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Cafeinst has pointed out that one week ago, Ashok Das (Rochester) and Pushpa Kalauni (Oklahoma) have published a 3-page preprint
I have personally tried a hundred of strategies to prove the Riemann Hypothesis so I could immediately recognize their operators \(O,O^\dagger\) from equations (10) and (11): I have played wi... |
This document will give you a brief tour of the capabilities of the IPython notebook.
You can view its contents by scrolling around, or execute each cell by typing
Shift-Enter.
The rest of the notebooks in this directory illustrate various other aspects and capabilities of the IPython notebook; some of them may require... |
I've been working with some dust solutions in General Relativity, practicing calculating the Riemann curvature tensor, and I came across an odd metric: the Tolman-Bondi-de Sitter metric. A quick internet search (to supplement the book I'm reading) can tell you that it describes spherical dust, while accounting for a co... |
2018-09-11 04:29
Proprieties of FBK UFSDs after neutron and proton irradiation up to $6*10^{15}$ neq/cm$^2$ / Mazza, S.M. (UC, Santa Cruz, Inst. Part. Phys.) ; Estrada, E. (UC, Santa Cruz, Inst. Part. Phys.) ; Galloway, Z. (UC, Santa Cruz, Inst. Part. Phys.) ; Gee, C. (UC, Santa Cruz, Inst. Part. Phys.) ; Goto, A. (UC,... |
Letting $X$ be a ring and $K$ be an $X$-module, I need to show that
if $K \cong A \times B$ for some $X$-modules $A,B$, then $\exists$ submodules $M'$ and $N'$ of $K$ such that:
$K=M' \oplus N'$
$M' \cong A$
$N' \cong B.$
I understand the concepts of internal and external direct sum of modules, and I showed that if $K ... |
This question already has an answer here:
I have seen the "objects pull down on space-time" explanations, but they assume a "pull down" force themselves. Could anyone explain the space-time explanation without assuming gravity in the first place?
Physics Stack Exchange is a question and answer site for active researche... |
Ex.12.1 Q3 Areas Related to Circles Solution - NCERT Maths Class 10 Question
Given figure depicts an archery target marked with its five scoring areas from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is \(21 \,\rm{cm}\) and each of the other bands is \(10.... |
Main Page The Problem
Let [math][3]^n[/math] be the set of all length [math]n[/math] strings over the alphabet [math]1, 2, 3[/math]. A
combinatorial line is a set of three points in [math][3]^n[/math], formed by taking a string with one or more wildcards [math]x[/math] in it, e.g., [math]112x1xx3\ldots[/math], and repl... |
@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... |
If water evaporates at room temperature because a small percentage of the molecules have enough energy to escape into the air, then why does a kitchen counter with a small amount of water eventually evaporate completely when at room temperature?
As your small percentage of molecules with high enough kinetic energy evap... |
So considering that set of all turing machines is countably infinite, can we also say that set of all FA machines(DFA/NFA) or set of all PDA machines(DPDA/NPDA) are countably infinite, Considering that we can build all of them with Turing machine?
The answer to your first question is yes, the sets of FAs and PDAs are c... |
Research Open Access Published: Dynamic analysis of a class of neutral delay model based on the Runge-Kutta algorithm EURASIP Journal on Wireless Communications and Networking volume 2018, Article number: 100 (2018) Article metrics
409 Accesses
Abstract
In this paper, we study the dynamics of a class of second-order ne... |
Let $G$ be a group and let $a \in G$ be a fixed element. Let $$H= \{\text{$g \in G$ | $g^{-1}ag=a$}\}.$$
Prove that $H$ is a subgroup of $G$.
So I know I need to show:
(i) $H$ is closed under the operation on $G$.
(ii) $H$ is closed under inversion.
(iii) $H\neq \emptyset$
For closure:
Suppose $x,y \in H.$ Then $x^{-1}... |
Ex.5.3 Q8 Arithmetic Progressions Solution - NCERT Maths Class 10 Question
Find the sum of first \(51\) terms of an AP whose second and third terms are \(14\) and \(18\) respectively.
Text Solution What is Known?
\({a_2}\) and \({a_3}\)
What is Unknown?
\({S_{51}}\)
Reasoning:
Sum of the first \(n\) terms of an AP is g... |
Probability - Complement Approach
Saturday 1 June 2019
: Two fair six-sided dice are rolled. What is the probability that at least one of the dice shows a five facing up? Question
Three different solutions are given below. Let
X be the random variable representing the # of fives. : Method 1 Analysing the sample space
“... |
It is important to understand that the only problem here is to obtain the extrinsic parameters. Camera intrinsics can be measured off-line and there are lots of applications for that purpose.
What are camera intrinsics?
Camera intrinsic parameters is usually called the camera calibration matrix, $K$. We can write
$$K =... |
Ex.13.2 Q4 Surface Areas and Volumes Solution - NCERT Maths Class 10 Question
A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are \(15 \,\rm{cm}\) by \(10 \,\rm{cm} \) by \(3.5 \,\rm{cm}\). The radius of each of the depressions is \(0.5\,\rm{... |
Impedance matching is tricky, but the role of a quarter wave transmission line is to map from one impedance to another. The actual impedance of the line will not match either the input or the output impedance - this is entirely expected.
However at a given frequency, when a correctly designed quarter wave line is inser... |
The purpose of this series of notebooks on Bayesian logic in clinical diagnostics is to give a mathematically robust and intelligible summary to help physicians, epidemiologists, nurses, NPs and in the field, as well as their consumers, understand clinical decisionmaking as an objective process amenable to analysis and... |
08:45
Non-termination of Dalvik bytecode via compilation to CLP
SPEAKER: Fred Mesnard
ABSTRACT. We present a set of rules for compiling a Dalvik bytecode program into a logic program with array constraints. Non-termination of the resulting program entails that of the original one, hence the techniques we have presented... |
Your task is to take an array of numbers and a real number and return the value at that point in the array. Arrays start at \$\pi\$ and are counted in \$\pi\$ intervals. Thing is, we're actually going to interpolate between elements given the "index". As an example:
Index: 1π 2π 3π 4π 5π 6πArray: [ 1.1, 1.3, 6.9, 4.2, ... |
Wolfram Alpha says that
$$\sum_{n=1}^{\infty} \frac{1}{n^2-3n+3} = 1 + \frac{\pi \tanh \left ( \frac{\sqrt{3}\pi}{2} \right )}{\sqrt{3}}$$
However I am unable to get it. It is fairly routine to prove that
$$\sum_{n=-\infty}^{\infty} \frac{1}{n^2-3n+3} = \frac{2\pi \tanh \left ( \frac{\sqrt{3}\pi}{2} \right )}{\sqrt{3}}... |
Metric signature convention: $(+---)$.
First, note that physical dynamics is ultimately decided by the equations of motion, which you get from the Lagrangian $\mathcal{L}$ after using the least action principle. The kinetic term in a $1$-derivative (before integration by parts) field theory goes like $\mathcal{L} \sim ... |
It is important to understand that the only problem here is to obtain the extrinsic parameters. Camera intrinsics can be measured off-line and there are lots of applications for that purpose.
What are camera intrinsics?
Camera intrinsic parameters is usually called the camera calibration matrix, $K$. We can write
$$K =... |
Ex. 6.6 Q7 Triangles Solution - NCERT Maths Class 10 Question
In Fig. below, two chords \(AB\) and \(CD\) intersect each other at the point \(P. \)
Prove that:
(i) \(\Delta APC\,\text{~}\Delta {\text{ }}DPB\)
(ii) \(AP. PB = CP. DP \)
Text Solution
Reasoning:
As we know that, two triangles, are similar if:
(i) Their co... |
Ex.14.2 Q1 STATISTICS Solution - NCERT Maths Class 10 Question
The following table shows the ages of the patients admitted in a hospital during a year:
Age ( in years) \(5-15\) \(15 - 25\) \(25 - 35\) \(35 - 45\) \(45 - 55\) \(55 - 65\)
Number of Patients \(6\) \(11\) \(21\) \(23\) \(14\) \(5\)
Find the mode and the me... |
MSD Module¶
Overview
Compute the mean squared displacement.
Details
The
freud.msd module provides functions for computing themean-squared-displacement (MSD) of particles in periodic systems.
MSD¶ class
freud.msd.
MSD(
box=None, mode=None)¶
Compute the mean squared displacement.
The mean squared displacement (MSD) measu... |
Let $f$ be a density on $\mathbb{R}^{p}$. Let $f_{\theta} = \sum_{i=1}^{d} \alpha_{i}\mathcal{N}_{p}(\cdot \, ; \, \theta_{i})$ be a mixture of $d$ Gaussian distributions on $\mathbb{R}^{p}$. For each $i$, $\theta_{i}$ is a vector of parameters (mean and covariance) which characterize the $i$-th component of the mixtur... |
$\def\cov{\mathop{\mathrm{cov}}}\def\var{\mathop{\mathrm{var}}}$My professor uses something that he calls the "projection theorem", to get rid of the condition in conditional probabilities (expectation and variance). I have not found anything about it on the internet, so I am wondering where it comes from, and if it is... |
This is an extension to my question here: Clay Institute Navier Stokes . Last time my solution was wrong because my velocity vector did not use bounded functions. Also someone said that I am only showing one example, but I'm trying to prove a statement that says "there exists" so I should only have to find one right? I... |
The sequence starts$$0, 1, -5, 25, -105, 105, 5355, \dots$$
We can observe that the statement is true not only for primes, but for odd numbers in general. Even though recurrences might be better for solving this kind of problem, here we can go for closed form formula (luckily there is one!). I have used approach inspir... |
There are some special functions of 3 or more complex variables that are analytic in some domain (a region in $\mathbb C^n$) with respect to each variable. To give some examples: the incomplete beta function $B(z; a, b)$, the Lerch transcendent $\Phi(z, s, a)$, the Weierstrass elliptic function $\wp(z;g_2,g_3)$, hyperg... |
I was very surprised when I first encountered the Mertens conjecture. Define
$$ M(n) = \sum_{k=1}^n \mu(k) $$
The Mertens conjecture was that $|M(n)| < \sqrt{n}$ for $n>1$, in contrast to the Riemann Hypothesis, which is equivalent to $M(n) = O(n^{\frac12 + \epsilon})$ .
The reason I found this conjecture surprising is... |
Practical and theoretical implementation discussion.
Post Reply
8 posts • Page
1of 1
Hi,
I have a simple question as in the title. Why is volumetric emission proportional to absorption coefficient? I often see the volumetric emission term is written as I can also see another representation, volumetric emittance functio... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Year of publication 1996 (22) (remove)
284
A polynomial function \(f : L \to L\) of a lattice \(\mathcal{L}\) = \((L; \land, \lor)\) is generated by the identity function id \(id(x)=x\) and the constant functions \(c_a (x) = a\) (for every \(x \in L\)), \(a \in L... |
上午8:00 | Latest Results for Synthese Abstract
We argue that causal decision theory (CDT) is no worse off than evidential decision theory (EDT) in handling entanglement, regardless of one’s preferred interpretation of quantum mechanics. In recent works, Ahmed (Evidence, decision, and causality, Cambridge University Pres... |
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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 ... |
This question already has an answer here:
What is the discrete fourier transform of the discrete fourier transform of any discrete time signal. Is result same signal? How?
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It on... |
Introduction
This is an alternative to j_random_hacker's solution, or more precisely, an alternative to his/her solution to the subproblem:
Given the ordered list of edge weights $x_1,\ldots,x_m$ encountered while traversing down a particular heavy path, we want to preprocess this list to enable us to be able to later ... |
All $LR(1)$ grammars -- indeed, all $LR(k)$ grammars -- are unambiguous, by definition. But the converse is not true: the fact that a grammar is unambiguous does not say anything about whether it can be parsed with an $LR(k)$ parser.
The grammar you present is not $LR(1)$, although the language itself is. (In fact, the... |
I am following Carroll
Spacetime and geometry.
I want to derive the continuity equation from the conservation of the stress-energy tensor: $$ \partial_t \rho + \nabla \cdot (\rho \vec{v}) = 0. $$
Suppose we assume that the Energy-stress tensor of a perfect fluid is conserved. Then since $u^\mu$ is the 4-velocity, $$ T^... |
How can I prove that the function $f(x)= 1-x^2$ will be greater than $g(x) = \cos(\pi x)$ on the interval $[-1,1]$? I feel like it should be pretty basic but it seems so hard.
Since both $f(x)$ and $g(x)$ are even it suffices to prove that for $x\in[0,1]$, and since for $x>\frac12$ $\cos(\pi x)< 0$ it suffices to consi... |
A random function $v(t)$ is said to be intermittent at small scales of its "Flatness" $F$, given as
$$ F(\Omega) = \frac{\langle (v_{\Omega}^{>}(t))^4\rangle}{\langle v_{\Omega}^{>}(t))^2\rangle} = \frac{\langle v_{\Omega}^{>}(t)v_{\Omega}^{>}(t))v_{\Omega}^{>}(t))v_{\Omega}^{>}(t))\rangle}{\langle v_{\Omega}^{>}(t)v_{... |
The formation of the diamminesilver(I) complex $\ce{[Ag(NH3)2]+}$ due to addition of ammonia has mainly three functions.
1. The Tollens test takes place under alkaline aqueous conditions. The complexation of $\ce{Ag+}$ with $\ce{NH3}$ prevents precipitation of brown $\ce{Ag2O}$:
$$\ce{2Ag+ + 2OH- <=> 2 AgOH <=> Ag2O + ... |
confidence intervals when the likelihood is not normalized
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7 posts • Page
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We are working with a model with a power spectrum different from the
\Lambda CDM model, P(k) = A_s k C(k), where C(k) includes two extra free parameters. We know from previous analysis that the spectra is not sensitive to huge va... |
DG advection equation with upwinding¶
We next consider the advection equation
in a domain \(\Omega\), where \(\vec{u}\) is a prescribed vector field, and \(q(\vec{x}, t)\) is an unknown scalar field. The value of \(q\) is known initially:
and the value of \(q\) is known for all time on the subset of the boundary \(\Gam... |
For comparison, consider a simple harmonic oscilllator. In this system, we have operators $a$ and $a^\dagger$ satisfying $[a,a^\dagger]=1$, and the Hamiltonian is $H=\omega a^\dagger a$. We can define the vacuum state $|0\rangle$ to be the state of lowest energy, and we can describe this state more explicitly as the on... |
Martins's (1997) Correlation Structure
Martins and Hansen's (1997) covariance structure: $$V_{ij} = \gamma \times e^{-\alpha t_{ij}}$$ where $t_{ij}$ is the phylogenetic distance between taxa $i$ and $j$ and $\gamma$ is a constant.
Keywords models Usage
corMartins(value, phy, form = ~1, fixed = FALSE)## S3 method for c... |
I was experimenting with series and numerically found this gem:
$$S=\sum_{n=0}^\infty \frac{2^{2n+1}}{(2n+1)^2 \binom{4n+2}{2n+1}}= \frac14 \left(\frac{\pi^2}{4}+\log^2 (2+\sqrt{3} ) \right)$$
Or, rewriting in hypergeometric form:
$${_4 F_3} \left(\frac12, \frac12, 1, 1; \frac34, \frac54, \frac32; \frac14 \right)= \fra... |
Ex.2.4 Q4 Polynomials Solution - NCERT Maths Class 10 Question
If two zeroes of the polynomial \({x^4}-6{x^3}-26{x^2} + 138x-35\) are \(2 \pm \sqrt 3 \) find other zeroes.
Text Solution What is known?
Two zeroes of the polynomial \(x^{4}-6 x^{3}-26 x^{2}+138 x-35\) are \(2 \pm \sqrt 3 .\)
What is unknown?
Other zeroes ... |
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... |
The \(R\) space¶
The function space \(R\) (for “Real”) is the space of functions which are constant over the whole domain. It is employed to model concepts such as global constraints.
An example:¶
Warning
This section illustrates the use of the Real space using the simplest example. This is usually not the optimal appr... |
Abbreviation:
DLOS
A
is a structure $\mathbf{A}=\langle A,\vee,\wedge,\cdot\rangle$ of type $\langle 2,2,2\rangle$ such that distributive lattice ordered semigroup
$\langle A,\vee,\wedge\rangle$ is a distributive lattice
$\langle A,\cdot\rangle$ is a semigroup
$\cdot$ distributes over $\vee$: $x\cdot(y\vee z)=(x\cdot y... |
This is NP-complete. In fact, it remains NP-complete when $F^+$ is restricted to be in 3-CNF form (not just CNF).
The proof is by demonstrating that this problem is at least as hard as testing 3-colorability of a graph. The correspondence is clean and elegant. Let $G=(V,E)$ be an undirected graph. Introduce variables $... |
$$\mathbb{E}\left[\frac{1}{X}\right] \geq \frac{1}{\mathbb{E}[X]}$$
My question is whether a similar inequality exists for the variance of $1/X$?
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 minut... |
According to the time evolution the system changes its state the with the passage of time. Is there any difference between time evolution and unitary time evolution?
Yes, there is a difference. Unitary time evolution is the specific type of time evolution where probability is conserved. In quantum mechanics, one typica... |
Mathematica seems not to to know the basic Laplace and inverse Laplace relation
$$\mathcal L(E_\alpha[−λt^α],t)(s)=\frac{s^{α-1}}{λ+s^α}$$
surrounding the Mittag Leffler function (
MittagLefflerE). The evaluations
LaplaceTransform[MittagLefflerE[alpha, -lambda t^alpha], t, s]Integrate[ Exp[-s t] MittagLefflerE[alpha, -... |
Lie algebras over rings (Lie rings) are important in group theory. For instance, to every group $G$ one can associate a Lie ring
$$L(G)=\bigoplus _{i=1}^\infty \gamma _i(G)/\gamma _{i+1}(G),$$
where $\gamma _i(G)$ is the $i$-th term of the lower central series of $G$. The addition is defined by the additive structure o... |
下記のミニワークショップを開催しますので，ご案内申し上げます．多くの方々のご参加を歓迎いたします．
世話人代表 俣野 博
日程： ２０１７年１月１８日（水）１０：００ 〜 １６：１５
場所： 東京大学大学院数理科学研究科棟 002号室
講師（講演順，敬称略）：
１．Matthieu Alfaro (University of Montpellier)
題目："Long range dispersion vs. Allee effect"
２．Xing Liang (Science and Technology University of China)
題目："The semi-wave solutions of the KPP eq... |
In 2009, J. Waldvogel and Peter Leikauf found the remarkable Euler-like polynomial,
$$F(m)=m^2+m+234505015943235329417$$
which is prime for $m=0\to20$, but composite for $m=21$. Define,
$$F(m)=m^2+m+A$$
such that $F(m)$ is prime for $m=0\to n-1$, but composite for $m=n$. Then the
least $\color{brown}{A>41}$ (compare to... |
Difference between revisions of "Geometry and Topology Seminar"
(→Spring 2017)
(→Spring 2017)
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|Jan 20
|Jan 20
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)
−
| [[#Carme... |
Difference between revisions of "Geometry and Topology Seminar"
(→Spring 2017)
(→Spring Abstracts)
Line 235: Line 235:
== Spring Abstracts ==
== Spring Abstracts ==
+ + + + +
===Bena Tshishiku===
===Bena Tshishiku===
Revision as of 16:54, 11 January 2017 Contents Fall 2016 Spring 2017
date speaker title host(s) Jan 20 ... |
One disadvantage of the fact that you have posted 5 identical answers (1, 2, 3, 4, 5) is that if other users have some comments about the website you created, they will post them in all these place. If you have some place online where you would like to receive feedback, you should probably also add link to that. — Mart... |
Author Message Lonely-Star Tux's lil' helper Joined: 12 Jul 2003 Posts: 82
Posted: Wed Apr 27, 2005 9:12 am Post subject: Mathematical Symbols in Xfig and gnuplot Hi everybody,
Studying physics I am starting to use Xfig and gnuplot.
Now I wonder How I can use symbols like omega or phi in the text in xfig or labels in g... |
1. Perturbations
As already mentioned, the Jahn-Teller effect has its roots in group theory. The essence of the argument is that the energy of the compound is stabilised upon distortion to a lower-symmetry point group. This distortion may be considered to be a normal mode of vibration, with the corresponding vibrationa... |
Let $\gamma=\gamma_1+\gamma_2+\gamma_3$, where $\gamma_1(t)=e^{it}$ for $0\leq t\leq 2\pi$, $\gamma_2(t)=-1+2e^{-2it}$ for $0\leq t\leq 2\pi$, and $\gamma_3(t)=1-i+e^{it}$ for $\pi/2\leq t\leq 9\pi/2.$ Determine all the values assumed by $n(\gamma, z)$ as $z$ varies over $\mathbb{C}\setminus|\gamma|.$
I do not understa... |
Let $a \in \Bbb{R}$. Let $\Bbb{Z}$ act on $S^1$ via $(n,z) \mapsto ze^{2 \pi i \cdot an}$. Claim: The is action is not free if and only if $a \Bbb{Q}$. Here's an attempt at the forward direction: If the action is not free, there is some nonzero $n$ and $z \in S^1$ such that $ze^{2 \pi i \cdot an} = 1$. Note $z = e^{2 \... |
Suppose $X$ has pdf $I(\mu, \tau)$ with density,
$$\sqrt{\frac{\tau}{2\pi x^{3}}}\exp\{-\frac{\tau}{2x\mu^{2}}(x-\mu)^2\}\quad; x>0, \quad \tau,\mu>0$$
I want to find the distribution of $V = \dfrac{\tau(x-\mu)^{2}}{x\mu^{2}}$.
My work: The distribution of $V$ can be written as follows.
$$f(v) = f_{X}(g^{-1}(v))\bigg|\... |
Mulliken atomic charges can be defined as[1]:
$$q_A = Z_A-\sum_{\mu\in A}\left( \mathbf{P\cdot S} \right)_{\mu\mu} \tag{Szabo 3.196}$$
Here I have used the same notation as in Szabo[1], with $\mathbf{P}$ being the density matrix and $\mathbf{S}$ beign the overlap matrix. $Z$ is the nuclear charge, and using the greek l... |
I'm trying to find the unique (up to a constant factor) positive solution to the eigenvalue problem: $$f''(x)-2f'(x)=-\lambda f(x) \ , \lambda>0 ,$$ with boundary conditions $f(1)=0$ and $f'(0)=0$.
I was able to solve the similar problem $f''(x)-f'(x)=-\lambda f(x)$ with the same boundary conditions.
In that case $f(x)... |
This is likely due to a truncation of your sine wave in the time interval you have chosen, such that there is not an integer multiple number of sine wave cycles chosen. I am guessing that your frequency view that you provide above is a subsequent measurement (DFT) from the resulting time domain waveform you have create... |
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Now showing items 1-1 of 1
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 ... |
Ex.15.1 Q20 Probability Solution - NCERT Maths Class 10 Question
Suppose you drop a die at random on the rectangular region shown in figure. What is the probability that it will land inside the circle with diameter \(1\rm{m}\)?
Text Solution What is known?
A die is dropped at random on the rectangular region as shown i... |
Proof of lemma $9.7$ in Haim Brezis'
Functional Analysis, Sobolev Spaces and Partial Differential Equations argues as follows:
For an element $u \in H_0^1(\Omega)$ we define $D_h u= \frac{u(x+h)-u(x)}{|h|}$, for $h \in \mathbb{R}^n$. Let's assume that $D_hu \in H_0^1(\Omega)$ and that: $$ ||D_hu||_{H^1(\Omega)} \leq ||... |
Cross posted on Mathoverflow
Ergodic TheoremA random walk on a finite group $G$ driven by a probability $\nu\in M_p(G)$ is ergodicif $\operatorname{supp}(\nu)$ is not concentrated on a proper subgroup $S\subset G$ nor the coset of a normal subgroup $N\triangleleft G$.
In this case the convolution powers of $\nu$ conver... |
You are likely familiar with the Doppler effect. You might have experienced it as a change in pitch of a car horn, ambulance siren or train whistle as the car/ambulance/train moved past you. In scientific terms, this change in pitch is described as a shift in the frequency of the sound.
The equation for the observed so... |
What is the purpose of normalizing the signal?
If we have two signals on hand, how is it used when comparing these two signals?
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It only takes a minute to sign up.Sign up to join... |
Answer
$T = \frac{u_k}{\sqrt{1+\mu_k^2}}$
Work Step by Step
In order to find the expression for the minimum tension needed, we take the derivative of the equation of the previous problem, which is: $\frac{T}{mg}=\frac{\mu_k}{cos\theta+\mu_ksin\theta}$ Taking the derivative gives the answer: $T = \frac{u_k}{\sqrt{1+\mu_... |
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Now showing items 1-10 of 26
Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
Let $a \in \Bbb{R}$. Let $\Bbb{Z}$ act on $S^1$ via $(n,z) \mapsto ze^{2 \pi i \cdot an}$. Claim: The is action is not free if and only if $a \Bbb{Q}$. Here's an attempt at the forward direction: If the action is not free, there is some nonzero $n$ and $z \in S^1$ such that $ze^{2 \pi i \cdot an} = 1$. Note $z = e^{2 \... |
also, if you are in the US, the next time anything important publishing-related comes up, you can let your representatives know that you care about this and that you think the existing situation is appalling
@heather well, there's a spectrum
so, there's things like New Journal of Physics and Physical Review X
which are... |
Imagine we've receive a signal, $R$, at a distance of $L$ from a transmitter. Then, we do FFT on the received signal. This is what FFT gives us:
\begin{align} R(f) &= A e^{j\phi} \tag1\\ \ \end{align}
where, $A$ is the amplitude, we can take it by abs() function over the FFT. And, $\phi$ is the phase and we can take it... |
Let $c$ denote the inverse of $a+b$, i.e., $ac+bc=ca+cb=1$. Multiplying this by $a$ and $b$ from the left and from the right and using $a^2=b^2=0$, we obtain $abc=a$, $cba=a$, and $cab=b$.
Let us show that $R=aR\oplus bR$. It follows from $ac+bc=1$ that $R=aR+bR$. If $ax=by$, then $bax=0$, implying $0=cbax=ax$ in view ... |
First, expand the logarithm into its Taylor series:\begin{align}S&\equiv \sum_{n\ge 1}n\log(1-e^{-nx}) \\&= -\sum_{n\ge 1} n \sum_{k\ge 1} \frac{e^{-knx}}{k} \\&= -\sum_{k \ge 1} \frac{1}{k}\sum_{n\ge 1}n\,e^{-nkx}\end{align}To sum the inner series,differentiate the following identity with respect to $\beta$,$$\frac{1}... |
@user193319 I believe the natural extension to multigraphs is just ensuring that $\#(u,v) = \#(\sigma(u),\sigma(v))$ where $\# : V \times V \rightarrow \mathbb{N}$ counts the number of edges between $u$ and $v$ (which would be zero).
I have this exercise: Consider the ring $R$ of polynomials in $n$ variables with integ... |
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Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
The derivative of $\sin(\omega_o t)$ is $\cos(\omega_o t)$.The Fourier transform of $\sin(\omega_o t)$ is $\frac{\pi}{j}[\delta(\omega-\omega_o) - \delta(\omega+\omega_o)]$.Differentiation in the ...
In many of the papers it is said that the derivative filter transfer function is given by: $$H(z) = \dfrac{1}{8T}\left(-... |
Determine for what values of $n$ the number $\frac{n+7}{2n+1}$ is an integer
Here's what I've tried
I think I solved the problem just for the positive integers:
Since $\frac{n+7}{2n+1}$ is a natural number (in this case) $$n+7\leq 2n+1$$ $$n\leq6 \rightarrow 0\leq n \leq 6$$
And the values that can only fit that satisf... |
2018-09-02 17:21
Measurement of $P_T$-weighted Sivers asymmetries in leptoproduction of hadrons / COMPASS Collaboration The transverse spin asymmetries measured in semi-inclusive leptoproduction of hadrons, when weighted with the hadron transverse momentum $P_T$, allow for the extraction of important transverse-momentu... |
You are talking about symmetry in two contexts :-
Gaussian Window
I will talk about these two contexts one by one
Gaussian
A symmetric 2-D gaussian
(I assume 1-D as in 1-D the question of symmetry does not arise) means that it does not have any directional preference ( dictated by equal variances $\sigma_x$ and $\sigma... |
There are a few method to synthesize $\ce{SrO2}$ from $\ce{SrO}$ and $\ce{O2}$. One of them uses $\ce{KClO3}$ as the source of $\ce{O2}$ [Ref. 1]. The paper is in German but has English abstract which states:
Abstract. Single crystals of $\ce{SrO2}$ have been oblained after high
pressure/high temperature reaction of a ... |
I need to calculate the length of a curve $y=2\sqrt{x}$ from $x=0$ to $x=1$.
So I started by taking $\int\limits^1_0 \sqrt{1+\frac{1}{x}}\, \text{d}x$, and then doing substitution: $\left[u = 1+\frac{1}{x}, \text{d}u = \frac{-1}{x^2}\text{d}x \Rightarrow -\text{d}u = \frac{1}{x^2}\text{d}x \right]^1_0 = -\int\limits^1_... |
I am currently studying gaseous state and I encountered the following problem.
A container with a volume 3 liter holds $\ce{N2(g)}$ and $\ce{H2O(l)}$ at $\pu{29 ^\circ C}$. The pressure is found to be $\pu{1 atm}$. The water is then split into hydrogen and oxygen by electrolysis according to the reaction $$\ce{H2O (l) ... |
OpenCV 4.0.0
Open Source Computer Vision
class cv::DenseOpticalFlow class cv::DISOpticalFlow DIS optical flow algorithm. More... class cv::FarnebackOpticalFlow Class computing a dense optical flow using the Gunnar Farneback's algorithm. More... class cv::KalmanFilter Kalman filter class. More... class cv::SparseOptical... |
Ex.12.2 Q4 Areas Related to Circles Solution - NCERT Maths Class 10 Question
A chord of a circle of radius \(10\, \rm{cm}\) subtends a right angle at the centre. Find the area of the corresponding
(i) minor segment (ii) major sector. (Use \(\pi = 3.14\))
Text Solution What is known?
Radius of the circle and angle subte... |
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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 am trying to solve the equation $$\left(\sin (x)+\cos (x)-\sqrt{2}\right)\cdot \sqrt{-11 x-x^2-30}=0$$ in Real domain. I tried
First way
Solve[{(Sin[x] + Cos[x] - Sqrt[2]) Sqrt[-11 x - x^2 - 30] == 0}]
I got
{{x -> -6}, {x -> -5}, {x -> [Pi]/4}}
Second way
Solve[{(Sin[x] + Cos[x] - Sqrt[2]) Sqrt[-11 x - x^2 - 30] == ... |
Lecture: H5116, F 8:00-9:40
Section: HGW2403, F(e) 18:30-20:10
Textbook: https://doi.org/10.1017/CBO9781107050884
Lecture: HGX205, M 18:30-21
Section: HGW2403, F 18:30-20
Syllabus
Exercise 01 Prove that \(\neg\Box(\Diamond\varphi\wedge\Diamond\neg\varphi)\) is equivalent to \(\Box\Diamond\varphi\rightarrow\Diamond\Box\... |
Both QPSK and $4$-QAM constellations have signal points at $45, 135, 225$, and $315$ degrees (note typo in your question). They arise from
amplitude modulation (or, ifyou prefer, phase modulation) of two carrier signals(called the inphase and quadrature carriers) that are orthogonal (meaning that theydiffer in phase by... |
List of Errors in The IMO Compendium (second edition)
These are the corrections to The IMO Compendium (Second Edition). Thanks to Alexander Bogomolny, Stijn Cambie, Jürgen Doenhardt, Jim Michael, Alberto Torregrosa, and Jozsef Pelikan. The list is updated on March 28, 2013.
Page 27, problem 5: Change \( AMKD \) to \( A... |
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