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I'm taking a course on waves and optics using Young and Freedman's
University Physics, but I'm a bit confused about a couple of things. I've also looked at Griffiths' Introduction to Electrodynamics and Taylor's Classical Mechanics, and the three of them seem to say the following: Young and Freedman A wave is (roughly)... |
Pullback attractors and statistical solutions for 2-D Navier-Stokes equations
1.
University of Warsaw, Institute of Applied Mathematics and Mechanics, Banacha 2, 02-097 Warsaw, Poland
Using time-averages and Banach generalized limits we construct a family of probability measures $\{\mu_t\}_{t\in \IR}$ on the pullback a... |
Coordinate systems are tools that let us use algebraic methods tounderstand geometry. While the
rectangular(also called Cartesian) coordinates that wehave been using are the most common, some problems are easier toanalyze in alternate coordinate systems.
A coordinate system is a scheme that allows us to identify any po... |
Yes I think so. We may assume that $\mathcal F$ is the $\sigma$-algebra generated by sets of the form $X_n^{-1}(a,\infty)$ as $n$ runs over the positive integers and $a$ runs over the reals as $\mathcal F$ already contains these sets. In so doing, we might be making $\mathcal F$ smaller, but that only makes the problem... |
Trail Trail, or caster, is the horizontal distance from where the steering axis intersects the ground to where the front wheel touches the ground. The measurement is considered positive if the front wheel ground contact point is behind (towards the rear of the bike) the steering axis intersection with the ground. Most ... |
Ballico, Edoardo ; Bernardi, Alessandra (2011)
Symmetric tensor rank with a tangent vector : a generic uniqueness theorem. [Preprint]
Full text available as:
Abstract
Let $X_{m,d}\subset \mathbb {P}^N$, $N:= \binom{m+d}{m}-1$, be the order $d$ Veronese
embedding of $\mathbb {P}^m$. Let $\tau (X_{m,d})\subset \mathbb {P... |
Let $\omega$ be a third root of unity, then $\mathbb{Z}[\omega]$ is a PID.
We have $m^3 = n^2 + n + 1 = (n-\omega)(n-\omega^2)$.
$\gcd(n-\omega,n-\omega^2) = \gcd(n-\omega,\omega-\omega^2) \mid (1-\omega)$, and $(1-\omega)$ is the ramified prime lying over $3$ in $\mathbb{Z}[\omega]$, so from unique factorization of $m... |
Imagine two rolls with the same diameter and mass. The mass of one roll is concentrated to the center of the roll while the mass of the other roll is concentrated to the edge of the roll. If the two are released from the same slope and the same height continuing to a flat platform, the roll whose mass is concentrated t... |
It’s always nice, intellectually, when two apparently unrelated areas collide.
I had an experience of this sort recently with an area of mathematics — one very familiar to me — and an ostensibly completely distinct area of science.
On the one hand, contact geometry — a field of pure mathematics, pure geometry.
And on t... |
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The sum of all values of aaa such that the equation(x2−x+a+1)2=4a(5x2−x+1)(x^2-x+a+1)^2=4a(5x^2-x+1)(x2−x+a+1)2=4a(5x2−x+1)has exactly three distinct real solutions, is of the form n+km\dfrac{n+\sqrt{k}}{m}mn+k, where k,m,nk,m,nk,m,n are integers, k≥0,k\geq 0,k≥0... |
As a part of my research (in array processing - the specifics are not too exciting :-)), I cant resolve one specific integral.
Assume $r\in\left[0 ,1\right]$, $N\in\mathbb{N}$.
The basic form is $$\int_{\cos{(x)}=-1}^{\cos{(x)}=1}{\frac{1-\cos{\left(Nx\right)}}{N^{2}\left(1-\cos{(x)}\right)+r^{2}\left(1-\cos{\left(Nx\r... |
J. D. Hamkins and R. Yang, “Satisfaction is not absolute,” to appear in the Review of Symbolic Logic, pp. 1-34, 2014.
@ARTICLE{HamkinsYang:SatisfactionIsNotAbsolute, author = {Joel David Hamkins and Ruizhi Yang}, title = {Satisfaction is not absolute}, journal = {to appear in the Review of Symbolic Logic}, year = {2014... |
@DavidReed the notion of a "general polynomial" is a bit strange. The general polynomial over a field always has Galois group $S_n$ even if there is not polynomial over the field with Galois group $S_n$
Hey guys. Quick question. What would you call it when the period/amplitude of a cosine/sine function is given by anot... |
Activity is a measure of the
effective concentration of a species under non-ideal (e.g., concentrated) conditions. This determines the real chemical potential for a real solution rather than an ideal one. Introduction
Activities and concentrations can both be used to calculate equilibrium constants and reaction rates. ... |
I'm going through the phase estimation algorithm, and wanted to sanity-check my calculations by making sure the state I'd calculated was still normalized. It is, assuming the square of the absolute value of the eigenvalue of the arbitrary unitary operator I'm analyzing equals 1. So, does it? Assuming that the eigenvect... |
Difference between revisions of "State Feedback"
(→Textbook Contents)
(27 intermediate revisions by the same user not shown) Line 1: Line 1:
{{chheader|Linear Systems|State Feedback|Output Feedback}}
{{chheader|Linear Systems|State Feedback|Output Feedback}}
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This chapter describes how feedback can be used shape the l... |
The omega one of chess
Infinite chess is chess played on an infinite edgeless chessboard. Since checkmates, when they occur, do so after finitely many moves, this is an open game and therefore subject to the theory of transfinite game values for open games.
Specifically, the
game value (for white) of a position in infi... |
In the past, I have argued it is so unlikely my vote will matter that voting is not worthwhile, even if I altruistically account for the vast number of people whom elections affect. That is, I've argued that the expected outcome of my vote—the chance it will swing the election, times the impact that would have on each ... |
Say I want to apply a zero-phase Butterworth bandpass filter, implemented in MATLAB using
butter and
filtfilt. So, for an order-$4n$ filter with passband $[f_{\mathrm{min}\,},f_{\mathrm{max}}]$, I believe the transfer function $H$ is given by$$ H(2\pi if) \ = \ \frac{1}{1+\left( \frac{f}{f_\mathrm{max}-f_\mathrm{min}} ... |
Here's a way to automate the solution of a system that, like the OP's, is a linear system whose coefficient matrix happens to have a constant eigenvector (constant in that it is independent of $t$).If $\dot x = Ax$ and $A$ is an $n \times n$ matrix that has some constant eigenvectors $v_1,v_2,\dots,v_k$,then completing... |
Suppose the hazard rate is $\lambda$ the default probability density function follow exponential
$f(t) = \lambda e^{-\lambda t}$
and cumulative probability function is
$F(t) = 1 - e^{-\lambda t}$
the probability of default
within 3 years is
$P(t<3) = F(3) = 1-e^{- 3 \lambda }$
and the
conditional that it default in 3rd... |
Can I be a pedant and say that if the question states that $\langle \alpha \vert A \vert \alpha \rangle = 0$ for every vector $\lvert \alpha \rangle$, that means that $A$ is everywhere defined, so there are no domain issues?
Gravitational optics is very different from quantum optics, if by the latter you mean the quant... |
Another way to look at this involves frequency domain aliasing due to time-domain sampling of a non-bandlimited function. The prototypical continuous-time Hann window function is (Fig. 1):
$$f(x) = \cases{\frac{1}{2}-\frac{1}{2}\cos(\pi x)&if $-1 < x < 1,$\\0&otherwise.}$$
Figure 1. The prototypical continuous-time Han... |
Search
Now showing items 1-10 of 22
Measurement of $W$ boson angular distributions in events with high transverse momentum jets at $\sqrt{s}=$ 8 TeV using the ATLAS detector
(Elsevier, 2017-02)
The $W$ boson angular distribution in events with high transverse momentum jets is measured using data collected by the ATLAS ... |
Search
Now showing items 1-7 of 7
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 i... |
How would you price the following option on underlying $S$ without dividends?
Time to maturity of option $\tau = 12$ months
Option has a strike $K > 0$ and constant barrier $B > 0$.
$t_0$ is the current point in time, while ${t_1, t_2,...t_{12}}$ are observation (potential trigger) dates and $t_{12}$ is the expiration ... |
Answer
$$\frac{2(\sin x-\sin^3x)}{\cos x}=\sin 2x$$ The process is explained step by step below.
Work Step by Step
$$\frac{2(\sin x-\sin^3x)}{\cos x}=\sin 2x$$ Let's see to the left side first. $$X=\frac{2(\sin x-\sin^3x)}{\cos x}$$ $$X=\frac{2\sin x(1-\sin^2x)}{\cos x}$$ - As to $(1-\sin^2x)$, recall that $\cos^2x=1-\... |
Consider an (arithmetic) Ornstein-Uhlenbeck process as a model of the asset price $X_t$:
$$dX_t = \kappa(\mu-S_t)dt + \sigma dW_t$$
where $\mu$ is the mean-reversion level, $\sigma$ is a volatility parameter, $W_t$ is Brownian motion, and $\kappa$ is the reversion speed. An Ornstein-Uhlenbeck process will revert to the... |
Little explorations with HP calculators (no Prime)
03-23-2017, 01:23 PM (This post was last modified: 03-23-2017 01:23 PM by pier4r.)
Post: #21
RE: Little explorations with the HP calculators
(03-23-2017 12:19 PM)Joe Horn Wrote: I see no bug here. Variables which are assigned values should never be used where formal va... |
This web page says that the microcanonical partition function $$ \Omega(E) = \int \delta(H(x)-E) \,\mathrm{d}x $$ and the canonical partition function $$ Z(\beta) = \int e^{-\beta H(x)}\,\mathrm{d}x $$ are related by the fact that $Z$ is the Laplace transform of $\Omega$. I can see mathematically that this is true, but... |
First of all, what's the motivation for the Yang-Mills action and how
should I understand the coupling constants $\theta$ and $g$?
I would say motivation comes from experiments. For instance it is an experimental fact that the electric charge is conserved. The associated current is also conserved, in the sense of$$\par... |
I am struggling to answer an old general relativity exam question, which is as follows:
"Consider a scalar field $\phi(t,x^i)$ with potential $V(\phi)$ on a general spacetime. Its stress tensor is given as $$T_{\mu\nu} = \nabla_\mu \phi \nabla_\nu \phi - \frac{1}{2} g_{\mu\nu} (\nabla^\alpha \phi \nabla_\alpha \phi)-g_... |
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 ... |
I am trying to perform contrast-transfer-function for pictures which were recorded in defocus. To do so, I have to calculate the contrast-transfer function from the Thon rings and fit the function to 1D radial average of the spectrum. Let's say that I have a picture in spatial domain where single pixel is 1.7 Angstrom ... |
Set Complement inverts Subsets
Jump to navigation Jump to search
Theorem
Let $S$ and $T$ be sets.
Then:
$S \subseteq T \iff \map \complement T \subseteq \map \complement S$
where:
$S \subseteq \map \complement T \iff T \subseteq \map \complement S$
\(\displaystyle S\) \(\subseteq\) \(\displaystyle T\) \(\displaystyle \... |
This is an interesting and not so easy question. Here's my 2 cents:First, you should distinguish between mathematical models for the dynamics of an underlying asset (Black-Scholes, Merton, Heston etc.) and numerical methods designed to calculate financial instruments' prices under given modelling assumptions (lattices,... |
The big issue, I think, is that you need a model of the data to work with. These could be regression models or simply your data fit to a distribution. Your data could theoretically be consistent with a number of models / distributions (such as the normal distribution, proportions of successes arising from a binomial di... |
Yield Surfaces and Plastic Flow Rules in Geomechanics
In order to ensure safe geotechnical building methods, specific applications require certain foundations and structure reinforcements. Tests are quite expensive to carry out, so simulation can be really useful and even essential. Many numerical models have been deve... |
Let $H \subset G$ be a closed subgroup of a lie group and $G/H$ the homogeneous coset space. There's an exact sequence of adjoint representations of $H$:
$$0 \to \mathfrak{h} \to \mathfrak{g} \to \mathfrak{g/h}\to 0 $$
The canonical principal $H$-bundle $G \to G/H$ gives an exact functor from representations of $H$ to ... |
Answer
$\cos{(-\frac{7\pi}{6})} = -\frac{\sqrt3}{2}$
Work Step by Step
Recall: (1) An angle and its reference angle either have the same trigonometric function values or differ only in signs. (2) $\frac{\pi}{6}$ is a special angle whose cosine value is known to be $\frac{\sqrt3}{2}$. Note that the reference angle of $-... |
Background of my question is an idea for generating an initial subtour for general symmetric TSPs:
Add to a MST a set of edges with minimal weight sum, that renders the resulting graph free of articulation points remove from that graph all MST-edgesthat appear in at least two shortest paths in the MSTbetween a pair of ... |
I want to solve the problem below
\begin{equation} \begin{aligned} \eta u-\Delta u &=f, &\text{in $\Omega$}\\ \end{aligned} \end{equation}
where $\Omega=(0,1)\times (0,1)$, My boundary are like this $\frac{\partial u}{\partial n} = 0$ if $y=0$ or $1$, and $u=0$ if $x=0$ or $1$. Using ghost nodes can handle the low orde... |
Linear Regression with Evenly-Spaced Abscissae
What a boring title. I wish I could come up with something snazzier. One word I learned today is studentization, which is just the normalization of errors in a curve-fitting exercise by the sample standard deviation (e.g. point \( x_i \) is \( 0.3\hat{\sigma} \) from the b... |
The ordinals of infinite time Turing machines The theory of infinite time Turing machines extends the operation of ordinary Turing machines into transfinite ordinal time. At successor stages of computations, the machines compute as expected, according to the rigid instructions of their finite programs, writing on the t... |
How do I prove that, given $A\in\mathbb C^{n\times n}$, if $A$ is irreducible and $\lambda$ is an eigenvalue of $A$ such that $\lambda\in\partial\left(\displaystyle\bigcup_{i=1}^nK_i\right)$, where $K_i$ is the $i$-th Gerschgorin circle and $\partial(\cdot)$ denotes the boundary of the set $\cdot$, then for all $i=1,\d... |
In chapter 9 of the book
Toric varieties by Cox-Little-Schenck several cohomology vanishing theorems for toric varieties are proved or mentioned.
In this question I am interested in references for versions (if existing) of the analogous vanishing theorems for toric Deligne-Mumford stacks (especially the smooth ones, e.... |
I believe that the intersection is not always finitely generated as a normal subgroup. The factor-group $F_g$ of $G$ over the normal subgroup $M=\langle a_1,...,a_g\rangle^N$ is freely generated by the images of $b_1,...,b_g$ which we shall denote by the same letters: $b_1,...,b_g$. Since $M$ is finitely normally gener... |
I’m trying to build a deterministic Turing Machine that takes 2 words w1, w2 ∈ {a, b, c, d}* separated in the form of Bw1#w2B and determine whether w2 is a substring of w1. Turing machine should reject eg; b#abcd or aaa#b. In other words, the length of w2 must be less than the length of w1 and w2 must be a substring of... |
I'm not a stats specialist, but I will give it a shot.
First, we can approximate the probability of each event by its empirical probability, i.e. the number of occurrences divided by the total number of trials:
$p(motif_i, condition_j) = \frac{\text{number of occurrences of motif i with condition j}}{ \sum_{i,j} \text{... |
ISSN:
1930-5311
eISSN:
1930-532X
All Issues
Journal of Modern Dynamics
January 2010 , Volume 4 , Issue 1
Select all articles
Export/Reference:
Abstract:
Let $M$ be a closed $3$-manifold, and let $X_t$ be a transitive Anosov flow. We construct a diffeomorphism of the form $f(p)=Y_{t(p)}(p)$, where $Y$ is an Anosov flow ... |
Let $w$ denote the weight on $A$ so that $1-w$ is the weight on $B$. Recall from the properties of variance that
$\sigma_p^2 = w^2\sigma_A^2 + 2w(1-w)\sigma_A\sigma_B \rho_{AB}+ (1-w)^2\sigma_B^2$
Without loss of generality, assume $\sigma_A \geq \sigma_B$. We wish to show that
$w^2\sigma_A^2 + 2w(1-w)\sigma_A\sigma_B ... |
I'll assume that you were using a radio tuned to a 1Mhz frequency ($\omega = 6.3\times 10^6$ s$^{-1}$) and that the radio was completely enclosed inside $t=3\,$mm of pure iron.
There are two important effects to consider. (i) How much power is reflected from the iron surface. (ii) How much of the transmitted power make... |
Projection is Surjection/Family of Sets Theorem
Let $\family {S_\alpha}_{\alpha \mathop \in I}$ be a family of sets.
Let $\displaystyle \prod_{\alpha \mathop \in I} S_\alpha$ be the Cartesian product of $\family {S_\alpha}_{\alpha \mathop \in I}$.
Let each of $S_\alpha$ be non-empty.
For each $\beta \in I$, let $\displ... |
65 4 Homework Statement In a double slit experiment let d=5.00 D=30.0λ. Estimate the ratio of the intensity of the third order maximum with that of the zero-order maximum. Homework Equations interference diffraction Homework Statement:In a double slit experiment let d=5.00 D=30.0λ. Estimate the ratio of the intensity o... |
J. D. Hamkins and J. Reitz, “The set-theoretic universe $V$ is not necessarily a class-forcing extension of HOD,” ArXiv e-prints, 2017. (manuscript under review)
@ARTICLE{HamkinsReitz:The-set-theoretic-universe-is-not-necessarily-a-forcing-extension-of-HOD, author = {Joel David Hamkins and Jonas Reitz}, title = {The se... |
What is the fundamental difference between convolutional neural networks and recurrent neural networks? Where are they applied?
Basically, a CNN saves a set of weights and applies them spatially. For example, in a layer, I could have 32 sets of weights (also called feature maps). Each set of weights is a 3x3 block, mea... |
To finish the job initiated by Sivaram Ambikasaran, first you can say that $\mu(x)=\alpha x+ \beta 1/x$
The stochastic integral term with $\beta=0$ case is answered by Sivaram Ambikasaran.
For the $\alpha=0$ case you have using Itô's lemma :
$dLnB_t= \frac{1}{B_t}dB_t-\frac{1}{2.B_t^2}dt$
So integrating this gives you ... |
In combinatorics there are quite many such disproven conjectures. The most famous of them are:
1) Tait conjecture:
Any 3-vertex connected planar cubic graph is Hamiltonian
The first counterexample found has 46 vertices. The "least" counterexample known has 38 vertices.
2) Tutte conjecture:
Any bipartite cubic graph is ... |
Answer
We can find the domain of $sin ~\theta$: domain: $-\infty \lt \theta \lt \infty$ We can find the domain of $cos ~\theta$: domain: $-\infty \lt \theta \lt \infty$ We can find the domain of $tan ~\theta$: domain: $\theta \neq \frac{\pi}{2}+\pi~n$, for any integer $n$ We can find the domain of $csc ~\theta$: domain... |
Set-theoretic arguments often make use of the fact that a particular property $\varphi$ is
local, in the sense that instances of the property can be verified by checking certain facts in only a bounded part of the set-theoretic universe, such as inside some rank-initial segment $V_\theta$ or inside the collection $H_\k... |
Rendezvous with Geostationary Destinations
Geostationary orbits are nontrivial to maintain. They are perturbed by non-round-earth forces represented by the J_{22} term in the spherical harmonics of the gravity field, forming attractors at 75 degrees east (above a point slightly east of the Maldives and south of India) ... |
We have seen how to solve a restricted collection of differential equations, or more accurately, how to attempt to solve them—we may not be able to find the required anti-derivatives. Not surprisingly, non-linear equations can be even more difficult to solve. Yet much is known about solutions to some more general equat... |
Rendezvous with Geostationary Destinations
Geostationary orbits are nontrivial to maintain. They are perturbed by non-round-earth forces represented by the J_{22} term in the spherical harmonics of the gravity field, forming attractors at 75 degrees east (above a point slightly east of the Maldives and south of India) ... |
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Now showing items 1-1 of 1
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... |
Update. I've improved the argument to use only the consistency of $T$. (2/7/12): I corrected some over-statements previously made about Robinson's Q.
I claim that for every statement $\varphi$, there is a variant wayto express it, $\psi$, which is equivalent to the originalstatement $\varphi$, but which is formally ind... |
Let $\phi$ be a scalar field in an interacting theory ($\phi^3$ or $\phi^4$, for example). If $|0\rangle$ is the vacuum of the interacting theory and $P^\mu$ is the four-momentum operator, we have that
$$\langle 0 | \phi(x) | 0 \rangle = \langle 0 | e^{-iPx} \phi(0) e^{iPx} | 0 \rangle = \langle 0 | \phi(0) | 0 \rangle... |
Consider all non-empty subsets \(S_1,S_2,\ldots,S_{2^n-1}\) of \(\{1,2,3,\ldots,n\}\). Let \(A=(a_{ij})\) be a \((2^n-1)\times(2^n-1)\) matrix such that \[a_{ij}=\begin{cases}1 & \text{if }S_i\cap S_j\ne \emptyset,\\0&\text{otherwise.}\end{cases}\] What is \(\lvert\det A\rvert\)?
(This is the last problem of this semes... |
Let $\mathcal{G}$ be the set of isomorphism classes of finite groups.
There is an operation $\mathrm{Aut} : \mathcal{G} \rightarrow \mathcal{G}$ which gives the automorphism group of a given group, up to isomorphism. In the most general setting, my question is:
What possible eventual behaviour can arise from iterating ... |
How to Model Optical Anisotropic Media with COMSOL Multiphysics®
On a bright evening in 1669, Professor Erasmus Bartholinus looked through a piece of an Icelandic calcite crystal he had placed onto a bench. He observed when he covered text on the bench with the stone, it appeared as a double image. The observed optical... |
(This post is a continuation of my previous one on Liouville structures , and hence is quite technical. It’s aimed at students of geometry, not the general public. It assumes you know some differential geometry. If you know what a Liouville structure is, read on.)
We’re going to take Liouville structures and move them ... |
Answer
The shortest day in Minneapolis is $~~8.6~hours$ The longest day in Minneapolis is $~~15.4~hours$
Work Step by Step
We can convert $44.88^{\circ}$ to units of radians: $L = (44.88^{\circ})(\frac{\pi~rad}{180^{\circ}}) = 0.7833~rad$ We can convert $-23.44^{\circ}$ to units of radians: $D = (-23.44^{\circ})(\frac{... |
Graduate Colloquium Spring 2019
McHenry Library Room 4130
Refreshments served at 3:30 in room 4161
For further information, please contact Graduate Student John McHugh or call 831-459-2969
Thursday April 11, 2019 Christy Hightower, Science & Engineering Distinguished Librarian, UCSC Scholarly communication is the syste... |
Recently I discovered the differential identity
$$ \frac{d^{k+1}}{dx^{k+1}} (1+x^2)^{k/2} = \frac{(1 \times 3 \times \dots \times k)^2}{(1+x^2)^{(k+2)/2}}$$
valid for any odd natural number $k$; for instance $\frac{d^6}{dx^6} (1+x^2)^{5/2} = \frac{225}{(1+x^2)^{7/2}}$. This identity was surprising at first, since usual... |
You should consider an unsupervised learning algorithm such as K-nearest neighbor ('KNN').KNN will measure the distance amongst the observations in your space. You can and probably should consider alternative distance functions (besides euclidean) particularly if you are clustering on features such as returns which hav... |
1
Share Trigonometry Quiz for SSC CGL & Railways RRB
4 years ago .
Here is a Trigonometry Quiz for
SSC CGL Railways RRB. This quiz contains important questions matching the exact pattern and syllabus of upcoming exams. Make sure you attempt today’s Quant Quiz for Upcoming Exams to check your preparation level.
If cosx ... |
Prescribed energy connecting orbits for gradient systems
1.
Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, I-60131 Ancona, Italy
2.
Dipartimento di Ingegneria Civile, Edile e Architettura, Università Politecnica delle Marche, Via Brecce Bianche, I-... |
Data Types for Control & DSP
There's a lot of information out there on what data types to use for digital signal processing, but there's also a lot of confusion, so the topic bears repeating.
I recently posted an entry on PID control. In that article I glossed over the data types used by showing "double" in all of my e... |
LaTeX supports many worldwide languages by means of some special packages. In this article is explained how to import and use those packages to create documents in
Portuguese.
Contents
Portuguese language has some accentuated words. For this reason the preamble of your file must be modified accordingly to support these... |
Post-Newtonian expansions in general relativity are used for finding an approximate solution of the Einstein field equations for the metric tensor. The approximations are expanded in small parameters which express orders of deviations from Newton's law of universal gravitation. This allows approximations to Einstein's ... |
Prologue: The big $O$ notation is a classic example of the power and ambiguity of some notations as part of language loved by human mind. No matter how much confusion it have caused, it remains the choice of notation to convey the ideas that we can easily identify and agree to efficiently.
I totally understand what big... |
Snell's Law, also known as the Law of Refraction, is an equation that relates the angle of the incident light and the angle of the transmitted light at the interface of two different mediums. Snell's Law can be applied to all materials, in all phases of matter. Most people are familiar with Snell's Law because of the a... |
Recap of Lecture 22
Last lecture address two unique aspects of electrons: spin and indistinguishability and how they couple into describing multi-electron wavefunctions. The spin results in an angular momentum that follows the same properties of orbital angular moment including commutators and uncertainty effect. The S... |
Let $F$ be a $p$-adic local field, and $G$ a connected reductive group over $F$. What is the meaning of a "highly ramified character" of $G(F)$? I have seen this terminology in many places in representation theory, e.g. "twisting an irreducible admissible representation of $G(F)$ by a highly ramified character," but I ... |
Hedging American Swaption
Hello, I priced an American swaption using Black model with swap rates diffusion to find the european (call) price at t.
$$ C_t = (\delta \sum_{j=n+1}^{M+1} Z_t^{T_j})[R(t,T_n,T_m) - \hat{R}]^{+} $$
$$ dR(t,T_n,T_M) = \sigma R(t,T_n,T_M) dW_t $$
Then I found the early exercice boundary via MC ... |
There is far more structure in entanglement than your simplistic definition seems to be implying. Yes, you could ask a question
Is there any entanglement in this pure state $|\psi\rangle$ of $n$ qubits?
Which can be answered by whether or not the entire state can be expressed as$$|\psi\rangle=|\phi_1\rangle|\phi_2\rang... |
Answer
$\frac{1}{2\pi}\sqrt{\frac{2a}{m}}$
Work Step by Step
We know that the force is given by $F=-\frac{dU}{dx}=-2ax$. Thus, we use Hooke's Law and the equation for frequency to find: $-kx=-2ax \\ k=2a$ Thus, it follows: $f= \frac{1}{2\pi}\sqrt{\frac{k}{m}}=\frac{1}{2\pi}\sqrt{\frac{2a}{m}}$ |
We can interpret the
sdr problem as a problem aboutgraphs. Given sets $A_1,A_2,\ldots,A_n$, with $\bigcup_{i=1}^n A_i=\{x_1,x_2,\ldots,x_m\}$, we define a graph with$n+m$ vertices as follows: The vertices are labeled$\{A_1,A_2,\ldots,A_n,x_1,x_2,\ldots x_m\}$, and the edges are$\{\{A_i,x_j\}\mid x_j\in A_i\}$.
Example ... |
5.1: Let \(G\) : \(\{0,1\}^{\lambda} \rightarrow \{0,1\}^{\lambda + \ell}\). Define \(im(G) = \{y \in \{0,1\}^{\lambda + \ell} \mid \exists s : G(s) = y\}\), the set of possible outputs of \(G\). For simplicity, assume that \(G\) is injective (i.e., 1-to-1).
(a). What is \(|im(G)|\), as a function of \(\lambda\) and \(... |
I'm trying to study the thermodynamics of an N particles system in a fixed volume. In particular, I'm using Metropolis algorithm for simulating the dynamics of such system. My interest is to calculate the average of the potential among the particles, this can be done by evaluating the potential at each step and summing... |
In thermodynamics one assumes that the energy (or other observables) of the system only depend on a few parameters like the temperature, the particle number and also the volume:
$dE = \left(\frac{\partial E}{\partial T}\right) dT + \left(\frac{\partial E}{\partial N}\right) dN + \left(\frac{\partial E}{\partial V}\righ... |
There is a following theorem:
$H$ is a commutative Hopf algebra over a field $k$. Then there exists a bijective correspondence between $$\{ \textrm{Hopf subalgebras }K\subset H \} \quad \leftrightarrow\quad\{\textrm{ normal Hopf ideals } I\subset H\}$$
Where Hopf subalgebra is a subalgebra $K$ satisfying $\Delta K\subs... |
Let
C be an $(\infty,1)$-category, incarnated as a complete Segal space, hence in particular a bisimplicial set. Is there a model structure on the slice category of bisimplicial sets over C which presents the $(\infty,1)$-presheaf category of C? Ideally, such a model structure would be Quillen equivalent to the contrav... |
Surjection if Composite is Surjection Theorem Then $g$ is a surjection. Proof
Let $g \circ f$ be surjective.
Fix $z \in S_3$.
Now find an $x \in S_1: \map {g \circ f} x = z$.
The surjectivity of $g \circ f$ guarantees this can be done.
Now find an $y \in S_2: f \paren x = y$.
It follows that:
\(\displaystyle \map g y\)... |
Let $a$, $b$ and $c$ be positive numbers. Prove that: $$\frac{a^4}{b}+\frac{b^4}{c}+\frac{c^4}{a}\geq a^3+b^3+c^3+25(a-b)(b-c)(c-a)$$
I tried the uvw's technique and BW and more but without some success.
For example, BW does not help here:
Let $a=\min\{a,b,c\}$, $b=a+u$ and $c=a+v$.
Hence, $$abc\left(\sum\limits_{cyc}\... |
Given an internal symmetry group, we gauge it by promoting the exterior derivative to its covariant version:
$$ D = d+A, $$
where $A=A^a T_a$ is a Lie algebra valued one-form known as the
connection (or gauge field) and $T$ the algebra generators.
For GR, we would like to do the same thing with the Poincaré group. But ... |
OK, let's actually take this seriously. As others have said, this is the so-called St Petersburg paradox, and the reason it isn't really much of a paradox is that (1) an extra dollar matters much less when you already have a lot of money and (2) our counterparty may not actually pay up. So let's model that.
The simples... |
Intro
Hey there reader! It has been quite a while since I wrote a blog post.. but I have had a ton of things on my mind I wanted to write about! I am stoked to be able to write about some of them now!
Since leaving my job in defense to go to graduate school — yes, I am obviously into being a poor student — I have been ... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
First off, great question.
Ok I have crunched the numbers. I made a 5 degree of freedom model of the rolling disk/wheel which includes, 2 variables $x$, $y$ for the location on the incline plane (with positive $x$ downwards and $y$ across the plane), $\psi$ for the orientation of the wheel ($\psi=0$ when wheel is facin... |
We now come to the first of three important theorems that extend theFundamental Theorem of Calculus to higher dimensions. (The FundamentalTheorem of Line Integrals has already done this in one way, but inthat case we were still dealing with an essentially one-dimensionalintegral.) They all share with the Fundamental Th... |
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