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At the conclusion of my talk today for the CUNY Math Graduate Student Colloquium, Freiling’s axiom of symmetry Or, throwing darts at the real line, I had assigned an exercise for the audience, and so I’d like to discuss the solution here.
The axiom of symmetry asserts that if you assign to each real number $x$ a counta... |
Ryder at the beginning of the chapter about renormalization defines the "superficial degree of divergence" of diagrams in $\lambda \phi^4$ theory. I'll recap the derivation.
A diagram in $\lambda\phi^4$ theory has $E$ external lines, $I$ internal lines of which $L$ are loops and $n$ vertices. Each internal line contrib... |
PCTeX Talk Discussions on TeX, LaTeX, fonts, and typesetting
Author Message zedler Joined: 03 Mar 2006 Posts: 15
Posted: Thu Mar 09, 2006 9:20 am Post subject: spacing Hello,
Please have a look at the spacing of these equations
- $[]_{\langle n\times m\rangle}$ (the brackets touch)
- $Z_{F1}$ (F and 1 spacing)
- $\frac... |
Zenithal Hourly Rate
Dominic Ford, Editor
An artistic depiction of the Leonid meteor storm seen over North America on the night of November 12-13, 1833, Edmund Weiss
The zenithal hourly rate (ZHR) of a meteor shower is a measure of the rate at which it produces meteors, expressed as the number of meteors seen per hour.... |
OpenCV 3.4.0
Open Source Computer Vision
Today it is common to have a digital video recording system at your disposal. Therefore, you will eventually come to the situation that you no longer process a batch of images, but video streams. These may be of two kinds: real-time image feed (in the case of a webcam) or prerec... |
Difference between revisions of "Literature on Carbon Nanotube Research"
m
m (→Tensile and Electrical Properties of Carbon Nanotube Yarns and Knitted Tubes in Pure or Composite Form)
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== Tensile and Electrical Properties of Carbon Nanotube Yarns and Knitted Tubes in Pure or Composite Form ==
== Tensi... |
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1. Why Who Marries Whom Matters: Effects of Educational Assortative Mating on Infant Health in the United States 1969–1994
Social Forces, ISSN 0037-7732, 05/2019
Journal ... |
Every where and book I search I get that the definition of linear momentum is the amount of speed (quantity of motion) contained in it or simply it is mass $\times$velocity? So, what is an appropriate definition of linear momentum? What did Newton think when he discovered it? He certainly did not think it as the amount... |
Given a photon dropping from $\lambda_1$ to $\lambda_2$, its energy will drop from $\frac{hc}{(\lambda_1)}$ to $\frac{hc}{(\lambda_2)}$. However, I was wondering if there is any significance in the energy of the change in wavelength itself. For $\Delta \lambda = \lambda_2 - \lambda_1$, this change in wavelength has an ... |
Well, surely you can compute it using matrix operations. But it won't be very natural. Let me instead provide you with a very similar solution (based on a similar matrix) that you'll hopefully find useful. It's not new at all (Kirchhoff, 1847) but I think it's not very well known. I first learned about it in this Wu's ... |
The Annals of Statistics Ann. Statist. Volume 8, Number 5 (1980), 1002-1016. Large Sample Theory for an Estimator of the Mean Survival Time from Censored Samples Abstract
This paper introduces and studies the large sample properties of an estimator for the mean survival time from censored samples. Let $X_1, \cdots, X_n... |
The question deals with a particular operator characterized by the commutation relation $[a, a^\dagger] = 1$. The polynomial to be expanded is also of a special form, $(a+a^\dagger)^n$. Also, the whole polynomial is supposed to be applied to the unique state vector $\vert 0\rangle$ that has the property $a \vert 0\rang... |
PCTeX Talk Discussions on TeX, LaTeX, fonts, and typesetting
Author Message murray Joined: 07 Feb 2006 Posts: 47 Location: Amherst, MA, USA
Posted: Wed Mar 15, 2006 10:53 pm Post subject: Y&Y TeX vs. MiKTeX with MathTimePro2 fonts I used updated fonts just prior to posting of 0.98.
Initially I had different page breaks... |
You're proposing a key-stretching algorithm that turns 128 bits of input into a much larger key. This isn't as good as simply using a much larger key of the same size, though it's not tl;dr- necessarily as weak as the 128 bits of input. That said, your bitmap looks very ordered, which strongly suggests that it's far we... |
You are asking several questions here, so it may be useful to separate out what is going on first in the setting of affine reflection groups. This is independent of the application to algebraic groups or loop groups.
The answer to your first question (how to write $s_0$ in terms of the presentation) is straightforward,... |
Home
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Integrals of Trig FunctionsAntiderivatives of Basic Trigonometric Functions
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Ineffable cardinal
Ineffable cardinals were introduced by Jensen and Kunen in [1] and arose out of their study of $\diamondsuit$ principles. An uncountable regular cardinal $\kappa$ is ineffable if for every sequence $\langle A_\alpha\mid \alpha<\kappa\rangle$ with $A_\alpha\subseteq \alpha$ there is $A\subseteq\kappa$... |
In this MathStackExchange post the question in the title was asked without much outcome, I feel.
Edit: As Douglas Zare kindly observes, there is one more answer in MathStackExchange now.
I am not used to basic Probability, and I am trying to prepare a class that I need to teach this year. I feel I am unable to motivate... |
I'm reading this book on Classical mechanics, and they show a derivation of the mentioned kinematic formula: $V_f^2=V_i^2+2a\left(x_f-x_0\right)$
They start by saying that the acceleration of an object down an incline is: $$\ddot{x}=gsin\theta$$, which I completelly understand. Then they mention:
"We can find the veloc... |
I've the $n$ (refractive index of the glass sheet ) and $t$ (the thickness of the glass sheet)
with this information, how can I find the amount light absorption of the glass sheet?
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to s... |
The identity you've used, $$\hat{a}^\dagger \longrightarrow \frac{1}{\sqrt{2}}(\hat{b}^\dagger + i \hat{c}^\dagger) \hat{a}^\dagger\qquad \text{(wrong!)}$$is incorrect. Instead, what you need to do is this:$$\hat{a}^\dagger = \frac{1}{\sqrt{2}}(\hat{b}^\dagger + i \hat{c}^\dagger) $$That is, the operator $\hat{a}^\dagg... |
In [1] I have found a definition of the covariant derivative of a Dirac field with a general connection $\omega_{\mu a}{}^{b}$ (with torsion and non-metricity) [see eq. (29)]:
$$\nabla_{\mu}\psi=\partial_{\mu}\psi-\frac{1}{4}\omega_{\mu ab}\gamma^{a}\gamma^{b}\psi$$
They use the so-called Kosmann lift, to build the spi... |
The nonlocal boundary problem with perturbations of antiperiodicity conditions for the eliptic equation with constant coefficients Abstract
In this article, we investigate a problem with nonlocal boundary conditions which are perturbations of antiperiodical conditions in bounded $m$-dimensional parallelepiped using Fou... |
Edit
It seems that I haven't written my question clearly enough, so I will try to develop more using the example of quantum tunnelling. As a disclaimer, I want to state that my question is not about how to perform a Wick rotation in the path integral formulation!
Let's look a the probability of quantum tunnelling in th... |
Consider a set of $n$ fixed point charges $q_1, q_2, \ldots, q_n$ in vacuum and let ${\bf E}({\bf x})$ be the electric field produced by these charges (see figure 1). Can we find a point ${\bf z}$ in space such that if a charge $q$ is placed there, it will remain in stable equilibrium?
Fig. 1: A set of $n$ fixed charge... |
Every time a commit is added to a git repository, a hash string which identifies this commit is generated. This hash is computed with the SHA-1 algorithm and is 160 bits (20 bytes) long. Expressed in hexadecimal notation, such hashes are 40 digit strings.
Since each commit must have a unique hash, one question that nat... |
I understand where the E step happens in the algorithm (as explicated in the math section below). In my mind, the key ingenuity of the algorithm is the use of the Jensen's inequality to create a lower bound to the log likelihood. In that sense, taking the
Expectation is simply done to reformulate the log likelihood to ... |
The effect you noticed is the result of the combination of Doppler effect and sound absorption.
Sound absorption in a fluid is proportional to
$exp(- \alpha \nu^2 x)$
where $\alpha$ is a dimensional constant, $x$ is the traveled path, and $\nu$ is the sound frequency.
In its own reference frame, the airplane emits alwa... |
On the cohomology ring of divided powers and free ∞-loop spaces
Orateur:
Lorenzo Guerra
Dates:
Vendredi, 14 Juin, 2019 - 14:00 - 15:00
Résumé:
Given a pointed topological space $(X, \ast)$, its loop space is the space $\Omega(X, \ast)$ of continuous maps $\gamma \colon [0,1] \to X$ such that $\gamma (0) = \gamma (1) = ... |
I should like to argue that the axiom of determinacy is true for all games having a small payoff set. In particular, the size of the smallest non-determined set, in the sense of the axiom of determinacy, is the continuum; every set of size less than the continuum is determined, even when the continuum is enormous.
We c... |
Difference between revisions of "Applied/ACMS/absS18"
(→ACMS Abstracts: Spring 2018)
(→ACMS Abstracts: Spring 2018)
Line 45: Line 45:
We introduce the variance based joint sparsity (VBJS) method for sparse signal recovery and image reconstruction from multiple measurement vectors. Joint sparsity techniques employing $\... |
Global Moderator Why am I getting negative A.I.C. scores?
It is correct that negative A.I.C. sent up red flags for you as it may tell you that something went wrong in your analysis - as logically log-likelihoods (or AICs) cant really be negative, well at least, not theoretically or 'technically speaking'. In practice, ... |
If the charge conjugation operator $\mathscr{C}$ changes a particle state into the corresponding anti-particle state then we must write $|\bar{K}^0\rangle=\mathscr{C}|K^0\rangle$. But instead, we write $|\bar{K}^0\rangle=\mathscr{CP}|K^0\rangle$ where $\mathscr{P}$ is the parity operator. $|K^0\rangle$ and $|\bar{K}^0\... |
This will be a talk for the Dartmouth Logic Seminar on January 23rd, 2014.
Abstract. I will discuss a number of theorems showing that the satisfaction relation of first-order logic is less absolute than might have been supposed. Two models of set theory can have the same natural numbers, for example, and the same stand... |
J. D. Hamkins, “Every countable model of set theory embeds into its own constructible universe,” J. Math. Logic, vol. 13, iss. 2, p. 1350006, 27, 2013.
@article {Hamkins2013:EveryCountableModelOfSetTheoryEmbedsIntoItsOwnL,
AUTHOR = {Hamkins, Joel David},
TITLE = {Every countable model of set theory embeds into its own
... |
Difference between revisions of "Kakeya problem"
(16 intermediate revisions by 4 users not shown) Line 1: Line 1: − +
'''Kakeya set''' <math></math> <math>\{\mathbb F}_3^n</math> that contains an [[algebraic line]] in every direction; that is, for every <math>d\in{\mathbb F}_3^n</math>, there exists <math>\in{\mathbb F... |
So I have a problem with finding theta. I can always see from where to where the theta is going. The problem occurs when calculating volumes. Sometimes in the solutions book, for the full circle
$$4\int_0^{\pi/2} \ d \theta$$
is used (sometimes $8$ instead of $4$) and sometimes
$$\int_0^{2\pi} \ d \theta$$
How can i be... |
I was just reading "Rare Earth" by Peter Ward and Donald Brownlee and they claim that $95\%$ of stars are less massive than the Sun. But, I was always told the Sun is an average star. Which is it?
The notion that the sun is an 'average' star, is a popular notion, not a scientific one. It is to my knowledge based on the... |
OpenCV 4.0.1
Open Source Computer Vision
In this tutorial you will learn:
To mention a few:
In this tutorial we will study the
corner features, specifically.
Consider a grayscale image \(I\). We are going to sweep a window \(w(x,y)\) (with displacements \(u\) in the x direction and \(v\) in the y direction) \(I\) and w... |
This is a problem in Tipler's
Modern Physics:
Laser pulses of femtosecond duration can be produced, but for such brief pulses it makes nosense to speak of the pulse’s color. To demonstrate this, compute the time duration of a laserpulse whose range of frequencies covers the entire visible spectrum ($4.0\times 10^{14}$ ... |
Hydejack offers a few additional features to markup your content. Don’t worry, these are merely CSS classes added with kramdown’s
{:...} syntax, so that your content remains compatible with other Jekyll themes.
Table of Contents A word on building speeds Adding a table of contents Adding message boxes Adding large text... |
Matrix inverse in mathematica
If $A$ is an invertible $n \times n$ matrix, then $A\cdot A^{-1} = I$.
To get this statement in Mathematica, you need the assumption
MatrixPower[A, 0] = IdentityMatrix[n]
$Assumptions = {Element[A, Matrices[{n, n}]], Det[A] != 0, ForAll[{A}, MatrixPower[A, 0] == IdentityMatrix[n]]}TensorEx... |
The concept of a “proliferating random walk” on a lattice is that at any time $ t \in \Bbb N \cup 0$ , there is some set consisting of at least one particle, each of which is on its own lattice point. When taking a time step, each particle also randomly decides whether to split into two particles, each of which moves t... |
Is it possible to have a planet that is both bigger than Earth and weaker in terms of gravity? I've got an idea about it being less dense, but I don't know what to do about its magnetic field. I need to know this because I desperately want to write a short story involving human-powered flight with artificial wings. To ... |
So much is known about hermitian and non-hermitian idempotents in a $C^*$-algebra, that someone must have written down the following.
TheoremThe universal $C^*$-algebra generated by one element $x$ subject to the relations $x^2=x$ and $ \| x \| \leq C$ is isomorphic to $$ \mathcal{I}_D= \left\{ f\in C\left([0,D],\mathb... |
Let $u,v\in W^{1,p}(\Omega )\cap L^\infty (\Omega )$, $p\in[1,\infty ]$. Then, $u,v\in W^{1,p}(\Omega )$ and $$\partial _i(uv)=u\partial _iv+v\partial _iu.$$
I have problem to understand the proof. Let $p\in [1,\infty )$ and let $D\subset \subset \Omega $ an open. Let $\rho_n$ ba a standard mollifier. Define for $n$ la... |
This is a crosspost of this question from MSE.
I'm confused about the definition of a projective family of probability spaces $(S_t,\mathscr S _t,\mu_t,f_{ts})_{s,t\in T}$. The conditions
$f_{tt}=1_{S_t}$ $f_{us}=f_{ts}\circ f_{ut}$ where $s\leq t\leq u$
are clear from the usual definition of a projective system as a f... |
So this problem basically has two parts. The answers so far have tried to answer the problems with evening heat out over the surface of the planet. I am working on a circulation model to do just that, but that is complicated and not ready. However, the other part of the problem is the question of insolation. How much s... |
Is there a topology $\tau$ on $\omega$ such that $(\omega,\tau)$ is Hausdorff and path-connected?
No, a path-connected Hausdorff space is arc-connected, whence it would be of (at least) continuum cardinality provided it has more than one point. This follows from a more general (and deep) result that a Peano space (a co... |
Suppose that we are given an exponential distribution model with a pdf $f(x,\theta) = \theta^{-1}\exp(-x/\theta)$ with an iid sample $X_1, ..., X_n$, and we would like to test hypothesis $H_0 : \theta = 1$ and $H_1 : \theta > 1$. We shall investigate the limiting distribution of the likelihood test statistic $2n(l_n (\... |
Often in BCS theory, people take the order parameter $\Delta$ to be real. I tried to construct a BCS theory with a real order parameter from the start and ran into some trouble. I'd be interested to see if anyone can point out why what I'm doing is wrong or why its a misguided idea in the first place (I have heard that... |
Factor investing is a broadly used approach in asset management, specially for the equity market, but, can we apply this idea in order to explain currency returns?
The idea at the core of factor investing is that there are different sources of risk in the market and that the exposure of the different assets to these so... |
Home
Integration by PartsIntegration by Parts
Examples
Integration by Parts with a definite integral
Going in Circles
Tricks of the Trade
Integrals of Trig FunctionsAntiderivatives of Basic Trigonometric Functions
Product of Sines and Cosines (mixed even and odd powers or only odd powers)
Product of Sines and Cosines (... |
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The pH of 0.1M0.1 M0.1M solution of NaHCO3NaHCO_3NaHCO3 (Given pK1=6.38pK_1 = 6.38 pK1=6.38 and pK2=10.32pK_2 =10.32 pK2=10.32 ) is
I have doubt in this question. Please type your method in solution.
Note by Megh Parikh 5 years, 5 months ago
Easy Math Editor
This... |
Is there a reference to literature where one explicitly constructs quantization of the free real scalar massless field in the 2-dimensional space-time? In particular, how the propagator looks like?
The 4d case is treated in many standard textbooks in QFT, but the 2d case seems to be different due to extra divergences w... |
There's actually a lot to potentially discuss here - let's go through it carefully.
Because of quantum effects, as you've shown in your bottom figure, there are discrete rotational and vibrational energy levels that a molecule may occupy. The vibrational levels are split further apart than the rotational levels. There ... |
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This examination was held 22 November,2015 conducted by IAPT (Indian Association of Physics Teachers).
Please leave your queries in the comments section below.
Note by Raven Herd 3 years, 10 months ago
Easy Math Editor
This discussion board is a place to discuss ... |
OpenCV 3.4.7
Open Source Computer Vision
In this tutorial, the basic concept of fuzzy transform is presented. You will learn:
The presented explanation demands knowledge of basic math. All related papers are cited and mostly accessible on https://www.researchgate.net/.
In the last years, the theory of F-transforms has ... |
Let $A$ and $B$ be two events and let $P(A|B)$ be the conditional probability of $A$ given that $B$ has occurred. Then Bayes' theorem states that: $$ P(B|A) = \displaystyle\frac{P(A|B)P(B)}{P(A|B)P(B)+ P(A|B^c)P(B^c)} $$
In other words, Bayes' theorem gives us the conditional probability of $B$ given that $A$ has occur... |
1) In this answer we provide more details for David Bar Moshe's correct answer. The action reads
$$\tag{1}S[q; t_i,t_f]~:=~\int_{t_i}^{t_f} \!dt~ L, \quad L~:=~T-V ,\quad T~:=~\frac{m}{2}\dot{q}^2,\quad V~:=~\frac{\alpha}{q^2}.$$
It is not hard to check that the action has an exact symmetry
$$\tag{2} S[q; t_i,t_f] \qua... |
Seven Problems in Equilateral Triangle Solution to Problem 1
Given an equilateral triangle $ABC$ with the base extended to twice its length: $AB'=AB.$ $B'E$ and $B'F$ are tangent to the circumcircle $(ABC).$
Prove that $EF$ passes through the midpoint $M$ of $AC.$
Solution
Join $B'$ to $C.$ By the construction, $AB'=AC... |
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PHYSICS LETTERS B, ISSN 0370-2693, 02/2014, Volume 729, Issue 370-2693, pp. 149 - 171
A search is performed for a massive new vector-like quark T, with charge 2/3, that i... |
Search response: 481 publications match your query. Listing starts with latest publication first: (7 - 8) MPP-2019-193 Measurements of inclusive and differential cross-sections of $t\bar{t}\gamma$ production in the $e\mkern-2mu\mu$ channel at 13 TeV with the ATLAS detector, The ATLAS collaboration, ATLAS-CONF-2019-042,... |
Modes
The term mode has varying meanings, according to the context, but the most common are permitted modes in amateur licensing.
Waves have three characteristics that can be changed, Amplitude, Frequency and Phase. A mode is the way of changing electromagnetic waves,
modulating them so that transmission of information... |
I'm sorry if this is a duplicate, but I can't seem to find the answer to this.
If $Z_t$ is a white noise process and $X_t$ satisfies
$$ \phi(B) X_t = \theta(B) Z_t $$
(where $B$ is the lag operator), then when is $X_t$ stationary?
If $\theta(z)$ and $\phi(z)$ have no common roots and $\phi(z)$ has a root with $|z| = 1 ... |
pepo wrote:
Bunuel wrote:
pepo wrote:
Great Post and thanks Bunuel for sharing it!
I have one question based on the following question: Example: If $20,000 is invested at 12% annual interest, compounded quarterly, what is the balance after 2 year? Solution: Balance=20,000∗(1+0.12/4)^2∗4=Balance=20,000∗(1+0.12/4)^2∗4= =... |
On model averaging the coefficients of linear models
“What model averaging does not mean is averaging parameter estimates, because parameters in different models have different meanings and should not be averaged, unless you are sure you are in a special case in which it is safe to do so.” – Richard McElreath, p. 196 o... |
Going off of the standard set up, we have $N$ observations and $P$ predictors stored in the data matrix $\mathbf{X} = \{ x_{i,j} \}$ for $i = 1, \ldots, N$ and $j = 1, \ldots, P$. The response is given by the vector $\mathbf{y} = (y_1, \ldots, y_n)$. The coefficients are given by $\beta_0$ (the intercept) and $\boldsym... |
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For each positive integer nnn, let an=2n+3n+6n−1a_n = 2^n + 3^n + 6^n - 1an=2n+3n+6n−1. Find all positive integers mmm where m<anm<a_nm<an such that gcd(m,an)=1gcd(m,a_n)=1gcd(m,an)=1 for all positive integers nnn.
Note by Sharky Kesa 3 years, 11 months ago
Easy ... |
The Mean Property of the Mean
Robert Muldoon (1921 - 1992), the erstwhile Prime Minister of New Zealand is reported to have said
New Zealanders who emigrate to Australia raise the IQ of both countries.
Might it really be possible?
Perhaps, not very surprisingly, the answer is Yes which is based on a simple property of ... |
A quick look at the primes in $\mathbb{Z}[i]$ suggests they might be evenly distributed by angle if we zoom out on a coarse enough scale.
I would like ask about the much weaker statement forgetting questions about angular bias.
Do all sectors $(\theta, \phi)$ have infinitely many primes $ \mathfrak{p} $?
The idea being... |
What is the exact use of the symbols $\partial$, $\delta$ and $\mathrm{d}$ in derivatives in physics? How are they different and when are they used? It would be nice to get that settled once and for all.
$$\frac{\partial y}{\partial x}, \frac{\delta y}{\delta x}, \frac{\mathrm{d} y}{\mathrm{d} x}$$
For what I know, $\m... |
Howto Raytracer: Ray / Sphere Intersection Theory
I will show you how to calculate the intersection point of a ray with a sphere.
A ray $$r(t)$$ can be represented by a point on the ray $$e$$ and the ray’s direction $$d$$. Any point on that ray can then be reached by walking $$t$$ times in the direction of $$d$$ from $... |
Suppose we release an object and make it fall on the surface of water, then the scatter of water is recorded,
Taking some observations, can we calculate the depth of the water by analyzing the scatter of water pattern?
Physics Stack Exchange is a question and answer site for active researchers, academics and students o... |
Difference between revisions of "Geometry and Topology Seminar"
m
(→Spring Abstracts)
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===Matthew Kahle (Ohio)===
===Matthew Kahle (Ohio)===
''TBA''
''TBA''
− + − + − −
== Archive of past Geometry seminars ==
== Archive of past Geometry seminars ==
Revision as of 12:18, 3 January 2014 Contents 1 Fall... |
Advances in Differential Equations Adv. Differential Equations Volume 4, Number 3 (1999), 413-456. Topological degree theories for densely defined mappings involving Operators of Type $(\mathrm{S}_+)^*$. Abstract
Let $X$ be a real separable reflexive Banach space with dual space $X^*.$ Assume that the operator $A:X\sup... |
If you are working in finance, you have almost surely heard of risk-reward ratios and probably used some of them to evaluate the performance of a stock, ETF, or any other investment strategy. Among the different alternatives, the most popular risk-reward ratio is the so-called Sharpe ratio, first introduced by William ... |
Here's a definition and a theorem.
Definition: A 2 point subset $\{\xi,\eta\} \subset \partial \mathbb{H}^2$ is called an axis endpoint pair if there exists an element of $\pi_1(S_g)$ having axis $L$ such that $\partial L = \{\xi,\eta\}$.
Theorem: The set of axis endpoint (ordered) pairs is dense in $\partial \mathbb{H... |
An even more compact defense of coefficient model averaging
The parameter that is averaged “needs to have the same meaning in all “models” for the equations to be straightforwardly interpretable; the coefficient of x1 in a regression of y on x1 is a different beast than the coefficient of x1 in a regression of y on x1 ... |
C.~D.~A.~Evans and J. D. Hamkins, “Transfinite game values in infinite chess,” Integers, vol. 14, p. Paper No.~G2, 36, 2014.
@ARTICLE{EvansHamkins2014:TransfiniteGameValuesInInfiniteChess,
AUTHOR = {C.~D.~A.~Evans and Joel David Hamkins},
TITLE = {Transfinite game values in infinite chess},
JOURNAL = {Integers},
FJOURN... |
Home
Integration by PartsIntegration by Parts
Examples
Integration by Parts with a definite integral
Going in Circles
Tricks of the Trade
Integrals of Trig FunctionsAntiderivatives of Basic Trigonometric Functions
Product of Sines and Cosines (mixed even and odd powers or only odd powers)
Product of Sines and Cosines (... |
Transient near tip fields in crack dynamics 40 Downloads Citations Abstract
Transient effects of stress-strain fields in the vicinity of a stationary crack tip under high rate loads are discussed. Exact analytical solutions to near tip stresses are compared to fields prescribed by leading terms (one or several) of Will... |
Have you read The Probabilistic Method by Joel Spencer and Noga Alon?
Although originally developed by Erdos, here's an example of the probabilistic method taken from combinatoricist Po-Shen Loh:
$A_1, \dots, A_s \subseteq \{ 1, 2, \dots, M \}$ such that $A_i \not \subset A_j$ and let $a_i = |A_i|$. Show that $$ \sum_{... |
The main problem with your circuit is that the time constant of 330 ohms and 1\$\mu\$F is only \$330\mu sec\$, which is not all that long, and the LED will not be especially bright for that brief time. You have to consider the physiological response of the human eye.
Your eye acts as a kind of integrator over a period ... |
Motivation
I know that in a
finite dimensional Euclidean space $\Bbb{E}^n$, for every basis $G=\{g_1,g_2,...,g_n\} \subset \Bbb{E}^n$ we can define a dual basis $G'=\{g^1,g^2,...,g^n\} \subset \Bbb{E}^n$ such that
$$g_i \cdot g^j = \delta_{i}^{j} \tag{1}$$
Also, it can be proved that such a basis exists and it is uniqu... |
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Global nonlinear optimization and optimal control for applications in pulp and paper industry
Dissertation
This work covers current problems of process simulation concerning energy efficiency in pulp and paper industry, discusses the numerical problems that arise from modeling with s... |
, EURASIP Journal on Advances in Signal Processing (2008), Article ID 258184.[21] SOUSA. R.—FERREIRA, A.—ALKU, P. : The Harmonic and Noise Information of the Glottal Pulses, Speech, Biomedical Signal Processing and Control 10 (2014), 137–143.[22] LECLERC, I.—DAJANI, H. R.—GIGUERE, C. : Differences in Shimmer Across For... |
This is a complicated question - it may be useful to add a diagram if you can, since each output and input to the pipe system will influence your question's answer, and by reading we may miss one.
The solution to problems like yours (where we know our requirements about the inputs and outputs of a pipe system) are ofte... |
The problem is to show that the random harmonic series
$X_n:=\sum_{n=1}^{\infty}\frac{\nu_n}{n}$ with $P[\nu_n = 1] = P[\nu_n = -1] = \frac{1}{2}$
converges.
It is obvious that the harmonic series diverges and the alternating harmonic series converges. Also I am positive that the random harmonic series converges almost... |
The basic idea is to take an affine cover $Y = \bigcup_{i} U_i$ and consider the induced affine cover $X = \bigcup_i V_i$ where $V_i = f^{-1}(U_i)$ (this only uses the affiness of $f$). Set $R_i = \mathcal{O}_X(V_i)$ and $S_i = \mathcal{O}_Y(U_i)$. We define for all $i$ an $R_i$-module $M_i$ by
$$M_i =\operatorname{Hom... |
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Journal of High Energy Physics, ISSN 1126-6708, 12/2014, Volume 2014, Issue 12, pp. 1 - 19
The Higgs boson may have decay channels that are not predicted by the Standard ... |
Home
Integration by PartsIntegration by Parts
Examples
Integration by Parts with a definite integral
Going in Circles
Tricks of the Trade
Integrals of Trig FunctionsAntiderivatives of Basic Trigonometric Functions
Product of Sines and Cosines (mixed even and odd powers or only odd powers)
Product of Sines and Cosines (... |
Asymmetric Propeller of Squares What Is This About?
Source
Problem
Given four similarly oriented squares that share a vertex: $APQ_aR_a,$ $BPQ_bR_b,$ $CPQ_cR_c,$ $DPQ_dR_d,$ consider the centroids $G_a,$ $G_b,$ $G_c,$ $G_d$ of triangles $APQ_d,$ $BPQ_a,$ $CPQ_b,$ $DPQ_c,$ respectively.
Prove that
$G_aG_c=G_bG_d$ and $G... |
Power of a Point Theorem
Given a point $P$ and a circle, pass two lines through $P$ that intersect the circle in points $A$ and $D$ and, respectively, $B$ and $C.$ Then $AP\cdot DP = BP\cdot CP.$
The point $P$ may lie either inside or outside the circle. The line through $A$ and $D$ (or that through $B$ and $C$ or both... |
This will be a talk for the CUNY Set Theory Seminar on November 6, 2015.
The Riemann rearrangement theorem states that a convergent real series $\sum_n a_n$ is absolutely convergent if and only if the value of the sum is invariant under all rearrangements $\sum_n a_{p(n)}$ by any permutation $p$ on the natural numbers;... |
How to linearize below LP problem :
\[ \max x_1 + x_2 + \ldots + x_n + y_1 + y_2 + \ldots + y_m\\ \text{s.t.}~ x_i + y_i \leq a_i ~\forall ~i \in N=M\\ x_1 + x_2 +..+ x_n \leq b_1\\ y_1 + y_2 +..+ y_m \leq b_2\\ x_1 + x_2 +..+ x_n + y_1 + y_2 +..+ y_m \leq b_3\\ x_1 * f_1/(x_1 + x_2 +..+ x_n) + .. + x_n * f_n/(x_1 + x_... |
In this paper, Guilherme França and André LeClair show that $$\gamma_{y}\sim 2 \pi \left(y-11/8\right)/W\left((y-11/8)e^{-1}\right)$$ where $W$ is the Lambert W function, and $\gamma_{y}$ is the imaginary part of the the $y$th non-trivial zero along the critical line. This formula can then be used in a similar way to G... |
Let $\phi$ be a scalar field, and $\Pi$ be the conjugate momentum of $\phi$. Let $\cal L=\cal L(\phi, \partial_\mu \phi)$ be the Lagrangian density.
Define the stress-energy tensor as $$ T^{\mu\nu}=\Pi^\mu \partial^\nu \phi - g^{\mu\nu}\cal L$$ and define $$ H=\int d^4\mathbf x (\Pi^0\partial^0 \phi - \cal L), \quad P^... |
Astrid the astronaut is floating in a grid. Each time she pushes off she keeps gliding until she collides with a solid wall, marked by a thicker line. From such a wall she can propel herself either parallel or perpendicular to the wall, but always travelling directly \(\leftarrow, \rightarrow, \uparrow, \downarrow\). F... |
Mercury (Hg) is a transition metal element that is unique because it is the only metal element that exist in a liquid form at room temperature. Due to this property, it is used in thermometers, barometers, gas-pressure regulators, electrodes, and electrical relays and switches.
Properties of Mercury
Atomic Number 80 Ma... |
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