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If you tried solving any math problem without knowing the exact formula or method, you may get confused. Surely the question that once pops into your mind or might come is if it is fine to quit this question. Some students memorize formulas and rules to complete many math problems, but this does not mean they are good ... |
Construct Definitions and Relationships In physics, many phenomena behave cyclically. Springs are the prototypical example of this. Elastic Object: An object, which when deformed (perhaps by squeezing it or stretching it) returns to its original shape. Spring: A coiled spiral shaped object that is constructed to be ela... |
I just want to add something to the correct @annav answer, with a practical example in basic Quantum Field Theory. Imagine a particle process with $2$ initial particles and $2$ final particles, you have some initial state (say at t= $-\infty$), which is $|i\rangle =|1\rangle |2\rangle$, where $|1\rangle$ and $|2\rangle... |
AliFMDMultCuts () AliFMDMultCuts (EMethod method, Double_t fmd1i, Double_t fmd2i=-1, Double_t fmd2o=-1, Double_t fmd3i=-1, Double_t fmd3o=-1) AliFMDMultCuts (const AliFMDMultCuts &o) AliFMDMultCuts & operator= (const AliFMDMultCuts &o) void Reset () Double_t GetMultCut (UShort_t d, Char_t r, Double_t eta, Bool_t errors... |
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b. 1.4.2002 Description
Description: b. is a bookmarking manager and is web based and accessible from any browser. The features are- A new and powerful feature is the ability to share bookmarks. These shared bookmarks may be publicly view... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
Spring 2018, Math 171 Week 3 Stopping/Non-Stopping times
Let \(T_1, T_2\) be stopping times for some Markov Chain \(\{X_n:n \ge 0\}\). Which of the following will also necessarily be stopping times? Prove your claims.
(Discussed) \(T_3=5\)
\(T_4=T_1 + T_2 + 1\)
(Discussed) \(T_5=T_1 + T_2 - 1\)
(Solution) \(T_5\) will ... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
Definition:Summation/Indexed Definition
Let $\tuple {a_1, a_2, \ldots, a_n} \in S^n$ be an ordered $n$-tuple in $S$.
The composite is called the summation of $\tuple {a_1, a_2, \ldots, a_n}$, and is written: $\displaystyle \sum_{j \mathop = 1}^n a_j = \paren {a_1 + a_2 + \cdots + a_n}$
The set of elements $\set {a_j \i... |
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Now showing items 1-10 of 18
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 in... |
Subharmonic solutions for a class of Lagrangian systems
1.
Department of Mathematics, Faculty of Sciences, University of Monastir, 5019 Monastir, Tunisia
2.
Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland
We prove that second order Hamiltonian system... |
Class 12 Physics is a very important subject for plus two students and so they prepare ahead hoping to do well in the exams. They reach out to all resources ranging from textbooks to class notes, solution books, previous year question papers, model question papers etc so that they can study well and also get the practi... |
I read that every chemical reaction is theoretically in equilibrium in an old textbook. If this is true how can a reaction be one way?
Yes, every chemical reaction can theoretically be in equilibrium. Every reaction is reversible. See my answer to chem.SE question 43258 for more details.
This includes even precipitatio... |
First, a trivial example that might anger you:
Let $A_i$ be the observables of the Mermin-Peres square, and $a_i$ their non-contextual values. Then $\prod_i A_i = -\mathbb{1}$, but $\prod_i a_i = 1$, contradiction. In this case $f$ is multiplicative. But the same contradiction can be obtained considering $\prod_i A_i+\... |
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Now showing items 1-2 of 2
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 ... |
If dark matter has gravity just like normal matter, does that mean it can also form planets, solar systems and so on? Any answer will be appreciated.
Planets and stars, no. Globular clusters and galaxies, yes.
Small scales
To condense into such relatively compact objects as planets, stars, and even the more diffuse sta... |
I am trying to download openjdk java 8 runtime so I can download minecraft but I keep getting an authentication error and it says I dont have permission and that I have to delete stuff
100mbps unmetered – can be upgraded to 1gig unmetered
We can offer 1U of… | Read the rest of http://www.webhostingtalk.com/showthread.p... |
Hydroquinone used as a photographic developer, is 65.4% C, 5.5% H, and 29.1% O, by mass. What is the empirical formula of hydroquinone?
Solution: In most cases, when a question asks us to find an empirical formula without giving us a specific sample size, it’s best to assume a sample size of 100 g. It makes the math ea... |
I am learning finite element method(galerkin method) for solving ode/pde.
when searching this topic,I often see examples using the hat function
UnitTriangle[x] as the basis function of the galerkin approximation.
I understand that the Galekin method is a method of expressing the objective function by the sum of a basis... |
This is really embarrassing, but I'm not quite sure where I'm going wrong here... Why is this calculation of the gravitational potential inside a sphere with uniform mass distribution incorrect?
Set-Up
Let's say the sphere has mass $M$ and radius $R$ (and uniform mass density $\mu$), and what we want to find is the pot... |
Evaluation of color characteristics
OptiLayer provides calculations of color properties in almost all existing color coordinate systems. You can view color coordinates in a graphical or tabular forms. Light source, detector, observer, integration step, reference white and incident angle used for color evaluation are sp... |
Title Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions Publication Type Journal Article Year of Publication 2012 Authors Correggi, M, Dell'Antonio, G, Finco, D, Michelangeli, A, Teta, A Journal Rev. Math. Phys. 24 (2012), 1250017 Abstract
We study the stability problem for a n... |
Example: In a factory there are two Machines, Machine $A$ and Machine $B$ producing an Item. We are told that Machine $A$ produces $30 \%$ of the items and $3 \%$ of the items were defective. Machine $B$ produces $70 \%$ of the item and $4 \%$ of items produced by Machine $B$ are defective. If an item is drawn and foun... |
Spring 2018, Math 171 Week 6 Exit Distributions
A person is terminally ill. On a day when the person is awake, there is an 0.2 chance they will die overnight, and they are equally likely to be awake or unconscious the next day. On a day when the person is unconscious, there is an 0.2 chance they will be awake the next ... |
Jets subgroup Goal of the group Group Contacts
Daniele del Re (CMS)
Bruce Mellado (ATLAS)
Gavin Salam (Theory)
Frank Tackmann (Theory)
Available Tools Settings for comparison studies H+2-jet NLO+shower comparison study Process/Inputs:
===============
* pure gg -> H + 2j NLO+shower at parton level
* m_H = 125 GeV
* \sqr... |
in the late 1960s, the strongly interacting particles were a jungle. Protons, neutrons, pions, kaons, lambda hyperons, other hyperons, additional resonances, and so on. It seemed like dozens of elementary particles that strongly interacted. There was no order. People thought that quantum field theory had to die.
Howeve... |
For a compact Riemannian locally symmetric space $\mathcal M$ of rank one andan associated vector bundle $\mathbf V_\tau$ over the unit cosphere bundle$S^\ast\mathcal M$, we give a precise description of those classical(Pollicott-Ruelle) resonant states on $\mathbf V_\tau$ that vanish undercovariant derivatives in the ... |
Question:
The 0.5-lb block is pushed against the spring at A and released from rest.
Neglecting friction, determine the smallest deflection of the spring for which the block will travel around the loop ABCDE and remain at all times in contact with the loop.
Energy Conservation:
The energy at every point for a particula... |
OpenCV 3.4.6
Open Source Computer Vision
void cv::accumulate (InputArray src, InputOutputArray dst, InputArray mask=noArray()) Adds an image to the accumulator image. More... void cv::accumulateProduct (InputArray src1, InputArray src2, InputOutputArray dst, InputArray mask=noArray()) Adds the per-element product of tw... |
So after a lot of research, and tons and tons of papers that I've went through, I finally have some idea how to solve the equations that will give me candidates for the asymptotic symmetry group for Kerr/CFT correspondence. One has boundary conditions $h_{\mu\nu}$, and metric that behaves like $g_{\mu\nu}=\bar{g}_{\mu\... |
What is a Blackbody?
A black body is an idealization in physics that pictures a body that absorbs all electromagnetic radiation incident on it irrespective of its frequency or angle. Through the second law of thermodynamics that a body always tries to stay in thermal equilibrium.
To stay in thermal equilibrium, a black... |
Rudin's Real and Complex Analysis Chapter 3 Exercise 4 is:
Assume that $\varphi$ is a continuous real function on $(a,b)$ s.t. $$\varphi\left(\frac{x+y}{2}\right)\leq \frac{\varphi(x)+\varphi(y)}{2}$$ for all $x,y\in(a,b)$. Prove that $\varphi$ is convex.
The conclusion does not follow if continuity is omitted from the... |
ASU Electronic Theses and Dissertations
This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree inform... |
Optical response functions¶
The optical response functions couple an external electric field, \(E_\mathrm{ext}\), with the internal electric field arising from the response of the crystal. It is convenient to introduce the displacement field, \(\bf{D}\), which determines the electric field from external charges, \(\rho... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
November 2008 , Volume 21 , Issue 4
Select all articles
Export/Reference:
Abstract:
We consider two (densely defined) involutions on the space of $q\times q$ matrices; $I(x_{ij})$ is the matrix inverse of $(x_{ij})$, and $J(x_{ij})$... |
Simulating Gaussian processes in julia
This is my interpretation of the information provided in this tutorial on Noise Problems in the DifferentialEquations package.
A Simple Wiener Process (White Noise)
A Wiener process is a continuous process that has:
Independent increments
Gaussian increments
Continuous paths, i.e.... |
We want to solve the eigenproblem $\hat{H}|\psi\rangle=\lambda |\psi\rangle$. Since $|\psi\rangle$ lives in an infinite dimensional Hilbert space, this isn't fit to put on to a computer. Instead, we discretize space into $N$ points. $\vec{\psi}$ is now an $N$ dimensional column vector, and $\bf H$ is now an $N\times N$... |
In Quantum mechanics, observables are represented by hermitian operator. But does every hermitian operator represent a observable? If not , how do we know that whether a hermitian operator represent observable or not? What is the precise definition of the term "observable"?
Given a quantum system with associated Hilber... |
The answer from the link provides a formula of ratio of likelihoods of the null and the alternative hypotheses with detailed derivation, and the R code below is my implementation for it with $\theta_1 = 1$, $\theta_2 = 2$, $n_1 = 70$, and $n_2 = 100$.
To generate samples, get cdf for exponential distribution first. If ... |
I got this question on an interview (Codility) the other day.
Imagine we have a system responsible for counting the total number of pages on a web site. It’s a single process on a single machine, and it has a RESTful HTTP API with one endpoint. It looks like
POST /increment?n=N
Whenever the endpoint is hit, the system ... |
There are two fascinating aspects of angular motion that don’t exist for linear motion in quite the same way. The first is that the rotational inertia is readily changed, as for example, when a skater extends or pulls in a leg. The second is related to the fact that both
p and L are vector quantities and can change in ... |
In this article we define and publish the exact pre-flop probabilities for each possible combination of two hands in Textas Hold’em poker. An online tool at tools.timodenk.com/poker-odds-pre-flop makes the data visually accessible.
Table of Contents Introduction
A deck of French playing cards, as it is used in Texas Ho... |
Equation of Circle
Jump to navigation Jump to search
Theorem $\paren {x - a}^2 + \paren {y - b}^2 = R^2$ $x = a + R \cos t, \ y = b + R \sin t$
Instead, the center of a circle is commonly denoted $\polar {r_0, \varphi}$, where $r_0$ is the distance from the origin and $\varphi$ is the angle from the polar axis in the c... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
SPPU Civil Engineering (Semester 3)
Geotechnical Engineering May 2015
Geotechnical Engineering
May 2015
Total marks: --
Total time: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons (2) Marks are given to the right of every question (3) Draw neat diagrams wherever necessary
(1) Assume ap... |
CDS 110b: Stochastic Systems
CDS 110b ← Schedule → Project
This set of lectures presents an overview of random processes and stochastic systems. We begin with a short review of continuous random variables and then consider random processes and linear stochastic systems. Basic concepts include probability density functi... |
HEALpix and spherical harmonic sampling
Laurent Jacques
Posts: 7 Joined: October 20 2004 Affiliation: FYMA/PHYS/UCL Contact:
Hi,
I have still a question about HEALpix grid in the particular context of spherical harmonic (SH) sampling and SH transform. Are we sure that SH transform can be exactly realized to all orders ... |
We highly recommend you (I can not stress enough) to download the LaTeX fonts (just 151 KB) to your PC, and install them. This will not only improve the look of the website, but also save bandwidth as you do not need to download the images every time you see an equation.
Instructions to install and enable fonts:
A. How... |
The pressure changes, so we cannot use the simplified equation you use. From the perfect gas law, we can calculate the volume change, but we don't need to go there. The big problem is that in addition to the heat transfer, pressure-volume work is done. Work is easy to determine at constant pressure. When pressure chang... |
Why does the following DFA have (to have) the state $b_4$?
Shouldn't states $b_1,b_2,b_3$ already cover "exactly two 1s"? Wouldn't state $b_4$ mean "more than two 1s", even if it doesn't trigger an accept state?
Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of... |
Definition:Positive/Integer Definition
Informally, the
positive integers are the set: $\Z_{\ge 0} = \left\{{0, 1, 2, 3, \ldots}\right\}$ As the set of integers $\Z$ is the Inverse Completion of Natural Numbers, it follows that elements of $\Z$ are the isomorphic images of the elements of equivalence classes of $\N \tim... |
The title says it all. Quaternions are widely used to represent the orientation of a spacecraft. Why is that, and how do quaternions compare to other alternatives?
What are quaternions and how are they used in spacecraft dynamics?
Background
Newtonian mechanics says we live in a universe with three spatial dimensions, ... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
that's a question from some exam in Calculus Can someone help?
does $\int _0^{\infty }\frac{\sin\pi \:x}{\left|\ln \left(x\right)\right|^{\frac{3}{2}}}$ converge?
I proved that it converges between 1 and infinity using comparison test with the integral of $\frac{1}{x^{\frac{3}{2}}}$ Between 1/2 and 1 i used Dirichlet e... |
I'm reading a proof of Multivariate CLT using Lindeberg Theorem.
Let $X_n = (X_{ni},... ,X_{nk})$ be independent random vectors all having the same distribution. Suppose that $E[X_{nu}]<\infty$; let the vector of means be $c=(c_1,..., c_k)$, where $c_u=E[X_{nu}],$ and let the covariance matrix be $\Sigma = [\sigma_{uv}... |
My following questions come from the understanding of the relations between the PSGs for two
gauge-equivalent mean-field (MF) Hamiltonians (or MF ansatz). Considering the Schwinger-fermion ($f_{\sigma}$) MF approach to spin-liquid phases of spin-1/2 system. Let $H$ and $H'$ be two $SU(2)$ gauge-equivalent MF Hamiltonia... |
Periodic and subharmonic solutions for a 2$n$th-order $\phi_c$-Laplacian difference equation containing both advances and retardations
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
We consider a 2$n$th-order nonlinear difference equation containing both many advances and r... |
Ground states of nonlinear Schrödinger equations with fractional Laplacians
1.
Center for Applied Mathematics, Guangzhou University, Guangzhou 510405, China
2.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
$ \begin{equation*} \left\{ \begin{aligned} (-\Delta)^\alpha u+u& = f(u),... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
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Now showing items 1-3 of 3
D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
The cost of 4 tables and 2 chairs cost Rs. 500 and the cost of 5 tables and 4 chairs cost Rs. 700, what will be the costs of 10 chairs and 10 tables. When we come across situations like this we need to frame the corresponding equations. We use application of linear equations to solve such real life problems. Linear equ... |
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... |
Find the points on the curve $x^2+xy+y^2=7$ where tangent is parallel to (a) X axis (b) parallel to Y axis.
For part (a) if we differentiate w.r.t $x$ we get $y'=\large-\frac{2x+y}{x+2y}$, this when equated to zero (parallel to X axis means slope is zero) gives $x=-y/2$, this when substituted in the equation of the cur... |
The title is pretty self explanatory. If I have $V$ nodes and $E$ edges in a connected undirected graph, is there a formula to determine an upper bound on the maximum possible diameter? The exact graph is unknown, but the number of edges and the number of vertices is. I do know that when $E=V(V-1)/2$ (complete graph), ... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
I have discovered that the following two tags are too similar to each other:
riemann-zeta-function, with 299 questions tagged, has the description
The Riemann zeta function is the function of one complex variable $s$ defined by the series $\zeta(s) = \sum_{n \geq 1} \frac{1}{n^s}$ when $\operatorname{Re}(s) > 1$. It ad... |
We all know the thin lens equation. For $o$ being a horizontal object distance and $f$ being the focal length, the horizontal image distance $i$ is described by:
$$\frac{1}{f} = \frac{1}{o} + \frac{1}{i}$$
However, I haven't seen this applied to determine where an incoming ray should go. This is a problem when writing,... |
A departmental store maintains its monthly sales details in a spread sheet. The rows are used to represent the items and the sales amount for the items are shown in columns representing the day in the month. Such arrangement of collective information in rows and columns is called a matrix.
The plural for matrix is matr... |
Najati, A., Abdollahpour, M., Park, C. (2017). On the stability of linear differential equations of second order. International Journal of Nonlinear Analysis and Applications, 8(2), 65-70. doi: 10.22075/ijnaa.2017.1078.1226
Abbas Najati; Mohammad Abdollahpour; Choonkil Park. "On the stability of linear differential equ... |
Spring 2018, Math 171 Week 7 Martingales
Let \((X_n)_{n \ge 0}\) be i.i.d. uniform on \([-1, 0) \cup (0, 1]\)
Show that \((M_n)_{n \ge 0}\) with \(M_n = X_0 + \dots + X_n\) is a Martingale.
Show that \((M_n)_{n \ge 0}\) with \(M_n = \frac{1}{X_0} + \dots + \frac{1}{X_n}\) is not a Martingale.
(Answer) \(\mathbb{E}|M_n|... |
I've read that realized kernels are the thing to use for calculating daily volatility from high-frequency data. So I've got minute data, how do I actually use such a kernel? Will it give me minute-ly volatility, do I have to normalize it somehow? Also, what data do I feed it - minute data since the start of the trading... |
Using PIPE-FLO ® Professional to Evaluate Compressible Choked Flow in Control Valves
PIPE-FLO Professional uses equations from recognized industrial standards for control valves, making it an excellent tool to evaluate cavitation and choked flow in compressible and incompressible fluid flow through control valves in a ... |
Definition:Number Definition
There are five main classes of number:
$(1): \quad$ The natural numbers: $\N = \set {0, 1, 2, 3, \ldots}$ $(2): \quad$ The integers: $\Z = \set {\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots}$ $(3): \quad$ The rational numbers: $\Q = \set {p / q: p, q \in \Z, q \ne 0}$ $(4): \quad$ The real number... |
@Rubio The options are available to me and I've known about them the whole time but I have to admit that it feels a bit rude if I act like an attribution vigilante that goes around flagging everything and leaving comments. I don't know how the process behind the scenes works but what I have done up to this point is lea... |
Daniel Soltész
I'm a PhD student at Budapest University of Technology and Economics, department of Computer science. My main interest is graph theory and extremal set theory.
Email: protosdrone (gmail)
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Budapest
Member for 6 years, 1 month
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Last seen Jul 27 at 18:3... |
Definition:Positive Part Definition Then the positive part of $f$, $f^+: X \to \overline \R$, is the extended real-valued function defined by: $\forall x \in X: f^+ \left({x}\right) := \max \left\{{0, f \left({x}\right)}\right\}$ Also defined as
Some sources insist that $f$ be a real-valued function instead.
However, $... |
FermiDirac¶ class
FermiDirac(
broadening)¶ Parameters: broadening(PhysicalQuantity of type energy or temperature) – The broadening of the Fermi-Dirac distribution. Usage Examples¶
Use the Fermi-Dirac occupation function with a broadening of 0.1 eV on an LCAOCalculator:
numerical_accuracy_parameters = NumericalAccuracyP... |
You've formulated the question very well, but you have left out just one variable. (Trying to understand something that is not in your grade level is a major crime, but that is your teacher's fault: he hasn't properly taught you not to think).
The way to split up the problem is:
Get from the surface of planet A to "out... |
Pigeonhole Principle Theorem
Then:
where $\ceiling {\, \cdot \,}$ denotes the ceiling function.
Proof
Then the maximum number of elements of any $S_i$ would be $\ceiling {\dfrac n k} - 1$.
So the total number of elements of $S$ would be no more than $k \paren {\ceiling {\dfrac n k} - 1} = k \ceiling {\dfrac n k} - k$.
... |
Zero sharp
$0^{\#}$ is a $\Sigma_3^1$ real number which cannot be proven to exist in $\text{ZFC}$. It's existence contradicts the Axiom of constructibility, $V=L$. In fact, it's existence is somewhat equivalent to $L$ being completely different from $V$.
Definition
$0^{\#}$ is defined as the set of all Gödel numberings... |
What is the relationship between the Flow Coefficient (C v) and the Discharge Coefficient (C d)? v) and the Discharge Coefficient (C d)?
Good communication between various groups involved with fluid piping systems is critical for the proper design, operation, and determination of cost for many systems in residential, c... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
I have a personal problem I want to solve. I have a system of linear inequalities with 97 unknowns and 150000 ineqaulities, I think formal notation of the problem should be something like this
\begin{equation} \begin{bmatrix} x_{00000101} & \cdots & x_{00000197}\\ \vdots & \ddots &\vdots\\ x_{15000001} & \cdots & x_{15... |
Introduction to Area
If you needed to cover the floor of your house from wall to wall, you would need to share the area of the floor at the carpet store, after which they would tell you how much carpet you would need and what it would cost. If you wanted to varnish the dining room table, you would need to know the area... |
What is the difference in energy between the two levels responsible for the ultraviolet emission line of the magnesium atom at 285.2 nm?
Solution:
Show me the final answer↓
We will first figure out the frequency, and use that value to calculate the difference in energy.
The first equation we will use is:
(Where v is fr... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
This is one of the accompanying workshops of the 50 Years Faculty of Mathematics Anniversary Conference.
The conference takes place at Bielefeld University. You can find detailed directions here.
All talks will be held in
T2-213.
If you are planning your trip to Germany, you might also be interested in the conference B... |
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... |
Loss Layers¶ class
MultinomialLogisticLossLayer¶
The multinomial logistic loss is defined as \(\ell = -w_g\log(x_g)\), where \(x_1,\ldots,x_C\) are probabilities for each of the \(C\) classes conditioned on the input data, \(g\) is the corresponding ground-truth category, and \(w_g\) is the
weightfor the \(g\)-th class... |
Spring 2018, Math 171 Week 5 Reversibility/Detailed Balance Condition
Show that Ehrenfest’s chain is reversible. \[P(x,y)= \begin{cases}\frac{N-x}{N}, & \mathrm{if\ } y=x+1 \cr \frac{x}{N}, & \mathrm{if\ } y=x-1 \cr 0, & \mathrm{otherwise}\end{cases}\]
(Answer) Show KCC on simple cycles: All simple cycles are length 2,... |
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Measurement of $J/\psi$ production as a function of event multiplicity in pp collisions at $\sqrt{s} = 13\,\mathrm{TeV}$ with ALICE
(Elsevier, 2017-11)
The availability at the LHC of the largest collision energy in pp collisions allows a significant advance in the measurement of $J/\ps... |
This article by Yngvason is probably a good start:
Yngvason, J. (2005). The role of type III factors in quantum field theory. Reports on Mathematical Physics, 55(1), 135–147. (arxiv)
The Type III property says something about statistical independence. Let $\mathcal{O}$ be a double cone, and let $\mathfrak{A}(\mathcal{O... |
$\vec{B}=\nabla \times \vec{A}\tag1$
This is true because at
every point $\nabla\cdot\vec{B}=0 \tag2$
In
free space points,
$\displaystyle \vec{B}=\dfrac{\mu_0}{4 \pi}\int_C \dfrac{I\ dl \times\hat{r}}{r^2}\tag3$
Consequently: $\nabla \cdot\vec{B}=0 \tag2$
At the
points on the circuit, there is a singularity and we can... |
Linear algebra is a branch of mathematics, but the truth of it is that linear algebra is the mathematics of data. Linear algebra is the study of vector spaces, lines and planes, mappings that are required for linear transforms and many more. Dealing with linear equations is also a very prominent part of linear algebra.... |
What is the difference between linearly and affinely independent vectors? Why does affine independence not imply linear independence necessarily? Can someone explain using an example?
To augment Lord Shark's answer, I just wanted to talk a little about the intuition behind it.
Intuitively, a set of vectors is linearly ... |
Learning Objectives
Explain the difference between mass and weight Explain why falling objects on Earth are never truly in free fall Describe the concept of weightlessness
Mass and weight are often used interchangeably in everyday conversation. For example, our medical records often show our weight in kilograms but nev... |
Difference between revisions of "Huge"
m (→Consistency strength and size: added relation to strong cardinals)
Line 24: Line 24:
=== Ultrahuge cardinals ===
=== Ultrahuge cardinals ===
−
A cardinal $\kappa$ is '''$\lambda$-ultrahuge''' for $\lambda>\kappa$ if there exists a nontrivial elementary embedding $j:V\to M$ for... |
Neurons (Activation Functions)¶
Neurons can be attached to any layer. The neuron of each layer will affect the output in the forward pass and the gradient in the backward pass automatically unless it is an identity neuron. Layers have an identity neuron by default [1].
class
Neurons.
Identity¶
An activation function th... |
Category:Fourier Series
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is called the
Let $\alpha \in \R$ be a real number. Let:
\(\displaystyle a_n\) \(=\) \(\displaystyle \dfrac 1 \pi \int_\alpha^{\alpha + 2 \pi} f \left({x}\right) \cos n x \rd x\) \(\displaystyle b_n\) \(=\) \(\displaystyle \dfrac 1 \pi \int_\alpha^{\alpha + 2 \p... |
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