text stringlengths 256 16.4k |
|---|
Let $q_i \in Q = \mathbb R_+$ denote the quantity produced by firm $i \in \{1,2\}$. Further let $\pi_i(q_1,q_2) = (1-q_1-q_2)q_i$ denote the profits of $i$. A Nash equilibrium $(q_1^*,q_2^*) \in Q^2$ satisfies \begin{align} &\pi_1(q_1^*,q_2^*) \geq \pi_1(q_1,q_2^*) \quad \forall q_1 \in Q\\ &\pi_2(q_1^*,q_2^*) \geq \pi... |
This turned out to be very obvious based on the definition of a prime number, so obvious I felt like not bothering, but I still want to see if there is a problem with the proof so far, seeings I am in general just terrible at proofs.
I observed that the greatest common divisor of the largest divisor of $n \cdot p_n$ an... |
What is a Functor? Definition and Examples, Part 1
Next up in our mini series on basic category theory: functors! We began this series by asking
What is category theory, anyway? and last week walked through the precise definition of a category along with some examples. As we saw in example #3 in that post, a functor ca... |
What is a Functor? Definitions and Examples, Part 2 Continuing yesterday's list of examples of functors, here is... Example #3: the chain rule
Let $\mathsf{E}$ be the category whose objects are the Euclidean spaces $\mathbb{R},\mathbb{R}^2,\mathbb{R}^3,\ldots,\mathbb{R}^n,\ldots$ and let's suppose each has a special po... |
Essay and Opinion A new graph density
Version 1Released on 08 April 2015 under Creative Commons Attribution 4.0 International License Authors' affiliations Laboratoire Electronique, Informatique et Image (Le2i). CNRS : UMR6306 - Université de Bourgogne - Arts et Métiers ParisTech Keywords Community discovery Density @G... |
A remark on minimal nodal solutions of an elliptic problem in a ball
DOI: http://dx.doi.org/10.12775/TMNA.2004.025
Abstract
Consider the equation $-\Delta u =
u_{+}^{p-1}-u_{-}^{q-1}$ in the unit ball $B$ with a homogeneous Dirichlet boundary condition. We assume $2< p,q< 2^{*}$. Let $\varphi(u)=(1/2)\int_{B} |\nabla u... |
Perhaps it will help to discuss this in a broader context, so let me explain this concept with regard to the resolution principle, which is used to check if some formula is unsatisfiable.Resolution for propositional logic's formulae is rather straightforward and is based on the Conjunctive Normal Form.
We want to apply... |
Dominated Convergence Theorem The Basic Idea
Given a sequence of functions $\{f_n\}$ which converges pointwise to some limit function $f$, it is
not always true that $$\int \lim_{n\to\infty}f_n = \lim_{n\to\infty}\int f_n.$$ (Take this sequence for example.)The Monotone Convergence Theorem (MCT), the Dominated Converge... |
The Annals of Statistics Ann. Statist. Volume 25, Number 6 (1997), 2512-2546. Optimal pointwise adaptive methods in nonparametric estimation Abstract
The problem of optimal adaptive estimation of a function at a given point from noisy data is considered. Two procedures are proved to be asymptotically optimal for differ... |
Difference between revisions of "Ineffable"
(→Subtle cardinal: for every class $\mathcal{A}$,)
m (→Ethereal cardinal: w)
(3 intermediate revisions by the same user not shown) Line 47: Line 47:
==Ethereal cardinal==
==Ethereal cardinal==
+ + + + + + + + + + + +
''To be expanded.''
''To be expanded.''
Revision as of 05:5... |
Settling is the process by which particulates settle to the bottom of a liquid and form a sediment. Settling velocity (\(v_{p}\), m/s) describes the rate at which a particle moves through the liquid either due to gravity or due to centrifugal force.
\(v_{p}=\frac{2}{9}\frac{\rho_{p}\rho _{f}}{\mu }gR^{2}\)
\(g\) - grav... |
I'd like to draw a closed plot path filled with pattern and surrounded by arrows:
When I used @Jake's solution to add arrows (Decorate a path with little arrows parallel to it) then the pattern made with the method proposed by @Domenico Camasta vanishes (Modified pattern does not see the pattern color option). The comm... |
If the particle density of suspended particulate matter (SPM) for a given size class, \(\rho _{spm,n}\), (kg/m 3) (which includes the inflow of "new" SPM from erosion or other tributaries) is greater than the density of water \(\rho _{w}\) (kg/m 3), then the settling of that sediment size class is triggered. The settli... |
Let $f : [a,+\infty[ \rightarrow \mathbb{R}_+$ a positive function, locally Riemann-integrable. It's assumed the improper integral $\int_{a}^{+\infty} f(x) dx$ is convergent.
For all $n \in \mathbb{N}$, we have $f_n = 1_{[a,n]} f$.
With the monotone convergence theoreme, we would like to prove that $f$ is Lebesgue-inte... |
$L$ is a linear operator acting on hilbert space $V$ of dimension $n$, $L: V \to V$. The trace of a linear operator is defined as sum of diagonal entries of any matrix representation in same input and output basis of $V$. But if $L$ is a linear operator acting on $V \otimes V$ and I want to take partial trace over the ... |
I wanted to better understand dfa. I wanted to build upon a previous question:Creating a DFA that only accepts number of a's that are multiples of 3But I wanted to go a bit further. Is there any way we can have a DFA that accepts number of a's that are multiples of 3 but does NOT have the sub...
Let $X$ be a measurable... |
Please assume that this graph is a highly magnified section of the derivative of some function, say $F(x)$. Let's denote the derivative by $f(x)$.Let's denote the width of a sample by $h$ where $$h\rightarrow0$$Now, for finding the area under the curve between the bounds $a ~\& ~b $ we can a...
@Ultradark You can try d... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
The procedure you suggest really cannot get too far. Here is an abstract result explaining what I mean (see
Aspects of incompleteness by Per Lindström): Given an r.e. sequence of r.e. theories that interpret arithmetic and whose union is consistent, there is a $\Pi^0_1$ formula that is not provable by any of them. That... |
It is claimed that the credit default swap (CDS) spread should approximate the risky par bond yield or coupon rate spread from the riskless bond on the same entity. This comes about when we assume discount factor $B(t)=e^{-rt}$ with constant riskless interest rate $r$ together with infinitesimal coupon period. However,... |
David Xiao dxiao@cs.princeton.edu
1 IntroductionLATEX is the standard mathematical typesetting program. This document is for people who have never usedLATEX before and just want a quick crash course to get started. I encourage all students in mathematics andtheoretical computer science to learn LATEX so you can use it ... |
I would like your help to understand the definition of
obedience in an incomplete information game at p.7 of this paper.
Let me summarise the definition provided 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 $\theta$ denoting a gene... |
Hydejack offers a few additional features to markup your content. Don’t worry, these are merely CSS classes added with kramdown’s
{:...} syntax, so that your content remains compatible with other Jekyll themes.
Table of Contents A word on building speeds Adding a table of contents Adding message boxes Adding large text... |
Let $$(a_n)_{n\in\mathbb{N}}$$ be a sequence and $$M$$ a real number. We say that the sequence is bounded from above by $$M$$ if all the terms are smaller than $$M$$, that is to say, if $$$a_n \leq M$$$ for all $$n$$.
Similarly, we say that the sequence is bounded from below by $$M$$ if all the terms are greater than $... |
We review the Metropolis algorithm — a simple Markov Chain Monte Carlo (MCMC) sampling method — and its application to estimating posteriors in Bayesian statistics. A simple python example is provided.
Follow @efavdb Follow us on twitter for new submission alerts! Introduction
One of the central aims of statistics is t... |
Can any telescope be capable to see some one walking on Mars? How much time dilation would there be? What is the theoretical best resolution?
From here, discussing images of Mars taken by Hubble while near to its closest approach to Earth:
The telescope snapped these pictures between April 27 and May 6, 1999, when Mars... |
Two Tricks Using Eisenstein's Criterion
Today we're talking about Eisenstein's (not
Einstein's!) Criterion - a well-known test to determine whether or not a polynomial is irreducible. Theorem (Eisenstein's Criterion) Let $R$ be a UFD and $p\in R$ be a prime. If $f(x)=x^n+a_{n-1}x^{n-1}+\cdots + a_0\in R[x]$ is a monic ... |
First, you need to ensure that the pixel has minimal value in its 8-neighborhood. SIFT, SURF and other keypoint detectors filter these pixels in step called "non-maximal suppression". This is basically a necessary condition for second-order approximation we will use to determine sub-pixel location.
If you imagine the s... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
Should I construct the disks $D_n$ / the function $f$ explicitly or just show the existence?
Showing the existence of $f$ suffices. But often the easiest way to show existence is giving an explicit example. As for the sequence of disks, I think an
explicit construction is way beyond the scope of the exercise (if at all... |
Difference between revisions of "Constructible universe"
(→Implications, equivalences, and consequences of $0^\#$'s existence: +)
(→Statements True in $L$: links etc.)
Line 27: Line 27:
== Statements True in $L$ ==
== Statements True in $L$ ==
−
Here is a list of statements true in $L$:
+
Here is a list of statements t... |
Although the atomic theory proposed by John Dalton created a basic structure of the atom, the general idea of molecules was not cleared. In 1809, Frech chemist Joseph-Louis Gay-Lussac and others began doing numerous experiments with gases by measuring the amounts of gass that actually reacted. They found that two volum... |
I am struggling with the proof that if G has a faithful complex irreducible representation then $Z(G)$ is cyclic:
Let $\rho:G \rightarrow GL(V)$ be a faithful complex irreducible representation. Let $z \in Z(G)$.
Consider the map $\phi_z: v \mapsto zv$ for all $v \in V$. This is a G-endomorphism on $V$, hence is multip... |
Random dynamics of non-autonomous semi-linear degenerate parabolic equations on $\mathbb{R}^N$ driven by an unbounded additive noise
School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
In this paper, we study the dynamics of a non-autonomous semi-linear degenerate... |
I have to express the following problem as a semidefinite program
$$\begin{array}{ll} \text{minimize} & F(x,y) := x + y +1\\ \text{subject to} & (x-1)^2+y^2 \leq 1 \tag{1}\end{array}$$
Only affine equality conditions should be used. The hint was to examine the structure of $\mathbb{S}^2_+$, the cone of symmetric positi... |
I have been trying to find the algorithmic complexity of a problem that I have. I am almost sure it is either NP-hard or NP-complete but I cannot find any proof. Recently, I found that my problem can be something similar to a special instance of the Maximum Capacity Representatives problem, which is NP-complete. Howeve... |
Update: This implementation is now a package called
CompoundMatrixMethod, hosted on github. It can be installed easily by evaluating:
Needs["PacletManager`"]
PacletInstall["CompoundMatrixMethod", "Site" ->
"http://raw.githubusercontent.com/paclets/Repository/master"]
This version also includes a function
ToMatrixSystem... |
You already have a correct answer, but I'd like to show you a little trick that allows you to derive the solution without solving any integrals. You've already figured out the analytical expression for $X_1(j\omega)$, which is an important step. Now you could observe that this expression contains a factor $j\omega$. Re... |
Fermat's little theorem says that the congruence $a^p \equiv a (mod p)$ if $p$ is a prime number. $a^{n+1} \equiv a (mod n)$ works for all integers $a$ and some positive integers $n$, how can we characterize the positive integers $n$ for which $a^{n+1} \equiv a (mod n)$ holds?
closed as off-topic by Lucia, Boris Bukh, ... |
Let $T = {\mathbb R}/{\mathbb Z}$ be the $1$-torus. Let $a_{ij}$ be integer numbers, $1 \leq i \leq m$, $1 \leq j \leq n$ and $A$ the $m \times n$ matrix whose $(i,j)$ entry is $a_{ij}$. Consider the following system of $m$ linear equations:
$$\left\{\begin{array}{rl} a_{11}x_1 + a_{12}x_2 + \cdots + a_{1n}x_n & = \ove... |
This question may be more suited for physics.stackexchange, but I saw this post was recommended for StackOverflow or Computational Science, so I'm asking my question here.
I am trying to write a program in Matlab to evaluate an expression with fermionic annihilation and creation operators. Define $$\{f, g \} \equiv fg ... |
Find all primitive roots modulo $13$.
We show $2$ is a primitive root first. Note that $\varphi(13)=12=2^2\cdot3$. So the order of $2$ modulo $13$ is $2,3,4,6$ or $12$.
\begin{align} 2^2\not\equiv1\mod{13}\\ 2^3\not\equiv1\mod{13}\\ 2^4\not\equiv1\mod{13}\\ 2^6\not\equiv1\mod{13}\\ 2^{12}\equiv1\mod{13} \end{align}
Hen... |
Suppose we have a function $f(x,y)$ differentiable as many times as you like in $\mathbb{R}^2$ the gradient is given by
$$ \nabla f (x,y) = \left(f_x,f_y \right)^T $$
cosine and sine of such vector are given by
$$ \left\{ \begin{array}{l} \cos \alpha = \frac{f_x}{\lVert \nabla f \rVert} \\ \sin \alpha = \frac{f_y}{\lVe... |
Following the work of
Lu (1967) (Full text available here!) I got stuck trying to derive the elasticity of substitution between factors. He use the formula developed by Allen, that when the production function is linear and homogeneous is the following:
$$\sigma =\frac{\frac{\partial V}{\partial K}\frac{\partial V}{\pa... |
In number theory, it's often required to check whether the proof of an expression can be done without resorting to prime numbers (Hence the prime free part). We are allowed to use concepts of coprime numbers though.
Now I have seen a prime free proof of $$\phi(mn)=\phi(m)\phi(n)$$ when $gcd(m,n):=(m,n)=1$. There is a g... |
Caveat: it can be misleading to write $\sigma$ for the noise variance instead of $\sigma^2$.
The formula for a linear combination of "signals" (noise included), considered as a sum of random variables, is given in SE.Stats: Variance of Uncorrelated Variables: for observation $Y$ composed of signal $X$ and noise $N$:
$$... |
This is how I'd approach the problem. Please point out any issues on this method as it is based on my own approach (I have no textbook to reference this to).
Based on the information you have, you would run a regression of log output on log-labor, log-capital and log-human capital. This would give you a model like this... |
First of all, here is a noise diode model for a PN junction from sourceforgeIt consists of the capacitance of the diode \$ c_d \$, the conduction (or resistance \$g_d = \frac{1}{r_d} \$) and a noise current source \$i_d\$.
The resistance is a standard thermal noise source:
\$S_{r_d} = 4 k T r_d\$
k is the Boltsmann con... |
Let $A_f\colon L^2([0,1]) \rightarrow L^2([0,1]^2)$ be given by
$(Af)(x)=\displaystyle\sum_{k=1}^\infty \frac{1}{k\pi^2}\int_0^1 f(x)\sin(k\pi x)\sinh(k\pi y)\,\mathrm{d}x\sin(k\pi x)$
where $f\in C^1([0,1])$.
I want to show that $A$ is not bounded.
What I can tell for sure is, that
$\displaystyle \int_0^1 f(x)\sin(k\p... |
Huge cardinal Huge cardinals (and their variants) were introduced by Kenneth Kunen in 1972 as a very large cardinal axiom. Kenneth Kunen first used them to prove that the consistency of the existence of a huge cardinal implies the consistency of $\text{ZFC}$+"there is a $\omega_2$-saturated $\sigma$-ideal on $\omega_1$... |
The possibility of recursive self-improvement is often brought up as a reason to expect that an intelligence explosion is likely to result in a singleton - a single dominant agent controlling everything. Once a sufficiently general artificial intelligence can make improvements to itself, it begins to acquire a compound... |
A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles on a sphere. These series are useful because they can often be truncated, meaning that only the first few terms need to be retained for a good approximation to the original function. Multipole expansions... |
Let's start with the mathematical definitions.
Discrete signal power is defined as$$P_s = \sum_{-\infty}^{\infty}s^2[n] = \left|s[n]\right|^2.$$
We can apply this notion to noise $w$ on top of some signal to calculate $P_w$ in the same way. The signal to noise ratio (SNR) is then simply$$P_{SNR}=\frac{P_s}{P_w}$$
If we... |
Consider the Correlated Random Effects model $y_{it} = \alpha + x_{it}\beta + \bar x \gamma + w_i + \epsilon_{it} $ where $x_{it}$ is a scalar explanatory variable.
The correlated random effects GLS estimator $ \hat \beta_{CRE} $ is the OLS estimator of $\beta$ in the quasi-demeaned regression
$\tilde y_{it} = \delta +... |
I have read quite a lot of times now that the only coordinate system whose coordinate basis is orthonormal is the cartesian coordinate system.
Even though this makes sense, more or less, I never succeed when I try to prove it for myself. Could anyone give me a hint, or a sketch of a part of the proof, so I can work fro... |
In the previous STT5100 course, last week, we’ve seen how to use monte carlo simulations. The idea is that we do observe in statistics a sample \{y_1,\cdots,y_n\}, and more generally, in econometrics \{(y_1,\mathbf{x}_1),\cdots,(y_n,\mathbf{x}_n)\}. But let’s get back to statistics (without covariates) to illustrate. W... |
Lephenixnoir af424d1baa update documentation after writing the wiki 3 maanden geleden config 4 maanden geleden include/TeX 3 maanden geleden src 3 maanden geleden .gitignore 3 maanden geleden Makefile 4 maanden geleden README.md 3 maanden geleden TODO.md 3 maanden geleden configure 3 maanden geleden font5x7.bmp 4 maand... |
Yesterday I went to the ETH Zurich library and got hold of Wilhelm Blaschke's 1917 paper
Über affine Geometrie III: Eine Minimumeigenschaft der Ellipse. Leipziger Berichte 69 (1917), pages 3–12.
In this paper he proves that any convex body $B$ in the plane contains a triangle $T$ with$${\rm area}(T)\geq{3\sqrt{3}\over ... |
Let $X\in\mathbb{R}^{n\times p}$ denote a matrix with $p$ linearly-independent columns, and let $L\in\mathbb{R}^{n\times n}$ denote a symmetric matrix. Furthermore, let $D\in\mathbb{R}^{n\times n}$ denote a diagonal matrix with positive-entries.
Now suppose that we are interested in computing solutions to the
symmetric... |
Fit the Matern Cluster Point Process by Minimum Contrast Using Pair Correlation
Fits the Matern Cluster point process to a point pattern dataset by the Method of Minimum Contrast using the pair correlation function.
Usage
matclust.estpcf(X, startpar=c(kappa=1,scale=1), lambda=NULL, q = 1/4, p = 2, rmin = NULL, rmax = N... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Year of publication 1998 (5) (remove) Keywords
306
In this paper we study the space-time asymptotic behavior of the solutions and derivatives to th incompressible Navier-Stokes equations. Using moment estimates we obtain that strong solutions to the Navier-Stokes... |
What is the difference between the three terms below?
percentile quantile quartile
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up.Sign up to join this community
0 quartile = 0 quan... |
To use Power Substitution, you should be familiar with the Integration by Substitution (or U-Substitution) and derivatives. The key thing to remember is:If
\(u=f(x)\)
, then
\(du=f'(x) \, dx\)
.For example:If
\(u=5{x}^{3}-4x+5\)
, then
\(du={15x}^{2}-4 \, dx\)
.The goal of power substitution is to replace any nth root ... |
My topology professor told me in a discussion that the suspension spectrum $colim \Omega_n \Sigma_n S_0$ is the same as the monoid $G$ where $G=colim G_n$ where $G_n$ are self homotopy equivalences of $S_n$.
I just want to ask if this is correct or whether I heard her wrong.
My first guess is that $G=\pi_0 \Omega^\inft... |
Let $f: [0,\infty) \to [0,\infty)$ be a continuous function such that $f(f(x)) = x^2, \forall x \in [0,\infty)$. Prove that $\displaystyle{\int_{0}^{1}{(f(x))^2dx} \geq \frac{3}{13}}$.
All I know about this function is that $f$ is bijective, it is strictly increasing*, $f(0) = 0, f(1) = 1, f(x^2) = (f(x))^2, \forall x ... |
I've found a number of closely related functions, each of which takes three complex numbers $z_1,\,z_2$, and $z_3$ (which we can consider as the vertices of a triangle) as its arguments, and outputs a complex number $w$. A few of these functions represent well-known triangle centers $w$, such as the centroid (that is, ... |
I personally like the following approach.
Define the tensor algebra $T^{\circ}(V)=\bigoplus V^{\otimes n} = k\oplus V \oplus V\otimes V +\cdots$. Because there natural isomorphisms $V^{\otimes m}\otimes V^{\otimes n} \cong V^{\otimes m+n}$, and tensor products distributes over direct sums, we have a natural multiplicat... |
The log function also called a logarithm function which comes under most of the mathematical problem. The logarithmic function is used to reduce the complexity of the problems by reducing multiplication into addition operation and division into subtraction operation by using the properties of logarithmic functions. Her... |
Hellow, I want to describe all involutions of full matrix ring over field and all involutions of matrix polynomial ring. Is it true or false that every involution of the full matrix ring $T = M_n(R)$ over field $R$ has the follwing form $$ A \to C^{-1}A^TC, $$ for all $A\in M_n(R)$ and some fixed matrix $C$? What can w... |
In electromagnetism we say that all the electromagnetic interactions are governed by the 4 golden rules of Maxwell. But I want to know: is this(to assume that there is no requirement of any other rule)only an assumption, a practical observation, or is there a deeper theoretical point behind it? Could there be a deeper ... |
Frankly, complex angles just aren't worth the hassle. As the answer you've linked to points out, they're just a complicated way to re-parametrize the evanescent wave$$e^{i\mathbf k\cdot \mathbf r}= e^{i(k_x,0,i\kappa)\cdot (x,y,z)}=e^{ik_x x}e^{-\kappa z}\ \ \stackrel{\rm as}{=} \ \ e^{ik(\sin(\theta),0,\cos(\theta))\c... |
I am not very big in mathematics yet(will be hopefully), naive set theory has a problem with Russell's paradox, how do they defeat this sort of problem in mathematics? Is there a greater form of set theory than naive set theory that beats this problem? (Maybe something like superposition if is both or neither)?
The
Zer... |
Problem 1. Here's an example: take $A=\mathbb{N}$, $B=\{0,1,2,3\}$, and let $f\colon A\to B$ map the natural numbers to their remainder when divided by $4$ (so $f(3) = 3$, $f(15) = 3$, $f(21) = 1$, etc). Let $R$ be the equivalence relation on $B$ given by $aRb$ if and only if $a^2\equiv b^2 \pmod{4}$.
The relation $S$ ... |
Probability distributions of clique numbers are an active area of research. Most of the known results are in terms of bounds or asymptotic behavior. The following might all be of interest:
Your problem can at least be reduced to an arguably simpler combinatorial problem. Let $a(n,k,c)$ denote the number of graphs with ... |
It is known that $\log(p_1),\cdots,\log(p_n)$ are linearly independet over $\mathbb{Q}$, where $p_i$ denotes the $i$-th prime. For a number $1 \le k \le n$ let $Log(k)$ denote the vector with respect to this basis for the numbers $1,\cdots,n$. For a subset $A$ of $1,\cdots,n$ let $rank(A)$ denote the rank of the matrix... |
A couple of questions about the Lemma 3.5.
Lemma 3.5. (Gauss) : Let $p \in M$ and $v \in T_p M$ such that $\exp_p v$ is defined. Let $w \in T_p M \approx T_v(T_p M)$. Then $$\left\langle (d \exp_p)_v (v), (d \exp_p)_v (w) \right\rangle = \left\langle v, w\right\rangle \;\;\;\;\; (2)$$ Proof. Let $w = w_T + w_N$ is para... |
Radioactivity is the process by which the nucleus of an unstable atom loses energy by emitting radiation, including alpha particles, beta particles, gamma rays and conversion electrons Although radioactivity is observed as a natural occurring process, it can also be artificially induced typically via the bombarding ato... |
From what little I've been able to gather, the complex envelope preserves all information required for the reconstruction of the original signal and that it basically sends a low pass version of a bandpass signal.(Correct me if I'm wrong).I need an explanation for how the complex envelope is being created as per this t... |
import syssys.path.append('../code')from init_mooc_nb import *init_notebook()
Populated the namespace with: np, matplotlib, kwant, holoviews, init_notebook, SimpleNamespace, pprint_matrix, scientific_number, pretty_fmt_complex, plt, pf, display_html from code/edx_components: MoocVideo, MoocDiscussion, MoocCheckboxesAss... |
What is the best method for ranking items that have positive and negative reviews? Some sites, including reddit, have adopted an algorithm suggested by Evan Miller to generate their item rankings. However, this algorithm can sometimes be unfairly pessimistic about new, good items. This is especially true of items whose... |
This tag should be applied to questions concerning acid and base reactions. An acid is capable of donating a hydron/ proton (Brønsted acid) or capable of forming a covalent bond with an electron pair (Lewis acid). A base on the other hand is a chemical species/ molecular entity having an available pair of electrons cap... |
I have met with a scalar control algorithm for a permanent magnet synchronous motor. I haven´t heard about it before so I decided to develop a dynamic model to further analyze this control algorithm. Unfortunatelly I haven´t got the Matlab with the SimPowerSystems library so I decided to create this model in Scilab.
I ... |
Example: Let $f(x,y)=x^2+\cos{y}$. The rate of change at $f$ at $(1,0)$ in the direction of $<1,1>$ is:
A. $1$ B. $\sqrt{2}$ C. $\frac{\sqrt{3}}{2}$ D. $\pi$ E. $0$
I'm confused on how to start this. Am I supposed to find the gradient, plug in $(1,0)$ and take the dot product of this with $<1,1>$?
Thanks! |
How can two angles of a triangle be equal to $90°$? If two angles were $90°$, this would mean that the two sides would be parallel and the angle of the third side would be equal to 0. Thus, there would be only two vertices and this wouldn't be a triangle at all, ultimately making $\sin 90° = 1$ impossible.
Consider pol... |
Introduction
(Hoffman & Johnson, 2016) proposed an elegantdecomposition of the
evidence lower bound, or ELBO, objective commonlyused to train unsupervised latent-variable models characterized by aprobabilistic decoder $p(x | z)$ and prior $p(z)$ over latentvariable $z$. Such models have the form:
\begin{equation} p_{\t... |
Let's assume a photon is moving in the $z$ direction and state of the photon is represented by $$|\psi\rangle = \alpha |x\rangle + \beta |y\rangle $$
This photon will pass through three polarizers. One is oriented in the y direction along the horizontal, second is by 45 degree and third one is along the $x$ direction.
... |
"One-Line" Proof: Fundamental Group of the Circle
Once upon a time I wrote a six-part blog series on why the fundamental group of the circle is isomorphic to the integers. (You can read it here, though you may want to grab a cup of coffee first.) Last week, I shared a proof* of the same result. In one line
. On Twitter... |
Let $G$ be a topological group the underlying set of which is infinite (e.g., $(\mathbb{R}\,;+)$ or $(\mathbb{Z}\,;+)$), and let $H$ be a topological group the underlying set of which is finite (e.g., the group $P(n\,;\mathbb{R})$ of $(n\times n)$ permutation matrices). My questions are:
Is it possible to have a non-tr... |
I am proving this, all improvements are good. If I am completely wrong tell me.
Let $h:M\rightarrow N$ and $i:N\rightarrow O$. Prove that if $i \circ h$ is injective, then $h$ is injective.
This is my proof for this. Lets assume that $i \circ h$ is one-to-one. This means that if $i(h(a_1))=i(h(a_2)) $ then $a_1=a_2$.
a... |
As it can be shown, there are no interacting helicity-3 (and higher) particles (i.e., massless spin-3 or higher particles) in soft limit (small momentums of emitting particles of given helicity). Сan this result tell us something about high-momentum limit (i.e., the principal possibility of interaction of corresponding... |
What are the differences in the provided functionalities between these (the ones I named and possibly others) TeX plugins?
Here is a couple of related questions on SO:
Vi and Vim Stack Exchange is a question and answer site for people using the vi and Vim families of text editors. It only takes a minute to sign up.Sign... |
Posted by Nate on August 24, 2017 A Data-Driven Approach to LaTeX Autocomplete Autocomplete
Nearly anywhere you go on the web today you will find some sort of autocomplete feature. Start typing into Google and you get immediate suggestions related to your query. If you code in other languages, many IDEs have built-in, ... |
This question arises when looking at a certain constant associated to (a certain Banach algebra built out of) a given compact group, and specializing to the case of finite groups, in order to try and do calculations for toy examples. It feels like the answer should be (more) obvious to those who play around with finite... |
By logic without equality I mean those kind of logics where equality is treated as a binary relation satisfying some axioms, as opposed to a logics where equality is a logical symbol satisfying some inference rules.
In my understanding there should be no difference at the syntactic level between logics with or without ... |
One form of the Gronwall's inequality is that
If $\alpha(x),u(x)$ are non-negative continuous functions on $[0,1]$, and $$\forall x\in [0,1], u(x)\leq C+\int_{0}^{x}[\alpha(s)u(s)+K]ds\;(C,K\geq0),$$ then we have that $u(x)\leq[C+Kx]e^{\int_{0}^{x}\alpha(s)ds}$.
One form of comparison theorem is the following.
Assume t... |
Just this week I started a
Data Structures and Algorithms at my alma mater, San Jose state. And in jsut this short week I have noticed that the ones ability to properly evaluate ones code will take you a long way. Moreover, the skills developed through practiing the analysis of algortihm can go far in other discplines ... |
Does there exist a triple of
distinctnumbers $a,b,c$ such that $$(a-b)^5 + (b-c)^5 + (c-a)^5 = 0$$ ?
SOURCE :Inequalities (PDF) (Page Number 4 ; Question Number 220.1)
I tried expanding the brackets and I ended up with this messy equation :
$$-5 a^4 b + 5 a^4 c + 10 a^3 b^2 - 10 a^3 c^2 - 10 a^2 b^3 + 10 a^2 c^3 + 5 a ... |
B. KRISHNAREDDY
Articles written in Journal of Astrophysics and Astronomy
Volume 40 Issue 2 April 2019 Article ID 0009
We report optical observations of TGSS J1054 $+$ 5832, a candidate high-redshift ($z = 4.8 \pm 2$) steep-spectrum radio galaxy, in $r$ and $i$ bands, using the faint object spectrograph and camera moun... |
Revista Matemática Iberoamericana Rev. Mat. Iberoamericana Volume 22, Number 2 (2006), 591-648. Riesz transforms for symmetric diffusion operators on complete Riemannian manifolds Abstract
Let $(M, g)$ be a complete Riemannian manifold, $L=\Delta -\nabla \phi \cdot \nabla$ be a Markovian symmetric diffusion operator wi... |
Monotone Convergence Theorem
Given a sequence of functions $\{f_n\}$ which converges pointwise to some limit function $f$, it is
not always true that $$\int \lim_{n\to\infty}f_n = \lim_{n\to\infty}\int f_n.$$ (Take this sequence for example.)The Monotone Convergence Theorem (MCT), the Dominated Convergence Theorem (DCT... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.