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A very simple but elegant approach to demodulate FSK is a delay and multiply. (Followed by a simple low pass filter). This is a non-coherent FM detector using the principal that the output of a multiplier is proportional to the phase of the two inputs. An XOR gate can be used as a such a multiplier. On its own it, a mu... |
Molar
... may refer to:
Molar(tooth), the fourth kind of tooth in mammals Molar(grape), another name for the Spanish wine grape ... Listan Negro Molar(unit), a unit of concentration equal to 1 mole per litre Molarmass Molarvolume El Molar, Tarragona, a ... village in the comarca (county) of Priorat, province of Tarrago... |
Background
Generally, all phase transitions require some input energy in order for the transition to occur. For instance, the transition from solid-to-liquid or vice versa requires what is called the enthalpy of fusion or
latent heat of fusion. This is the amount of energy needed to change the total interal energy (i.e... |
For most physical properties of substances, it's useful to know how those properties depend on other parameters. For example, the various coefficients of thermal expansion (CTEs) indicate how rapidly the dimension(s) of a substance change when the temperature is changed by a given amount. A common CTE used when working... |
I am able to prove the iff in the forward direction. But, I am having trouble proving the statement in other direction. I am trying to use the definition of dense, but I am not getting anywhere with it.
Let $U \subseteq X$ be an open set and let $S \subseteq X$ be the set in question. Denseness is equivalent to saying ... |
A proof can be made with the following thought experiment. (In relativity thought experiments are ubiquitous). I'm sorry if I can't make drawings, but if you search "light clock experiment" you will see what I'm talking about with drawings and possibly a more detailed explanation.
Take a box with two reflective walls a... |
Stationary Kernels
Stationary kernels can be expressed as a function of the difference between their inputs.
Note that any norm may be used to quantify the distance between the two vectors \mathbf{x} \ \& \ \mathbf{y}. The values p = 1 and p = 2 represent the
Manhattan distance and Euclidean distance respectively.
Inst... |
Definition 28.35.1.reference Let f : X \to SJersey Football Jets Nfl Cheap Color Jerseys Discount Jerseys Rush White be a morphism of schemes. Let \mathcal{L} be an invertible \mathcal{O}_ X-module. We say \mathcal{L} is
relatively ample, or f-relatively ample, or ample on X/S, or f-ample if f : X \to S is quasi-compac... |
Different post-stack inversion methods such as model based, sparse spike, colored and recursive inversion methods use high cut frequency impedance logs (low frequency) and mid-frequency seismic trace in order to generate an inverted impedance model. Then why are high frequency components are not taken into account duri... |
We have the following nice relations for Striling numbers of the first kind
$$\left[n\atop 2\right] = \Gamma(n) H_{n-1}$$
$$\left[n\atop 3\right] = \frac{\Gamma(n)}{2} ((H_{n-1})^2-H_{n-1}^{(2)})$$
Where
$$H^{(p)}_n = \sum^n_{k=1} \frac{1}{k^p}, \,\,\,H^{(1)}_n \equiv H_n$$
Questions I want an algebraic proof (not comb... |
Is the x_e equation in CAMB correct or not?
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I am looking at the Antony Lewis' paper
https://arxiv.org/pdf/0804.3865.pdf for Eq.(B3) on page 11, there is this equation of number of free electron per hydrogen atom. But for this equation, if [tex]z \rightarrow[/tex] large values, then y=(1+... |
For people like me who study algorithms for a living, the 21st-century standard model of computation is the
integer RAM. The model is intended to reflect the behavior of real computers more accurately than the Turing machine model. Real-world computers process multiple-bit integers in constant time using parallel hardw... |
> Input
> Input
>> 1²
>> (3]
>> 1%L
>> L=2
>> Each 5 4
>> Each 6 7
>> L⋅R
>> Each 9 4 8
> {0}
>> {10}
>> 12∖11
>> Output 13
Try it online!
Returns a set of all possible solutions, and the empty set (i.e. \$\emptyset\$) when no solution exists.
How it works
Unsurprisingly, it works almost identically to most other answe... |
NA62
Louvain-La-Neuve
Our group is contributing in the design and construction of the pixel detector of this experiment.
Members Professors Research scientists Postdocs Visitors PhD students ProjectsClick the title to show project description.
Gigatracker is in the core of one of the spectrometers used in NA62. It's co... |
Functions An online exercise on function notation, inverse functions and composite functions.
This is level 1, describe function machines using function notation. You can earn a trophy if you get at least 9 correct and you do this activity online. The first question has been done for you.
Instructions
Try your best to ... |
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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 ... |
I believe your suggested method is likely to be the best way to do it in general.
step 1: sample an interval to generate from, using the discrete probability distribution of the trapezoid areas.
step 2: sample from the conditional distribution given you're within the trapezoid (i.e. as if it was scaled to be its own de... |
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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 ... |
I was reading CLRS' book on how to use the substitution method to solve recurrences, where they have the following example:
$T(n) = 2T(\lfloor{\frac{n}{2}}\rfloor) + n$ where $T(1) = 1$
They assume that $T(n) = O(n \log n)$ and go on to prove it by using induction.
I understand the inductive step, but I do not understa... |
Functions An online exercise on function notation, inverse functions and composite functions.
This is level 4, find the inverse of the given functions. You can earn a trophy if you get at least 9 correct and you do this activity online.
Instructions
Try your best to answer the questions above. Type your answers into th... |
Bounds of the Reciprocal of a Quadratic
Suppose we want to find the bounds of
\[\frac{2}{x^2+4x+9}\].
Numerator and denominator are both positive, and as
\[x \rightarrow \infty 0\], the denominator tends to infinity also, so the fraction tends to zero. Hence
\[0 \lt \frac{2}{x^2+4x+9}\].
Completing the square for the d... |
The state of a spin-$\frac12$ particle that is spin up along the axis whose direction is specified by the unit vector $n=\sin\theta\cos\phi i+\sin\theta\sin\phi j+\cos\theta k,$ is given by $$|+n \ \rangle=\cos\frac{\theta}{2}|+z \ \rangle + e^{i\phi}\sin\frac{\theta}{2}|-z \ \rangle.$$
a. Suppose that a measurement of... |
From Becker, Becker and Schwarz
String Theory and M-Theory:
For the infinitesimal conformal transformation $$\tag{3.25}\delta z=\varepsilon(z)\quad\text{and}\quad \delta\bar z=\tilde\varepsilon(\bar z),$$ the associated conserved charge that generates this transformation is $$\tag{3.26}Q=Q_\varepsilon+Q_{\tilde\varepsi... |
I just finished reading Feynman's
Lectures on Physics vol.I, §34-9: "The momentum of light". The author explains that there is a relation between the wave 4-vector $k^{\mu}$ and the energy-momentum 4-vector $p^{\mu}$ of an EM wave, namely
$$p^{\mu}=\hbar k^{\mu}, $$ or equivalently $$\tag{deB}W=\hbar \omega, \mathbf{p}... |
There's a lot of important information contained in the subscripts of the summation signs. It's almost certainly a good idea to break up the subscript material into two or, better still, three lines to simplify the task of actually reading this material. Breaking up these lines may be achieved with, e.g., the
\substack... |
Functions An online exercise on function notation, inverse functions and composite functions.
This is level 6, mixed questions. You can earn a trophy if you get at least 9 correct and you do this activity online.
Instructions
Try your best to answer the questions above. Type your answers into the boxes provided leaving... |
I have a problem transforming from one system to another when the direction of motion is changed. To demonstrate the problem I'll set up an easy example with intuitive numbers:
enlarge ↵ left: external observer (correct), right: moving observer (obviously wrong); v=c/2
I have a square with side length $S = 1 \text{ Ls}... |
The Annals of Statistics Ann. Statist. Volume 16, Number 1 (1988), 356-366. Asymptotic Behavior of Likelihood Methods for Exponential Families when the Number of Parameters Tends to Infinity Abstract
Consider a sample of size $n$ from a regular exponential family in $p_n$ dimensions. Let $\hat\theta_n$ denote the maxim... |
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D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
Suppose we have 2 inputs a and b , output is
y=f(a,b).In the long run, let us suppose profits are maximized at a* and b*.Profit is py-wa-kb[p is price and w and k are constants]. Now for max profit, profit equals py-wa*-kb*.Now for constant/increasing returns to scale firms, doubling input clearly doubles or more the p... |
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Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
9.2.1 - Confidence Intervals
Given that the populations are known to be normally distributed, or if both sample sizes are at least 30, then the sampling distribution can be approximated using the \(t\) distribution, and the formulas below may be used. Here you will be introduced to the formulas to construct a confidenc... |
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 ... |
Previously I asked some questions on quantum coherence on physics stackexchange(PSE) (https://physics.stackexchange.com/questions/424578/what-is-quantum-coherence-what-does-it-really-signify-and-what-does-it-tell-us) and the answer helped me to clear the concept. I did some more literature review to understand the basi... |
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 ... |
0. Caveat Lector: This was done before I drank my morning coffee, so there may be some errors in the reasoning (well, the physical reasoning, the mathematics should be kosher).
1. Perfect Fluid. So we have two stress-energy tensors here. One is the stress energy tensor for a perfect fluid$$\tag{1}T^{\alpha\beta}_{\text... |
Use this forum to ask questions and talk about GPT theory.
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Steven,
I believe its in your paper (otherwise..on one of your other posts) where you state that electric potential can be linked to an atom's velocity. As I understand it, temperature is also an atoms velocity. As it pertains to... |
The distance $d_K^H(x,y)$ between two points on the hyperboloid $H_K$ with curvature $K<0$ can be emulated on the distance $d_{-1}(x,y)$ of the hyperboloid $H_{-1}$ of curvature ($K=-1$) as follows: $$ d_K^H(x,y)=R\cdot d_{-1}^H(x/R,y/R) $$ where $R$ is the radius and is related to the curvature as follows: $R=\frac{1}... |
Given ${a_n}$ is infinite sequence, and $0 < a_n < 1$, how to prove
$$\prod_{i=1}^{\infty} (1-a_n) = 0 \text{ if and only if } \sum_{i=1}^{\infty} a_n = \infty$$
Thanks for your help.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It o... |
This is a cute problem.
I would look at it like this: if we are going to show $U$ is a ball, we have to identify a good candidate for its radius $R$ and its center $c$.
For $R$, we should think it should be the largest possible radius of a ball contained in $U$. So let $A \subset \mathbb{R}$ be the set of all numbers $... |
Let $Z$ be a topological space. Given a subspace $A$ of $Z$, define an equivalence relation $R_A$ such that its equivalence classes are $\{x\}$ for $x\in Z\setminus A$ and $A$. Let $Z/A$ be the appropriate quotient space.
Let $Z=\mathbb{R}$, and let $A_1 = [0,1]$, $A_2=(0,1)$, $A_3=[0,1)$. I need to find for which $i=1... |
If $X$ is an irreducible algebraic variety (over $\mathbb C$), an algebraic vector bundle of rank $r$ over $X$ is a couple $(E,\pi)$ where $E$ is an algebraic variety and $\pi: E\longrightarrow X$ is a surjective morphism, with the following properties:
1) $\pi^{-1}(x)$ is a vector space isomorphic to $\mathbb C^r$ for... |
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D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
A solid hemisphere of uniform density $\rho$ occupies the region $$x^2+y^2+z^2\le a^2,\qquad z\le0.$$ Find the gravitational potential due to the hemisphere at the point $(0,0,s)$ where $s\gt0$. A uniform rod of density $m$ per unit length lies on the $z$-axis between $(0,0,c)$ and $(0,0,d)$ where $d\gt c\gt0$. Show th... |
Least Squares SVM
Least Squares Support Vector Machines are a modification of the classical Support Vector Machine, please see Suykens et. al for a complete background.
LSSVM Regression¶
In case of LSSVM regression one solves (by applying the KKT conditions) the following constrained optimization problem.
Leading to a ... |
To begin with, The Amplituhedron formalism only works for a specific theory, N=4 SYM in the planar limit (only planar Feynmann diagrams are considered).Because of supersymmetry, you can classify scattering processes with two parameters: $n$ and $k$. n is the number of particles involved, and k is, roughly speaking, the... |
"Abstract: We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, insta... |
Given the Lie algebra, what is the systematic way to construct the matrix representation of the generators of the desired dimension? I ask this question here because it is the physicists for whom representation of groups is more important than mathematicians.
Let us, for example, take $SU(2)$ for concreteness. Starting... |
Sometimes we are interested in more than one linear combination or variable. In this case we may be interested in the association between those two linear combinations. More specifically, we can consider the covariance between two linear combinations of the data.
Consider the pair of linear combinations:
\(Y_1 = \sum_{... |
2018-08-25 06:58
Recent developments of the CERN RD50 collaboration / Menichelli, David (U. Florence (main) ; INFN, Florence)/CERN RD50 The objective of the RD50 collaboration is to develop radiation hard semiconductor detectors for very high luminosity colliders, particularly to face the requirements of the possible u... |
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 know MRS is independent of prices and compares the ratio of goods which the consumer will exchange one good for the other good. But is the marginal rate of substitution affected by the consumption of those goods or not? It seems trivial but can't get my head around it.
Different consumer preferences will lead to diff... |
I'm solving this BVP problem.
$u''(x) + u^2(x) = \frac{15}{4} |x|^{1/2} + |x|^5$, $u(-1)=u(1)=1$,
$x \in A=(-1,1)$.
The solution is $u(x)=|x|^{5/2}$. What can we say about the convergence order to the analytical solution?
I have to solve this problem with finite centred differences, of order two. My discretization for ... |
Formal asymptotic expansions for symmetric ancient ovals in mean curvature flow
1.
Department of Mathematics, UW Madison, Madison, WI53705, United States
For any $p, q$ with $p+q=n$, $p\geq1$, $q\geq2$ we find a formal ancient solution which is a small perturbation of an ellipsoid. For $t\to-\infty$ the solution become... |
For starters, it is incorrect to think of the ground state being substantially more populated in NMR spectroscopy. Because the energy difference between aligned and misaligned nuclear spins in the external magnetic field is very low, we can say that both states are almost equally populated due to thermal excitation alo... |
Previously, we have discussed briefly the simple linear regression. Here we will discuss
multiple regression or multivariable regression and how to get the solution of the multivariable regression. At the end of the post, we will provide the python code from scratch for multivariable regression. Motivation
A single var... |
We will use the value of $10^{12}\,\text{kg}$, proposed in OP, for black hole initial mass for estimates.
This value is large enough that the evaporation time through Hawking radiation for such a black hole is longer than the current age on Universe, moreover, the accretion rates if such a black hole is placed inside t... |
Descriptive modelling of utterance transformations in chains:
short-term linguistic evolution in a large-scale online experiment
Sébastien Lerique
IXXI, École Normale Supérieure de Lyon
HBES 2018, Amsterdam
Camille Roth
médialab, Science Po, Paris
Adamic et al. (2016)
Online opinion dynamics
Transmission chains for cul... |
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... |
2.2.5 - Measures of Spread Variance and standard deviation are measures of variability. The standard deviation is the most commonly used measure of variability when data are quantitative and approximately normally distributed. When computing the standard deviation by hand, it is necessary to first compute the variance.... |
Karl Theodor Wilhelm Weierstrass (German: Weierstraß; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a teacher, eventually teaching mathematics, physics, botany and gymnasti... |
I would like your help to understand the concept of
expansion of an information structure in the incomplete information game at p.6-9 this paper.
Let me summarise the game as described in the paper.
There are $N\in \mathbb{N}$ players, with $i$ denoting a generic player.
There is a finite set of states $\Theta$, with $... |
Quick question...For some reason I'm having trouble finding an identity or discussion for the commutator of the gamma matrices at the moment...i.e $$\gamma^u\gamma^v-\gamma^v \gamma^u$$ but I am not finding this anywhere. I have an idea of what it may be, but then again I'm not always right. Can anyone fill me in here ... |
Assume $$g: R^n \times R^m \rightarrow R^n$$ $$h: R^n \times R^m \rightarrow R$$ $$(x,y) \in R^n \times R^m$$
I would like to show that the following vectors are linearly independent: \begin{equation} \left[ \begin{array}{c} \frac{\partial g_1}{\partial x_1}\\ \vdots\\ \frac{\partial g_1}{\partial x_n}\\ \frac{\partial... |
2.2.8 - z-scores
Often we want to describe one observation in relation to the distribution of all observations. We can do this using a
z-score. z-score
Distance between an individual score and the mean in standard deviation units; also known as a
standardized score. z-score \(z=\dfrac{x - \overline{x}}{s}\)
\(x\) = ori... |
→ → → → Browse Dissertations and Theses - Mathematics by Title
Now showing items 850-869 of 1147
application/pdfPDF (1MB)
(1970)
application/pdfPDF (3MB)
application/pdfPDF (3MB)
(1988)Let Y$\sp{\rm (n)}$ be the 1 x n matrix containing indeterminate entries $\{$Y$\sb1,\dots$,Y$\sb{\rm n}\}$ and X$\sp{\rm (n)}$ be the n... |
So what are spin-networks? Briefly, they are graphs with representations ("spins") of some gauge group (generally SU(2) or SL(2,C) in LQG) living on each edge. At each non-trivial vertex, one has three or more edges meeting up. What is the simplest purpose of the intertwiner? It is to ensure that angular momentum is co... |
I read on the Wikipedia page that bounded variation (BV) functions have only jump-type discontinuities. Why is that? Suppose at some $a\in\mathbb{R}$, the limit $\lim_{x\rightarrow a^+}f(x)$ doesn't exist (or is infinite). Why would such a function $f$ not be BV?
If $f$ is unbounded near $a$, it can clearly not have bo... |
Stability analysis¶
The condition of initial stability for any floating structure is expressed using the metacentric heights (see
stability).
where
\(\overline{GM_T}\) is the transverse metacentric height, \(\overline{GM_L}\) is the longitudinal metacentric height,
these height can be computed as
where
\(K\) is the low... |
If you need a pdf version of these notes you can get it here
The 2014 video was corrupted..again. I have made some changes on my computer and hopefully the problem will not happen again..
In a transformer two coils are coupled by an iron core so that the flux through the two coils is the same. The iron core is usually ... |
The Split-plot ANOVA is perhaps the most traditional approach, for which hand calculations are not too unreasonable. It involves modeling the data using the linear model shown below:
Model: \(Y_{ijk} = \mu + \alpha_i + \beta_{j(i)}+ \tau_k + (\alpha\tau)_{ik} + \epsilon_{ijk}\)
Using this linear model we are going to a... |
Example 9-2: Section
Download the text file containing the data: dog1.txt
Using SAS
We will use the following SAS program below to illustrate this procedure.
Download the SAS Program here: dog2.sas
View the video explanation of the SAS code.
Using Minitab
Currently not available in Minitab
Analysis
Run the SAS program ... |
I (think) I've found the Heisenberg Lie algebra representation through quantization. Where we have $q \mapsto q$ and $p \mapsto -i \hbar \frac{\partial}{\partial q}$.
So this is only a Lie algebra representation. $\rho_*: \mathfrak{h} \to \text{End}(V) $.
Where $V$ is the hilbert space (representation space). And $\mat... |
I'm trying to fit a hierarchical model using jags, and the rjags package. My outcome variable is y, which is a sequence of bernoulli trials. I have 38 human subjects which are performing under two categories: P and M. Based on my analysis, every speaker has a probability of success in category P of $\theta_p$ and a pro... |
EDIT: see below the original question
Having got a great task of re-TeX-ing, i.e. transforming a PDF original of a lost LaTeX source back into LaTeX, I've got the recommendation to use
bussproof.sty to recreate a bunch of proofs. https://github.com/leanprover/logic_and_proof/blob/master/bussproofs.styhttps://www.math.u... |
Let $M$ be a subspace of $R^n$ and $z\notin M$. Show that the orthogonal proyection of $z$ in $M$ is $\bar x$ if and only if:
$(z-\bar x,x)=0, $ $ \forall x \in M$
How can i prove it? I know that for a convex, closed and not empty $C \subset R^n$, there is an only $\bar x \in C$ orthogonal projection of $z$ in $C$, tha... |
$$\int\frac{\sqrt{a+x}}{\sqrt{a}+\sqrt{x}}\, dx$$
A few days ago I asked a similar (looking) question where all the pluses here were minuses. It could be much more easily manipulated than this one using difference of $2$ squares. The other method used to solve the previous problem is replacing $x$ with $\arccos^2x$. Ou... |
Euler’s formula states that $e^{i x} = \cos(x) + i \sin(x)$.I can see from the MacLaurin Expansion that this is indeed true; however, I don’t intuitively understand how raising $e$ to the power of $...
I would like to proof that:$$z = |z|\big(\cos(\phi) + i \sin(\phi)\big)$$of course the second part can be shown using ... |
Today i ran onto this simple problem, which seemed to be interesting to me. Given the illustration bellow, the problem is states as:
Two identical cylinders roll in between two identical planks. If the velocity of each cylinder is $\vec{v}$ and the velocity of the bottom plank is $\vec{u}$ ($|\vec{v}| > |\vec{u}|$), fi... |
6.4 - Practical Significance
In the last lesson you learned how to identify statistically significant differences. If the p-value is less than the \(\alpha\) level (typically 0.05), then we say that the results are
statistically significant. In other words, results are said to be statistically significant when the obse... |
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... |
This exercise is inspired by exercises 83 and 100 of Chapter 10 in Giancoli's book
A uniform disk ($R = 0.85 m$; $M =21.0 kg$) has a rope wrapped around it. You apply a constant force $F = 35 N$ to unwrap it (at the point of contact ground-disk) while walking 5.5 m. Ignore friction.
a) How much has the center of mass o... |
6.5 - Power
The probability of rejecting the null hypothesis, given that the null hypothesis is false, is known as power. In other words, power is the probability of correctly rejecting \(H_0\).
Power \(Power = 1-\beta\) \(\beta\) = probability of committing a Type II Error.
The power of a test can be increased in a nu... |
Factor scores are similar to the principal components in the previous lesson. Just we plotted principal components against each other, a similar scatter plot of factor scores is also helpful. We also might use factor scores as explanatory variables in future analyses. It may even be of interest to use the factor score ... |
The problem with the multivariate procedure outlined in the above is that it makes no assumptions regarding the temporal correlation structure of the data, and hence, may be overparameterized leading to poor parameter estimates. The mixed model procedure allows us to look at temporal correlation functions involving a l... |
It appears to be common in the discussion of perturbative FRW cosmologies to choose a gauge using hypersurfaces for special values of some quantity, like surfaces of constant density $\rho$, constant inflaton field $\phi$, or zero spatial curvature $\Psi = 0$.
What guarantees that this foliates spacetime?
It seems clea... |
8.2.3.1.2 : Example: Pulse Rate
A research study measured the pulse rates of 57 college men and found a mean pulse rate of 70.4211 beats per minute with a standard deviation of 9.9480 beats per minute. Researchers want to know if the mean pulse rate for all college men is different from the current standard of 72 beats... |
Magnetic force is a consequence of electromagnetic force and is caused due to the motion of charges. We have learned that moving charges surround itself with a magnetic field. With this context, the magnetic force can be described as a force that arises due to interacting magnetic fields.
What is Magnetic Force?
If we ... |
Wikipedia only lists two problems under "unsolved problems in computer science":
What are other major problems that should be added to this list?
Rules:
Only one problem per answer Provide a brief description and any relevant links
Theoretical Computer Science Stack Exchange is a question and answer site for theoretica... |
July 6th, 2015, 07:28 AM
# 3
Newbie
Joined: Jun 2015
From: Sweden, Kalmar
Posts: 7
Thanks: 1
I think the correct answer is the coefficient in front of x^17 in 2*((x^1+x^2+...+x^9)^0+(x^1+x^2+...+x^9)^1+(x^1+x^ 2+...+x^9)^2+...) =
2/(1-x-x^2-...-x^9) which is 129920
July 6th, 2015, 03:17 PM
# 5
Math Team
Joined: Dec 201... |
I encountered some problems when implementing the cloth simulation algorithm from Baraff & Witkin 98's Large Steps in Cloth Simulation.
Baraff & Witkin 98
Consider the cloth as a particle system in 3D, which consists of N particles.
Equation of motion
In each time step, the implicit integration of particle system is:
$... |
At the moment there are deep seas and high mountains. But imagine that the land elevation of the Earth is equal everywhere. How deep would the ocean be in that case?
An approximation can be obtained quite simply by dividing the volume of water in the oceans by the surface area of an ellipsoid with a smooth surface repr... |
Prosthaphaeresis Formulas/Sine plus Sine Theorem $\sin \alpha + \sin \beta = 2 \sin \left({\dfrac {\alpha + \beta} 2}\right) \cos \left({\dfrac {\alpha - \beta} 2}\right)$ Proof
\(\displaystyle \) \(\) \(\displaystyle 2 \sin \left({\frac {\alpha + \beta} 2}\right) \cos \left({\frac {\alpha - \beta} 2}\right)\) \(\displ... |
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In the typical undergrad curriculum for mathematics, you will find at least these two concepts that often lack motivation and proper intuition: Determinants and compactness. Here is my take on the latter.
Compactness
The usual definition of a compact space is as follows:
A space is compact if every open cover contains ... |
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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 ... |
There are two players 1 and 2, playing a two-period public good contribution game. The benefits from the public good per-period to each player is $b_1$ and $b_2$ respectively, which are common knowledge. For the provision of the public good only one player needs to contribute. Once a player contributes and the good is ... |
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1. Search for heavy ZZ resonances in the ℓ + ℓ - ℓ + ℓ - and ℓ + ℓ - vv - final states using proton–proton collisions at √s=13 TeV with the ATLAS detector
European Physic... |
In Peskin & Schroeder section 9.2, they derive the two-point function in the path integral formalism:
$$\langle \Omega | \mathcal{T} \left\{ \hat{\phi}(x_1)\hat{\phi}(x_2)\right\} | \Omega \rangle = \frac{\int \mathcal{D}\phi \ \phi(x_1) \phi(x_2) e^{ i\int d^4 x\ \mathcal{L} }}{\int \mathcal{D}\phi \ e^{ i\int d^4 x\ ... |
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 ... |
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