, y_n$ converging to any arbitrary $c$. Note that your $x_n, y_n$ both converge to $0$ (also that $y_n$ is necessarily even a sequence of irrationals - consider $n = 4$). I'm guessing you are to come up with the sequences yourself, and I ... |
This question already has an answer here:
I recently encountered this following proposition:
For every polynomial, there is some positive integer for which it is composite.
What is the most elementary proof of this?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and profe... |
Any integer greater than 1 is called a prime number if and only if its positive factors are 1 and the number p itself. The basic ideology involved in this post is flawed and the post has now been moved to Archives. – The Editor Prime Generating Formulas We all know how hard it is to predict a formula for prime numbers!... |
I read that the elliptical wing has the lowest induced drag. Why is that so? I welcome a mathematical and intuitive explanation.
Induced drag is caused by the backward inclination of the lift vector. Lift is defined as the aerodynamic force perpendicular to the flow direction, and since lift is created by deflecting th... |
Is there any expression for the direct change in conductivity of metals with temperature ?
I am aware of change in resistivity with temperature.
Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. It only takes a minute... |
I am wondering about
correct answer to this task from a yesterday’s test:
A function
Pow which calculates $ y = a^k$ is given, where $ k$ is an integer of length $ n$ bits:
function Pow(a, k) { k >= 0 } z := a; y := 1; m := k; while m != 0 do if m mod 2 = 1 then y := y * z; end if m := m div 2; z := z * z; end while re... |
In the chapter on Artinian rings in "Introduction to Commutative Algebra" by Atiyah and MacDonald, we have:
Proposition 8.6. Let $(A,\mathfrak{m})$ be a local Noetherian ring. Then exactly one of the following holds:
$\frak{m}^n\neq\frak{m}^{n+1}$ for all $n \in \mathbb{N}$;
$\frak{m}$ is a nilpotent ideal, in which ca... |
a) Correct. The new equilibrium position occurs at distance $x=mg/k$ below the initial position (where the collision occurred). Alternatively it is $X=(M+m)g/k$ below the top of the unloaded spring (with no cymbal attached).
b) The new angular frequency of oscillations can be written down without any calculation : $\om... |
If the time complexity $T(n)$ of two functions $x(n)$ and $y(n)$ are mutually recursive, as in Time complexity of mutually recursive functions, this gives $T(n)=O(2^n)$. But how do you measure an algorithm with two or more (4 in the example below) recursive functions that are not necessarily mutually recursive?
Example... |
$\beta$ in statistical mechanics is equal to $\frac{1}{k_BT}$ in in thermodynamics, but I do not understand why $\beta\propto T^{-1}$ instead of, say, $\beta\propto T$?
Because by convention, we want to write $\beta$ as the coefficient in front of energy $E$ in the exponent $\exp(-\beta E)$. Exponents have to be dimens... |
Difference between revisions of "User:Nikita2"
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I am Nikita Evseev
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I am Nikita Evseev Novosibirsk, Russia.
My research interests are in [[Mathematical_analysis | Analysis]] and [[Sobolev space|Sobolev spaces]].
My research interests ... |
a) Correct. The new equilibrium position occurs at distance $x=mg/k$ below the initial position (where the collision occurred). Alternatively it is $X=(M+m)g/k$ below the top of the unloaded spring (with no cymbal attached).
b) The new angular frequency of oscillations can be written down without any calculation : $\om... |
I would like your opinion about the following question:
Let $\{f_n\}$ be a sequence of integrable functions in $[a,b]$which uniformly converges to integrable function $f$, then let $F(x)=\int_a^xf(t)dt $, and $F_n(x)=\int_a^xf_n(t)dt$, I want to prove that $F_n$ uniformly converges to $F$ on $[a,b]$.
Can I just use the... |
Optical depth
Let's start by looking at the idea of optical depth. Optical depth is a quantity that describes how light is attenuated as it travels through a medium. There are two commonly used equations for optical depth, $\tau$. In a homogeneous
1 medium, they are$$\tau=n\sigma x,\quad\tau=\kappa\rho x$$Here, $n$ and... |
How does one prepare for the exams? Read up the textbooks, write down the important formulae? Redo the previous year question papers? Well, each and every student may have their own ways of preparing for the exams. Meanwhile, has anyone ever tried solving the important questions from a subject? How can a student access... |
Let us consider testing the null hypothesis that there is zero correlation between two variables \(X_{j}\) and \(X_{k}\). Mathematically we write this as shown below:
\(H_0\colon \rho_{jk}=0\) against \(H_a\colon \rho_{jk} \ne 0 \)
Recall that the correlation is estimated by sample correlation \(r_{jk}\) given in the e... |
An image burbled up in my social-media feed the other day, purporting to be a list of “17 Equations that Changed the World.” It’s actually been circulating for a while (since early 2014), and purports to summarize the book by that name written by Ian Stewart. This list is typo-ridden, historically inaccurate and genera... |
that the electron and the proton are a particle pair
This may appear inconsistent with current theory, as it is widely assumed that particle pairs created in a single event, must have opposite charge and equal mass (matter/antimatter). This assumption turns out to be wrong.
We shall see that the difference in mass betw... |
Low Risk
1. INTRODUCTION
Low-risk investing is a portfolio strategy, where buying low-risk and selling high-risk stocks have historically delivered superior risk-adjusted returns. More precisely, the reported alphas in several publications vs. the FF-3 factor model are impressive
. Some even argue that the low-risk ano... |
Recently, I read the definition of oxidation state on Wikipedia. It read that a 100% ionic bond is impossible. So what does a 75% ionic and 25% covalent bond mean at all?
A "100% ionic" bond would be a bond whose bonding electron(s) were
never in the vicinity of the cation, but rather always in unperturbed valence orbi... |
Linear Classifiers are one of the most commonly used classifiers and Logistic Regression is one of the most commonly used linear classifiers. The concepts we are going to learn here will actually extend a lot of other classification methods beyond linear classifiers. We’re going to learn the fundamental concepts, but a... |
8.2.3.1 - One Sample Mean t Test, Formulas Five Step Hypothesis Testing Procedure
Data must be quantitative. In order to use the t distribution to approximate the sampling distribution either the sample size must be large (\(\ge\ 30\)) or the population must be known to be normally distributed. The possible combination... |
In musing on how a family tree is kind of like Pachinko, I wondered if this could be animated somewhat like a Pachinko machine in the family tree visualization I have been playing with (available at https://learnforeverlearn.com/ancestors).
I took some first steps towards this by pulling out the Bezier curve parameters... |
In a quasistatic process (reversible), the difference between the external pressure and the internal pressure is infinitesimal for each infinitesimal change in the volume of the system.
$P_{ext}=P_{int} \pm dP $,
As you know that the term for work in terms of pressure is given by, $dW=PdV$. This means that work obtaine... |
I have a confession: despite knowing a reasonably large amount about formal language theory and automata, I’ve never bothered to learn how to prove how to turn a finite automaton back into a regular expression.
My attitude has always been that I have a vague sense of how a proof would go and couldn’t be bothered to sor... |
I need to evaluate the following integral \begin{equation} \int_{-1}^1 \frac{d^4P_l(x)}{dx^4}P_n(x)dx\end{equation}. Of course the answer I need is in terms of $l$ and $n$. Does anyone have any idea how to proceed?
The facts below should allow you to compute the integral in question in terms of $l$ and $n$:
The Legendr... |
I have to solve a linear system of three equations and 3 unknowns and can't find a way to solve it. Applying Cramer's rule I obtain $\Delta = 0$, $\Delta_x \neq 0$, $\Delta_y \neq 0$, $\Delta_z \neq 0$ so that may exist a solution. How to deal with the system in such a situation?
Just solve it directly by applying Gaus... |
I dont understand completely a proof of the dominated convergence theorem stated in page 104 of
Analysis III of Amann and Escher. I will transcribe here the proof and comment about my thoughts.
In the next: $(X,\mathcal A,\mu)$ is a $\sigma$-finite measure space, $E$ is a Banach space and $\mathcal L_1(X,\mu, E)$ is th... |
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... |
For building a recommendation system, I also use the Pearson correlation coefficient. This is the definition:
$r(x, y)=\frac{\sum_{i=1}^n (x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum_{i=1}^n (x_i-\bar{x})^2 \cdot \sum_{i=1}^n (y_i-\bar{y})^2}}$
$x$ and $y$ are part of $\mathbb{R}$.
Now for coding, it is important to take car... |
Difference between revisions of "Linear representation theory of symmetric group:S5"
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==Summary==
==Summary==
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{| class="sortable" border="1"
{| class="sortable" border="1"
! Item !! Value
! Item !! Value
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... |
Consider the Segre embedding $(\mathbb P^1)^n \rightarrow \mathbb P^{2^n-1}$. What is the ideal corresponding to the image of this embedding? It is known that it is generated by quadratic relations. Is there a proper reference where the relations are written explicitly for this particular map in terms of $x_i$'s and $y... |
I have to build the stability diagram of mercury and I have a problem with this couple:
$\ce{Hg^2+}/\ce{Hg2^2+}$ $E^\circ=0.91\ \mathrm{V}$
The exercise says that a the border the concentration is $C=0.10\ \mathrm{mol \cdot L^{-1}}$ for all ions.
So I have : $\ce{2Hg^2+ +2e^- <=> Hg2^2+}$
Then by Nernst relation I have... |
My task is this:
Let $f:\mathbb{R} \to \mathbb{R}$ be a differentiable function and assume that the only stationary point $f$ has is a local max in the point $A = (a,f(a))$. Show that $A$ must be a global max for $f$.
My work so far:
Since $f$ is differentiable we have that $\ f'(a) = 0$. Since $A$ is the only stationa... |
So I was wondering if anybody could help me tackle this problem that I've been assigned in my real analysis course (book used is
Foundations of Analysis by Steven G. Krantz). From my understanding, this text was just recently written.
First, I could use some help understanding exactly what this problem is asking. The w... |
Q1 Find the equation to the straight line passing through the point of intersection of the lines 5x+6y +1 = 0 and 3x + 2y +5 =0 and perpendicular to the line 3x-5y+11 = 0
Q2 Given that vectors P=3i+4j+5k and Q=3i+4j+5k , \[P\dot Q\] is __________
Q3 The value point A(1, -1) inside the circle is \[x^{2}+y^{2}-3x+4y=12\]... |
My professor in class went a little over chaos theory, and basically said that Newtonian determinism no longer applies, since as time goes to infinity, no matter how close together two initial points are, the distance between them will increase greatly. But why isn't this merely a matter of the imprecision of our measu... |
TL;DR Interkosmos and the first Asian in Space I solved global warming with orbital mechanics! This week in space history
I'm always down for a little representation out and about the cosmos! On July 23, 1980, Pham Tuan became the first Asian in space, launching on Soyuz 37 to the Salyut 6 space station.
Commander Vikt... |
Geometric mean formula, as the name suggests, is used to calculate the geometric mean of a set of numbers. To recall, the geometric mean (or GM) is a type of mean that indicates the central tendency of a set of numbers by using the product of their values. It is defined as the nth root of the product of n numbers. It s... |
9.3 - Lesson 9 Summary Objectives
Upon successful completion of this lesson, you should be able to:
Identify situations in which the z or t distribution may be used to approximate a sampling distribution Construct a confidence interval to estimate the difference in two population proportions and two population means us... |
The idea is through conformal transformations satisfying the conditions requested of the problem make this an easier problem to deal,but i don't know which be this transformation. I would appreciate any hint how to solve this. thank you very much
Mathematics Stack Exchange is a question and answer site for people study... |
Simulation Tools for Solving Wave Electromagnetics Problems
When solving wave electromagnetics problems with either the RF or Wave Optics modules, we use the finite element method to solve the governing Maxwell’s equations. In this blog post, we will look at the various modeling, meshing, solving, and postprocessing op... |
The ratio wherein the addition of the values to the number of the value is a population mean – if the possibilities are equal. A population mean include each element from the set of observations that can be made.
The population mean can be given in the following formula:
\[\large \mu=\frac{\sum x_i}{N}\]
Where,
$x_{i}$... |
Lasted edited by Andrew Munsey, updated on June 15, 2016 at 2:08 am.
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Inductance circuit (eg., L circuit) is an electr... |
I doubt that your reasoning goes through without caveats. It's true that when you analytically continue the Minkowski spacetime
two-point function to imaginary time, you get a function (the two-point Schwinger function $S(x,y)$) which is symmetric in the two Euclidean spacetime points and is covariant with respect to E... |
(Original on SE https://physics.stackexchange.com/questions/459086/continuous-transition-of-degrees-of-freedom-in-thermodynamics-with-simple-exampl, though I usually get better answers here.)
In thermodynamics books I have read, I have often come across statements about how certain degrees of freedom are relevant only ... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
I was assigned this problem as homework, and got it wrong. I have not gotten a chance to ask the teacher about the solution.
Can someone tell me why I am wrong, and how to do this correctly?
Let $\zeta_n = e^{2\pi i/n}.$ Prove that $\zeta_5 \notin \mathbb{Q}(\zeta_7).$
Since $\zeta_5 = e^{2\pi i/5}$ and $\mathbb{Q}(\ze... |
Can someone explain me this proof please:
We have $\prod_{i\in I} \overline{A_i}=\cap_{i\in I} F_i$ where $F_i=\prod_{j\in I} B_j$ with $B_i=\overline{A_i}$ and $B_j=E_j$ if $j\neq i$. We have that $E\setminus F_i=\prod_{j\in I} U_j$ with $U_i=E_i\setminus \overline{A_i}$ and $U_j=E_j$ if $j\neq i$. Then $E\setminus F_... |
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Now showing items 21-27 of 27
Measurement of transverse energy at midrapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV
(American Physical Society, 2016-09)
We report the transverse energy ($E_{\mathrm T}$) measured with ALICE at midrapidity in Pb-Pb collisions at ${\sqrt{s_{\mathrm {NN}}}}$ = 2.76 T... |
Search
Now showing items 31-40 of 165
Transverse sphericity of primary charged particles in minimum bias proton-proton collisions at $\sqrt{s}$=0.9, 2.76 and 7 TeV
(Springer, 2012-09)
Measurements of the sphericity of primary charged particles in minimum bias proton--proton collisions at $\sqrt{s}$=0.9, 2.76 and 7 TeV ... |
Let $N \unlhd G$. In the factor group $G/N$, the subgroup $N$ acts as identity element. Regard N as being collapsed to a single element, to the identity element. This collapsing of N together with the algebraic structure of G require that other subsets of G, namely the cosets of N, also collapse into a single element i... |
Gaussian transformation¶
This tutorial demonstrates the basic working principles of PennyLane for continuous-variable (CV) photonic devices. For more details about photonic quantum computing, the Strawberry Fields documentation is a great starting point.
The quantum circuit¶
For this basic tutorial, we will consider a ... |
I have a question regarding the proof of the time-independent Schrödinger equation. So if we have a time-Independent Hamiltonian, we can solve the Schrödinger equation by adopting separation of variables method: we write our general solution as $ \psi(r,t) = \psi(r)*f(t)$ and we get to the two equation : one for the f(... |
The problem goes as follows:
Let $r_{n}$ be an enumeration of the rationals. Using Fubini-Tonelli, show that:
$$ F(x) = \sum_{n \geq 1} \frac{1}{n^{2}} \frac{1}{|r_{n} - x |^{1/2}}$$
is finite almost everywhere.
Attempt at solution:
My idea is that I want to show the $F(x)$ is integrable. Then using Fubini-Tonelli, tak... |
a) Correct. The new equilibrium position occurs at distance $x=mg/k$ below the initial position (where the collision occurred). Alternatively it is $X=(M+m)g/k$ below the top of the unloaded spring (with no cymbal attached).
b) The new angular frequency of oscillations can be written down without any calculation : $\om... |
From my perspective, this is easiest to tackle from a straight forward energy balance.
The energy balance determines how energy, heat and work are distributed when you go from State 1 to State 2.
Thermodynamic States
Just to emphasize this, a state is a fixed point where all properties are set in stone. So state 1 can ... |
Expected Value
The expected value is a weighted average of all possible values in a data set.
Learning Objectives
Compute the expected value and explain its applications and relationship to the law of large numbers
Key Takeaways Key Points The expected value refers, intuitively, to the value of a random variable one wo... |
Stokes theorem for smooth differential forms is well-known. If $\alpha$ is a smooth differential $n$-form defined on an $(n+1)$-dimensional compact oriented manifold with boundary, then we have $$\int_Md\alpha=\int_{\partial M}\alpha.$$
In physics, one considers a generalized form of this equation, where the manifold n... |
a) Correct. The new equilibrium position occurs at distance $x=mg/k$ below the initial position (where the collision occurred). Alternatively it is $X=(M+m)g/k$ below the top of the unloaded spring (with no cymbal attached).
b) The new angular frequency of oscillations can be written down without any calculation : $\om... |
Consider the problem of finding the maximum number of knights that can be placed on a chessboard without two of them attacking each other. The answer is 32: it's not too difficult to find a perfect matching (the graph induced by knight moves is bipartite, and there's a perfect matching for a 4 × 4 board), which is obvi... |
1. Not all states produced by $\text{CNOT} \; (H \otimes I)$ are entangled.
For the first part of your question: no, not all states which arise as the output of $\text{CNOT} \; (H \otimes I)$ are entangled. Specifically, you can consider$$\begin{align*}|\psi\rangle \;&=\; (H \otimes I) \; \text{CNOT} \;\Bigl[ \tfrac{1}... |
Consider a system of $N$ spin $1/2$ particles. Assume the spin is the only degree of freedom and hence there is no spatial component. Then the dimension of the Hilbert space in this case is $2^N$. This follows since in this case we have $j_1 = j_2 = \ldots = j_N = 1/2. $ And the dimension of the product space is $$ (2j... |
In basic chemistry, we are taught that an atom has roughly the same number of neutrons and number of protons, this doesn't seems to hold for larger atoms, but it is always roughly proportional (i.e. you seldom find an atom with 100 protons but 1 neutron, that just does not happen). Why is that?
You probably know that t... |
A portfolio can be viewed as a combination of assets held by an investor.
For each asset held, such as company stocks, the logarithmic or continuously compounded
rate of return \(r\) at time \(t\) is given by $$ r_t = \log \left(\frac {P_t} {P_{t-1}} \right) $$ where \(P_t\) is the stock price at time \(t\), and \(P_{t... |
Let $M$ come from an ensemble of $N\times N$ matrices. The Wigner surmise is density function $p^W_0(s)=\frac{\pi}{2}se^{-\pi s^2/4}$. From a random matrix point of view, we can write $\rho^W_0(s)=\frac{d^2}{ds^2}E((0,s))$, where $E(I)$ is the eigenvalue gap probability: $M$ has no eigenvalues in interval $I$. $E(I)$ a... |
$\newcommand{\R}{\mathbb{R}}$ $\newcommand{\al}{\alpha}$
Let $\Phi:\R^2 \to \R$ be a function which has partial derivatives at the point $(x_0,y_0)$. Let $\al:I \to \R^2$ be a path satisfying:
$\al(0)=(x_0,y_0),\dot \al(0)=v=(v_1,v_2)\neq (0,0)$.
Assume $\Phi \circ \al$ is differentiable at $t=0$ and the directional de... |
Attention conservation notice: Unless you fit into a very similar academic niche to me this post likely uses techniques you don’t know to solve problems you don’t care about. Even if you are in that niche this is more of a theoretical curiousity than a useful technique at present, but it was useful for me to think thro... |
AliFMDMultCuts () AliFMDMultCuts (EMethod method, Double_t fmd1i, Double_t fmd2i=-1, Double_t fmd2o=-1, Double_t fmd3i=-1, Double_t fmd3o=-1) AliFMDMultCuts (const AliFMDMultCuts &o) AliFMDMultCuts & operator= (const AliFMDMultCuts &o) void Reset () Double_t GetMultCut (UShort_t d, Char_t r, Double_t eta, Bool_t errors... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
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... |
Differentiation
\[4x^3\]differentiated is
\[4 \times 3 x^{3-1}=12x^2\]
We can differentiate a sum usinf the same rule for each term.
\[2x^5-4x^7\]when differentiated is
\[2 \times 5x^{5-1}-4 \times 7x^{7-1}=10x^4-8x^6\].
This rule 'times by the power and take one off the power' works for
\[x\]'s and constants too.
To d... |
The Graphene Revolution: Part 5
In a paper titled “Choosing a Gate Dielectric for Graphene Based Transistors“, the applications of a semiconducting form of graphene are examined. As we have seen before, single-layer graphene is not a semiconductor, it is a zero bandgap conductor (a semimetal). Efforts are well underway... |
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Now showing items 1-10 of 33
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... |
We consider the finite-amplitude instability of incompressible spherical Couette flow between two concentric spheres of radii $R_1$ and $R_2$ $({>}R_1)$ in the narrow-gap limit, $\varepsilon\,{\equiv}\,(R_2-R_1)/R_1\,{\ll}\,1$, caused by rotating them both about a common axis with distinct angular velocities $\Omega_1$... |
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... |
Plugins and Hybrid computation¶
This tutorial introduces the notion of hybrid computation by combining several PennyLane plugins. We first introduce PennyLane’s Strawberry Fields plugin and use it to explore a non-Gaussian photonic circuit. We then combine this photonic circuit with a qubit circuit — along with some cl... |
On non-linear discrete boundary-value problems and semi-groups
The following discrete boundary - value problem for non-linear system $x_k=\varphi_k(x_{k-1},y_k),\,y_{k-1}=\psi_k(x_{k-1},y_k)$, $k=\overline{1,\,N},\,\,N<\infty,\,\,x_0=a,\,\,y_N=b, $ is considered. Here the functions $\varphi_k(x,y),\,\psi_k(x,y)\geq0$ a... |
Hey I want to convert Cartesian to spherical coordinate system. I referred many site and for calculating elevation angle $\theta$ from positive z axis they all used formula $\arctan \frac { \sqrt{x^2+y^2}}{z}$ but my problem is $\theta$ can be anything from 0 to 180 degrees but the range of inverse tan is from -90 to 9... |
Example 7-15: Swiss Bank Notes Section
An example of the calculation of simultaneous confidence intervals using the Swiss Bank Notes data is given in the expression below:
\(\bar{x}_{1k}-\bar{x}_{2k} \pm \sqrt{\frac{p(n_1+n_2-2)}{n_1+n_2-p-1}F_{p,n_1+n_2-p-1,\alpha}}\sqrt{\left(\frac{1}{n_1}+\frac{1}{n_2}\right) s^2_k}... |
If you need a pdf version of these notes you can get it here
We can begin our analysis of this circuit by applying Kirchoff's loop rule to the find potential at any given time.
$V=V_{R}+V_{L}+V_{C}$
However an important consequence of the voltages not being at the same phase in the different components is that the peak... |
The paper "Subquadratic Algorithms for 3SUM", by Ilya Baran, Erik D. Demaine, Mihai Patrascu has the following complexity for the
3SUM problem: given a list $L$ of $n$ integers if there are $x,y,z \in L$ such that $x+y=z.$
They state, "On a standard word RAM with $w-$bit words, we obtain a running time of $O(n^2/ \max\... |
This was described by EIP 658 which was implemented in the Byzantium fork. The text of the EIP is here, though strangely it doesn't seem to have been formally finalised before the fork.
In any case, the relevant text is this:
For blocks where block.number >= METROPOLIS_FORK_BLKNUM, the
intermediate state root is replac... |
As in the one-sample case, the simultaneous confidence intervals should be computed only when we are interested in linear combinations of the variables. If the only intervals of interest, however, are the confidence intervals for the individual variables with no linear combinations, then a better approach is to calcula... |
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... |
For solving systems of autonomous differential equations we use Jordan normal forms as typically they give us an easy way to calculate the solution to our system.
If we have the IVP:$$\left\{\begin{matrix}\frac{dx}{dt} = Ax\\ x(0) = x_0\end{matrix}\right.$$ where $A$ is a constant $n \times n$ matrix and $x_0 \in \math... |
I wanted to look into the case where you have an experiment in which your units of analysis are naturally clustered (e.g., households in villages), but you randomize
within clusters. The goal is to estimate a treatment effect in terms of difference in means, using design-based principles and frequentist methods for inf... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
As before, the next step is to determine how these notes differ. This may be carried out using the simultaneous \((1 - α) × 100\%\) confidence intervals.
For Large Samples: simultaneous \((1 - α) × 100\%\) confidence intervals may be calculated using the expression below:
\(\bar{x}_{1k} - \bar{x}_{2k} \pm \sqrt{\chi^2_... |
In the context of superstring compactification on a 6-manifold which admits a covariantly conserved spinor $\eta$, which we normalize so that $\eta^{\dagger} \eta = 1$, I am trying to show that the almost complex structure
$$J_m^{\,\,n} = -i \eta^{\dagger} \gamma_{m}^{\,\,n}\gamma \eta$$
satisfies $$J_m^{\,\,n} J_n^{\,... |
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