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Before answering the question more or less directly, I'd like to point out that this is a good question that provides an object lesson and opens a foray into the topics of
singular integral equations, analytic continuation and dispersion relations. Here are some references of these more advanced topics: Muskhelishvili,... |
No:
Consider the case in which $F = \Bbb Q$, the rationals, and $K = \Bbb R$, the reals;let $\tau$ be any transcendental real number, e.g. we might take $\tau = e$ or $\tau = \pi$. Let $R$ be the ring $\Bbb Q [\tau]$, i.e. polynomial expressions in $\tau$ with rational coefficients. Then $\Bbb Q \subset R \subset \Bbb ... |
One may think it is maybe possible to reproduce the reasoning that leads to this equation from the Schrödinger one in any quantum system where the Schrödinger equation holds (i.e. surely QFT and QED, I don't know about string theory). However, this is actually rather difficult, and it is not possible to obtain the nice... |
I asked this question for many people/professors without getting a sufficient answer, why in QM Lebesgue spaces of second degree are assumed to be the one that corresponds to the Hilbert vector space of state functions, from where this arises? and why 2-order space that assumes the following inner product:
$\langle\phi... |
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Explain logically, not algebraically, why (n1)+(n3)+(n5)...=2n−1 \dbinom{n}{1}+\dbinom{n}{3}+\dbinom{n}{5}...= 2^{n-1} (1n)+(3n)+(5n)...=2n−1 By logically I mean, some argument by which we can calculate the sum orally.
Note by Vikram Waradpande 6 years, 5 months ... |
M. Schechter introduced an operational quantity characterizing strictly singular operators as follows:
For an operator $T:X\rightarrow Y$, we set $$\tau(T)=\sup_{M}\inf_{x\in S_{M}}\|Tx\|,$$ where $M$ represent an infinite-dimensional closed subspace of $X$.
If $A$ and $B$ are two nonempty subsets of a Banach space $X$... |
It says that enthalpies of combustion are always negative as these reactions are exothermic. The heat of combustion tables list positive values for all substances. Why do these values differ in sign?
Looking at Wikipedia for the definitions:
The
standard enthalpy of combustion is the enthalpy change when one mole of a ... |
Let $K$ be a convex body and let $\| \cdot \|_{K}$ be the correspoding Minkowski functional $$\| x \|_{K} = \inf\{\lambda > 0 : x \in \lambda K \}$$
Let us consider the following map $f: K \rightarrow \partial \mathring K$ such that $f(x) = \nabla \| x \|_{K}$ Here $\partial \mathring K$ stands for the polar set, i.e. ... |
How would you prove this identity using combinatorics? Any hints or advice?
For all positive integers $n>1$,
$\sum_{k=0}^{n} \frac{1}{k+1} {n\choose k} (-1)^{k+1}=\frac{-1}{n+1} $
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only ... |
Algebra, esp. ring theory is about the relationship between addition and multiplication. One concept of exceptional importance is the relation of being a
$k$th root of a number (with $k\in \mathbb{N}$ not considered as an element of the ring):
$x$ is
a $k$th root of$y$ when $\underbrace{x\cdot x\cdot \dots \cdot x}_{k ... |
The basic point is the following:
If an element commutes with more than half of the other elements, it already commutes with all elements.
This is basically Lagrange's theorem: Let $C_R(x) = \{r \in R | rx = xr\}$ be the centralizer of $x$. We assume $|C_R(x)| > \frac{1}{2} |R|$. $C_R(x)$ is a subgroup of $R$ and thus ... |
Last edited: January 26th 2018
Splines is a type of data interpolation, a method of (re)constructing a function between a given set of data points. Interpolation can be used to represent complicated and computationally demanding functions as e.g. polynomials. Then, using a table of a few function evaluations, one can e... |
Difference between revisions of "De Bruijn-Newman constant"
(Created page with "For each real number <math>t</math>, define the entire function <math>H_t: {\mathbf C} \to {\mathbf C}</math> by the formula :<math>\displaystyle H_t(z) := \int_0^\infty e^{t...")
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(51 intermediate revisions by the same user not s... |
Assumptions
There is a no function in (all) target operating systems that gives you the maximum/minimum values of the accelerometer
You do not want to spend a lot of money and time to build a database of these values on your own
Suggested solutions
I assume there is no way of getting around a kind of calibration proced... |
Difference between revisions of "De Bruijn-Newman constant"
(→Threads)
(50 intermediate revisions by the same user not shown) Line 7: Line 7:
:<math>\displaystyle \Phi(u) := \sum_{n=1}^\infty (2\pi^2 n^4 e^{9u} - 3 \pi n^2 e^{5u}) \exp(-\pi n^2 e^{4u}).</math>
:<math>\displaystyle \Phi(u) := \sum_{n=1}^\infty (2\pi^2 n... |
I have created a channel model in GNU Radio (a modified version of the default GNU Radio Channel Block). Its performance under AWGN (without timing, phase or frequency offsets) aligns properly with theory (for BPSK). I'm currently evaluating the effect of carrier frequency offset on BER by means of the flowgraph below.... |
Difference between revisions of "De Bruijn-Newman constant"
(→Threads)
(49 intermediate revisions by the same user not shown) Line 7: Line 7:
:<math>\displaystyle \Phi(u) := \sum_{n=1}^\infty (2\pi^2 n^4 e^{9u} - 3 \pi n^2 e^{5u}) \exp(-\pi n^2 e^{4u}).</math>
:<math>\displaystyle \Phi(u) := \sum_{n=1}^\infty (2\pi^2 n... |
I am referring to the following three reactions. Two of these reactions are imaginary ($\ce{M}$ and $\ce{X}$ are imaginary).
$$\begin{alignat}{3} \ce{X- + 2e- \;&<=> X^3-} \qquad &&E^\circ_{\ce{X^3-}/\ce{X-}}=0.9\ \mathrm{V}\qquad &&&\text{(a)}\\ \ce{2H+ + MO^2+ + e- \;&<=> M^3+ + H2O} \qquad &&E^\circ_{\ce{MO^2+}/\ce{... |
Ex.11.1 Q1 Constructions Solution - NCERT Maths Class 10 Question
Draw a line segment of length \(7.6 \,\rm{cm}\) and divide it in the ratio \(5:8\). Measure the two parts.
Text Solution
What is known?
Length of line segment and the ratio to be divided.
What is unknown?
Construction
Reasoning: Draw the line segment of ... |
In some Yang-Mills theory with gauge group $G$, the gauge fields $A_{\mu}^{a}$ transform as $$A_{\mu}^{a} \to A_{\mu}^{a} \pm \partial_{\mu}\theta^{a} \pm f^{abc}A_{\mu}^{b}\theta^{c}$$ $$A_{\mu}^{a} \to A_{\mu}^{a} \pm \left(\partial_{\mu}\theta^{a}-A_{\mu}^{b}f^{bac}\theta^{c}\right)$$ $$A_{\mu}^{a} \to A_{\mu}^{a} \... |
This post is part 3 of the "clustering" series:
Generate datasets to understand some clustering algorithms behavior K-means is not all about sunshines and rainbows Gaussian mixture models: k-means on steroids How many red Christmas baubles on the tree? Chaining effect in clustering Animate intermediate results of your ... |
The nozzle is the part of a rocket that limits the speed of the exhaust velocity. (It's also the part that converts the pressure and temperature of the expanding propellant into velocity.)
The speed of sound in the exhaust likewise regulates the expansion of the propellant gas.
For rockets using nozzles, the exhaust ve... |
Show that the first excited state of 8-Be nucleus fits the experimental value of the rotational band $E(2^+) = 92 keV$ (this is the first excited state, which is 92 keV above the ground state). To do so model 8-Be to be made of 2 alpha particles $4.5 fm$ apart rotating about their center of mass.
The method I used is:
... |
In many textbooks, the derivation of the energy levels in a hydrogen atom starts from the basic Hamiltonian $H = \frac{\mathbf{p}^2}{2m} + \frac{e^2}{4\pi\epsilon_0\mathbf{r}}$ and then adds relativistic fine structure or hyperfine structure as corrections to these basic energy levels. The effect of an electromagnetic ... |
Ex.6.5 Q11 Triangles Solution - NCERT Maths Class 10 Question
An aeroplane leaves an airport and flies due north at a speed of \(1000\; \rm{}km\) per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of \(1200\; \rm{}km\) per hour. How far apart will be the two planes after... |
Ex.7.4 Q4 Coordinate Geometry Solution - NCERT Maths Class 10 Question
The two opposite vertices of a square are \(\begin{align}\left( { - 1,\,2} \right){\text{ }}{\text{ and}}\left( {3,\,2} \right).\end{align}\) Find the coordinates of the other two vertices.
Text Solution Reasoning: What is known?
The \(x\) and \(y\)... |
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... |
Forgive me if this question is poorly worded, I'm not sure if centroid is the word to use here.
Say I want to interpolate the peak of a cross-correlation function in order to get sub-sample delays. I can fit a parabola with three points, or simply upsample my signal through zero-padding/sinc-interpolation. However, I h... |
Note: In the below, I used $X$ instead of $H$ by accident. Also, $X^*$ is my notation for $X^H$.
We can find this inverse by the chain rule. Note that $f = f_1 \circ f_2 \circ f_3$, where$$f_1(A) = Tr(A)\\f_2(A) = A^{-1}\\f_3(A) = XAX^* + I$$The derivatives of these functions are given by$$[f_1'(A)](B) = Tr(B)\\[f_2'(A... |
Ex.5.3 Q4 Arithmetic Progressions Solution - NCERT Maths Class 10 Question
How many terms of the AP. \(9, 17, 25 \dots\) must be taken to give a sum of \(636\)?
Text Solution What is Known?
The AP and sum.
What is Unknown?
Number of terms.
Reasoning:
Sum of the first \(n\) terms of an AP is given by \({S_n} = \frac{n}{... |
OpenCV 3.4.7
Open Source Computer Vision
This tutorial will demonstrate the basic concepts of the homography with some codes. For detailed explanations about the theory, please refer to a computer vision course or a computer vision book, e.g.:
Briefly, the planar homography relates the transformation between two planes... |
I've implemented the Earth harmonics calculation in JGM-3 model, using the coefficients from here
2 0 -0.10826360229840e-02 0.02 1 -0.24140000522221e-09 0.15430999737844e-082 2 0.15745360427672e-05 -0.90386807301869e-063 0 0.25324353457544e-05 0.0
Now, I want to switch to EGM2008, the coefficients are taken from here (... |
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Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
In a solution to a problem, to calculate Molecular mass of unknown gas from a mixture containing $\ce{O2}$ in $80~\%$, the author used the formula :
$\frac{1}{\sqrt{M_\text{mix}}}=\frac{X_{\ce{O2}}}{\sqrt{M_{\ce{O2}}}}+\frac{X_\text{gas}}{\sqrt{M_\text{gas}}}$.
The exact problem is:
Pure $\ce{O_2}$ diffuses through an ... |
Colloquia/Fall18 Contents 1 Mathematics Colloquium 1.1 Spring 2018 1.2 Spring Abstracts 1.2.1 January 29 Li Chao (Columbia) 1.2.2 February 2 Thomas Fai (Harvard) 1.2.3 February 5 Alex Lubotzky (Hebrew University) 1.2.4 February 6 Alex Lubotzky (Hebrew University) 1.2.5 February 9 Wes Pegden (CMU) 1.2.6 March 2 Aaron Be... |
The Tarski-Vaught test for $\preceq$ states that given a structure $\mathfrak{B}$ and $A\subseteq B$ then $A$ is the underlying set of an elementary substructure of $\mathfrak{B}$ iff for all formulas $\psi(x_1,\cdots ,x_m,y)$ in $L$ and every sequence $a_1,\cdots , a_m$ of elements in $A$ when $\mathfrak{B}\models \ex... |
The adèles $\mathbb A$ arise naturally when considering the Berkovich space $\mathcal M(\mathbb Z)$ of the integers. Namely, they are the stalk $\mathbb A = (j_\ast j^{-1} \mathcal O_\mathbb Z)_p$ where $p \in \mathcal M(\mathbb Z)$ is the trivial norm, $j: U \to \mathcal M(\mathbb Z)$ is the inclusion of its complemen... |
To describe the evolution of a (in this example non-relativistic) fluid system, the evolution equations for all relevant variables, conservation laws, the second law of thermodynamics, and appropriate (a)n appropriate equation(s) of state have to be considered.
The evolution equation for momentum is the Navier-Stokes e... |
I don't know how to explain the bending mode, but there is a nice mathematical explanation for the difference in stretching modes.
Take $\ce{CO2}$, carbon dioxide, as an example. I'll use B3LYP/6-31G(d,p) values. $\nu_{1}$, the symmetric stretch, is 1372 cm$^{-1}$, and $\nu_{3}$, the asymmetric stretch, is at 2436 cm$^... |
Lang is very lazy at learning English. He is always getting distracted during English classes. Being happy with the sweet message he got from his girlfriend yesterday, Lang invented a game to play during his English class.
Lang has an English dictionary containing $n$ words, denoted as $T_1, T_2, \ldots , T_ n$. Denoti... |
This is a really beautiful problem!
As there is some discussion in the question/comments/one of the answers about the history of this problem, let me narrate here what I found. I’m making this community-wiki as it is not exactly an answer to the question.
In
Mathematics Magazine, which is published five times a year by... |
Let $\mathcal{O}$ be the $\sigma$-algebra on $\omega_1$ generated by its countable subsets. Is there a ($\sigma$-additive) probability measure on $\mathcal{O}$ that is not concentrated on a countable set? (I am trying to construct a real random variable whose support has size $\aleph_1$.)
Another nice example is relate... |
In
Numerical Determination of Eigeinenergies for the Harmonic Odcillator, we showed how to numerically determine the eigenenergies of the harmonic oscillator potential. Using the fact that the potential was symmetric, and hence the wave functions symmetric or anti-symmetric, we could easily choose the correct boundary ... |
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 \... |
the background of my question is that I want to calculate an arbitrary square matrix $A \in \mathbb{R}^{n \times n}$ in a convex optimization problem and ensure it is regular, i.e., it can be inverted. For this reason, I would like to add a second, also convex summand to the optimization problem, or, alternatively, add... |
I can’t write this computer simulation for you (at least not based on the data provided) but will instead explain a few basic relationships that govern the heating and cooling of objects. I hope this helps.
Consider a building an object that is composed of $n$ objects of masses $m_i$ with specific heat capacities $c_{p... |
Ex.9.1 Q11 Some Applications of Trigonometry Solution - NCERT Maths Class 10 Question
A TV tower stands vertically on the bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is \(60^\circ\). From another point \(20 \,\rm{m}\) away from this point o... |
Event detail On Gaussian-width gradient complexity and mean-field behavior of interacting particle systems and random graphs
Seminar | November 1 | 3:10-4 p.m. | 1011 Evans Hall
Ronen Eldan, Weizmann Institute of Science
The motivating question for this talk is: What does a sparse Erd\"os-R\'enyi random graph, conditio... |
OpenCV 3.4.7
Open Source Computer Vision
In this tutorial, you will learn how image inpainting using F-transform works. It consists in:
The goal of this tutorial is to show that the inverse F-transform can be used for image reconstruction. By the image reconstruction, we mean a reconstruction of a corrupted image where... |
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... |
I first learnt about consistent hashing from a paper
1 that my manager at Google suggested I read. Recently I started thinking about it again as I was considering implementing it in one of my projects. I wanted to make sure that it was reliable enough but, looking again at the paper and searching online, I could only f... |
Since $(a_n)$ is bounded, $S$ is nonempty and bounded above. So by AoC there exists an upper bound $s=\sup S$.
Consider $s-\frac1k$ and $s+\frac1k$ where k is an arbitrary but fixed natural number. Since any number smaller than $s$ is not an upper bound of $S$, so $\exists (s'\in S)(s-\frac1k < s')$. Observe the proper... |
I am trying to figure out what is the largest possible order that an element of the multiplicative group $\bmod{n}$ can have if $n=p_1^{k_1} \cdot p_2^{k_2} \cdot \dots \cdot p_m^{k_m}$.
then I can prove that
$$U(n) \cong U(p_1^{k_1}) \times U(p_2^{k_2}) \times \dots \times U(p_m^{k_m})$$
Now I know from my number theo... |
Deterministic models. Clarification of the question:
The problem with these blogs is that people are inclined to start yelling at each other. (I admit, I got infected and it's difficult not to raise one's electronic voice.) I want to ask my question without an entourage of polemics.
My recent papers were greeted with s... |
Is it correct to represent Higgs VEV as the coherent state?
I mean, suppose translational invariant coherent state
$$
|\alpha\rangle = Ne^{\alpha \hat{a}^{\dagger}_{\mathbf p =0}}|\alpha =0\rangle, \quad N: \quad \langle \alpha|\alpha\rangle = 1 $$
of massless particles with zero dispersion relation. In principle, it i... |
Let $\{g_i:X\subset\mathbb{R}\rightarrow\mathbb{R};\;i=1,...,m\}$ be a linerly independet set of real functions.
Given $n$ points $(x_1,y_1),...,(x_n,y_n)\in X$, consider the following function
$$G(\beta_1,...,\beta_n)=\sum_{k=1}^n\left(\sum_{l=1}^m\left[ \beta_lg_l(x_k)-y_k\right]\right)^2$$
I need to prove that $G$ a... |
Two mistakes.
For all $\epsilon > 0$ the will indeed exist an $n_\epsilon\in \mathbb N$ so that $\alpha -\epsilon < n_\epsilon \le \alpha$ and $n_\epsilon < \alpha +\epsilon$ but that does not mean $n_\epsilon < \alpha + \epsilon$ for all $\epsilon$.
$n_\epsilon < \alpha + \epsilon$ is only true for
that $n_\epsilon$ a... |
First of all I define the convention I use.
The matrices $\bar{\sigma}^\mu$ I will use are $\{ Id, \sigma^i \}$ where $\sigma^i$ are the Pauli matrices and $Id$ is the 2x2 identity matrix.I will use the Chiral Fierz Identity$$(\bar{\sigma}^\mu)[\bar{\sigma}^\nu] = (\bar{\sigma}^\mu][\bar{\sigma}^\nu) + (\bar{\sigma}^\n... |
24 0
Hiya!
Somewhere in thermodynamics, the thermal wavelength [tex] \lambda = \frac {h}{\sqrt{2 \pi m k T}} [/tex] appears, apparently out of nothing (well, out of the canonical state integral).
Does anyone know what the physical meaning of this wavelength is?
Also, what is the physical meaning of the fugacity [tex] z... |
Ex.13.2 Q6 Surface Areas and Volumes Solution - NCERT Maths Class 10 Question
A solid iron pole consists of a cylinder of height \(220\,\rm{cm}\) and base diameter \(24\,\rm{cm},\) which is surmounted by another cylinder of height \(60\,\rm{cm}\) and radius \(8\,\rm{cm}\).
Find the mass of the pole, given that \(1\,\rm... |
When proving that conditions $A$ and $B$ are equivalent, it is often an arbitrary choice whether to first prove $A\implies B$ or $B\implies A$. Are there examples where the second implication uses the first in a nontrivial way, and becomes significantly more difficult without invoking the former?
The proof of the Sheph... |
Belyi's theorem states that the following properties of a nonsingular projective algebraic curve $X$ are equivalent:
1) $X$ is defined over $\overline{\mathbb{Q}};$
2) There exists a meromorphic function $\phi: X\to\mathbb{P}^1\mathbb{C} $ ramified at most at $0,1,$ and $\infty$;
3) $X$ is isomorphic to $\Gamma \backsl... |
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Search for new resonances in $W\gamma$ and $Z\gamma$ Final States in $pp$ Collisions at $\sqrt{s}=8\,\mathrm{TeV}$ with the ATLAS Detector
(Elsevier, 2014-11-10)
This letter presents a search for new resonances decaying to final states with a vector boson produced in association with a... |
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Search for new resonances in $W\gamma$ and $Z\gamma$ Final States in $pp$ Collisions at $\sqrt{s}=8\,\mathrm{TeV}$ with the ATLAS Detector
(Elsevier, 2014-11-10)
This letter presents a search for new resonances decaying to final states with a vector boson produced in association with a... |
The definition of the entropy is
$$H(Y) = -\sum p(y_j)\log_2 p(y_j)\,.$$
Now my text book says to compute the entropy for each attribute we consider the grouping of the data by that attribute now in each group we calculate the entropy (with respect to classes in each subgroup) and do a weighted sum. In this way the att... |
I've been reading David Marker's Introduction to Model Theory, and found
Vaught's two cardinal theorem (4.3.34): if a theory $T$ has a $(\kappa,\lambda)$-model, where $\kappa > \lambda \geq \aleph_0$, then $T$ has an $(\aleph_1,\aleph_0)$-model. The proof is made using Vaught pairs, and uses the following: existence of... |
Errata List for “Intuitive Gide to Fourier Analysis and Spectral Estimation”, First Edition Feel embarrassed that after reading the stuff more than twenty times, I did not notice so many glaring errors.Well, that’s my excuse any way! Your indulgence required until the next edition.
Here I have listed all the errors and... |
In general $$F(\alpha) = \sum_{n=1}^\infty \frac{\cot(n\pi \alpha)}{n^3}$$converges and can be explicitly calculated when $\alpha$ is a
quadratic irrational. The convergence in this case is easily seen as $\alpha$ has irrationality measure $2$. More precisely, $F(\alpha)/\pi^3 \in \mathbb{Q}(\alpha)$ when $\alpha$ is q... |
I'm reading about induced representations for research. Particularly, I'm trying to get a firm grasp on the finite group case before venturing on to the locally compact case. I've been looking at Wikipedia and more or less get the idea with one somewhat significant issue: why should we look to $\bigoplus g_iV$ (where t... |
I'm reading Kudla's Article on the Local Langlands Conjecture for $p$-adic general linear groups, and specifically I'm trying to understand how the ideas of Bernstein-Zelevinski yield show that you only need to prove the LLC for supercuspidal representations (on the automorphic side) and irreducible representatons (on ... |
I have $n$ objects $O_i$, each of them having $3$ values, $O_i = (A_i, B_i, C_i)$. I am trying to group them into $k$ groups $P_u$ such as $P_u =(A_u, B_u, C_u)$ such that
$$\text{minimize} \quad \sum_u^k M_k \left( a A_u + b B_u + c C_u \right)$$
for all $O_i \in P_u$, $A_i \leq A_u$, $B_i \leq B_u$, $C_i \leq C_u$. H... |
Since the Apollo 11 code is on GitHub, I was able to find the code that looks like an implementation of sine and cosine functions: see here for the command module and here for the lunar lander (it looks like it is the same code).
For convenience, here is a copy of the code:
# Page 1102
BLOCK 02
# SINGLE PRECISION SINE ... |
Ex.5.3 Q17 Arithmetic Progressions Solution - NCERT Maths Class 10 Question
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.... |
I think I've figured this out. The point is that, the rigorous meaning one can draw from the formal covariance of $J^\mu$ is that the momentum-space coefficient functions of $J^\mu$ (i.e. the functions in front of monomials of $a_p$ and $a^\dagger_p$) transform covariantly under the change of variable $p\to \Lambda p$.... |
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J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed i... |
Tautology (logic)
Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921; (it had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternate sense). A formula is satisfiable if it is true under at least one interpretation, and thus a t... |
Wikipedia says that a linear transformation is a $(1,1)$ tensor. Is this restricting it to transformations from $V$ to $V$ or is a transformation from $V$ to $W$ also a $(1,1)$ tensor? (where $V$ and $W$ are both vector spaces). I think it must be the first case since it also states that a linear functional is a $(0,1)... |
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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 ... |
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... |
Plot of the Chebyshev rational functions for
n = 0, 1, 2, 3, 4
for
0.01 ≤ x ≤ 100
, log scale.
In
mathematics, the Chebyshev rational functions are a sequence of functions which are both rational and orthogonal. They are named after Pafnuty Chebyshev. A rational Chebyshev function of degree is defined as: n R n ( x ) =... |
An abelian group is the same thing as a module over the ring $\mathbb{Z}$ (think about it). The ring $\mathbb{Z}$ is a PID, thus submodules of free $\mathbb{Z}$-modules are free. Reformulated in the context of abelian groups, submodules of free abelian groups are free abelian. You can use this fact to show that every a... |
Let me add some detail first.
An Anosov automorphism on $R^2$ is a mapping from the unit square $S$ onto $S$ of the form
$\begin{bmatrix}x \\y\end{bmatrix}\rightarrow\begin{bmatrix}a && b \\c && d \end{bmatrix}\begin{bmatrix}x \\y\end{bmatrix}mod \hspace{1mm}1$
in which (i) $a, b, c, and \hspace{1mm} d$ are integers, (... |
I've been following the news around the work they are doing at the LHC particle accelerator in CERN. I am wondering what the raw data that is used to visualize the collisions looks like. Maybe someone can provide a sample csv or txt?
Different pieces of equipment will produce somewhat different looking data, but typica... |
Ex.13.1 Q5 Surface Areas and Volumes Solution - NCERT Maths Class 10 Question
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter
\(l \) of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
Text Solution What is known?
Di... |
What is Electric Field Intensity?
The space around an electric charge in which its influence can be felt is known as the
electric field. The electric field Intensity at a point is the force experienced by a unit positive charge placed at that point. Electric Field Intensity is a vector quantity. It is denoted by ‘E’. F... |
You have forgotten that there is work done by the battery after $t=0$, so that there is energy lost before S1 is opened and S2 is closed.
The work done by the battery to transfer charge $Q$ onto the 1st capacitor is $W=QV=\frac{Q^2}{C}$.
The final charges on the capacitors are $\frac12Q, \frac14Q, \frac{1}{16}Q, \frac{... |
Can anyone state the difference between frequency response and impulse response in simple English?
The impulse response and frequency response are two attributes that are useful for characterizing linear time-invariant (LTI) systems. They provide two different ways of calculating what an LTI system's output will be for... |
Recall that in the category of Topological spaces or in the category of Manifolds, a
submersion is a (not necessarily surjective!) map $f: X \to Y$ so that for each point $x\in X$, there exists open neighborhood $f(x) \in U \subseteq Y$ and a map $g: U \to X$ splitting $f$, i.e. $f \circ g = \operatorname{id}_U$. This ... |
I) OP is right, ideologically speaking. Ideologically, OP's first eq.
$$ \tag{1} \left| \int_{\mathbb{R}}\! \mathrm{d}x_f~K(x_f,t_f;x_i,t_i) \right| ~\stackrel{?}{=}~1 \qquad(\leftarrow\text{Turns out to be ultimately wrong!}) $$
is the statement that a particle that is initially localized at a spacetime event $(x_i,t_... |
HINT 1:Your matrix $A$ is $$(a-b)I + b e e^T$$
Can you now compute the determinant?
Move your mouse over the gray area below for another hint.
HINT 2: Make use of the fact that $\det(\lambda A) = \lambda^n \det(A)$
Move your mouse over the gray area below for another hint.
HINT 3: $\det(I + \alpha e e^T) = (1+n \alpha)... |
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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 ... |
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Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c wit... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
Chapter 10 of Advanced Topics in Types and Programming Languages; gives a very comprehensive description of type inference by constraints solving.
They introduce the
free program indentifiers of an environment $\Gamma$ with the pair of equations $fpi(\emptyset) = \emptyset$ and $fpi(\Gamma;x:\sigma) = fpi(\Gamma) \cup ... |
Harry Svensson
Harry.Nossnevs@gmail.com
Electrical Engineer (Bachelor)
If you feel that I've helped you in a way you deem worthy of a payment. Then just paypal me.
Buzz words I have reasonably good knowledge about:
DSP Control theory Digital Filters Analog Filters Digital logic Buck converters 3-phase motors and househ... |
Mark's answer is correct, but in my opinion is not clear enough. Let's make it a bit simpler:Is it possible that the geomagnetic field reversal led to the extinction of Dinosaurs?NO, DEFINITELY NOTHere's why:The cause for the K-Pg extinction event (in which many living species, including dinosaurs, died) is well known:... |
I have recorded Signal_A, and downloaded signal_B from the internet (therefore two different microphones/settings are used for recording)
You might be able to achieve a "seamless" mix (or transition) but the fact that you have two different microphones and settings might add artifacts in the final product. You can tell... |
I'm having trouble determining whether the infinite product in $(1.)$ converges or diverges, my attack was to use the convergence cretina stated in $(0.)$
$(0.)$
An Infinite Product is said to be convergent if there exists a non-zero limit of the sequence of partial products:
$$P_{n}=\prod_{k=1}^n(1 + u_{k})$$.
as $n \... |
My friend gave me a problem, which can be reduced to the following.
Let $$$S(k)$$$ be the set of all arrays of size $$$n$$$ that contains $$$k$$$ ones and $$$n - k $$$ zeroes. Let for some array $$$s \in S(k)$$$ , $$$pos_s[1..k]$$$ denotes the position of those ones (say in increasing order, it doesn't matter actually)... |
Let $f$ be a monotone decreasing, continuously differentiable function with $\lim_{x\rightarrow \infty}f(x)=0$. Let $\chi$ be a non-principal Dirichlet character. It is standard to show that $\sum_{n\geq x}\chi(n)f(n)=O(f(x))$, where the big-O constant is easily computable and depends only on $\chi$. In particular, we ... |
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