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Background
Recently, I have been writing up some notes on derived functors and I came across the Eilenberg-Watts theorems [1], which essentially explain why it is hard to find derived functors besides Ext and Tor. Before asking my question, allow me to briefly state these theorems.
Let $R$ and $S$ be rings and $M$ and ... |
Before I’ll present the exposition of this theory, I’ll speak a little bit about the Mereological concept it is meant to catpure.
The idea is to work in Atomic General Extensional Mereology
“AGEM”, one can think of it easily as a theory about collections of atoms, where atoms are indivisible objects, i.e. objects that ... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
Impedance matching is tricky, but the role of a quarter wave transmission line is to map from one impedance to another. The actual impedance of the line will not match either the input or the output impedance - this is entirely expected.
However at a given frequency, when a correctly designed quarter wave line is inser... |
Step 1: Note down the given values
Step 2: Set up the formula for arc length.
NOTE: The formula is arc length= 2 \pi (r)(\frac{\theta }{360}) ,
where {\displaystyle r} equals the radius of the circle and {\displaystyle \theta } equals the measurement of the arc’s central angle, in degrees.
or
Arc length = r * \theta
St... |
Given my blog title, how have I gone this long without discussing triangle geometry? I will rectify this gross negligence in the next few weeks. Let’s begin with a seemingly impossible fact due to Frank Morley.
Start with a triangle
ABC, with any shape you wish. Now cut its angles into three equal parts, and extend the... |
Suppose we have the following experimental values for $\eta' \rightarrow \eta \pi \pi$ decay width:
$\Gamma_{\eta' \rightarrow \eta \pi^+ \pi^-} = 0.086 \pm 0.004$
$\Gamma_{\eta' \rightarrow \eta \pi^0 \pi^0} = 0.0430 \pm 0.0022$
We are investigating this decay in the isospin invariant limit and want to compare our res... |
I'm a high school student who never studied any relativity before, but I'm just wondering what was THE question that Einstein asked himself before going into this field. I knew he has done lots of work such as Brownian motion, photoelectric effect,etc. What was the question that baffled and therefore motivated him to w... |
As I was studying about sufficiency I came across your question because I also wanted to understand the intuition about From what I've gathered this is what I come up with (let me know what you think, if I made any mistakes, etc).
Let $X_1,\ldots,X_n$ be a random sample from a Poisson distribution with mean $\theta>0$.... |
I'm trying to reproduce Figure 2 from this paper. In summary, I have the regression model
$$Y \sim N(\mu, \sigma^2) \\ \mu = \alpha + \beta_1X_1 + \beta_2X_2 $$
The prior distributions for the parameters are
$$ \alpha, \beta_1 , \beta_2 \sim N(0, 10)\\ \sigma \sim \vert N(0, 1)\vert $$
The goal is to compute posterior ... |
This is an old revision of the document!
In this tutorial, we write an Alphabets program, starting from a mathematical equation for LU decomposition. Then we will generate code to execute the alphabets program, and test the generated code for correctness.
The equation for LU Decomposition, derived from first principles... |
Let's put the succinct answer by @TheAlmightyBob into an abstract model:
We want to model the labor market.
Markets' structure assumptions: goods market and labor markets are perfectly competitive. All participants are "too small" economically, and they cannot affect equilibrium price through their quantities demanded/... |
[This is the 6th post in the current series about Wythoff’s game: see posts #1, #2, #3, #4, and #5.
Caveat lector: this post is a bit more difficult than usual. Let me know what you think in the comments!]
Our only remaining task from last week was to prove the mysterious Covering Theorem: we must show that there is ex... |
The expansion of alcohol in a thermometer is one of many commonly encountered examples of
thermal expansion, which is the change in size or volume of a given system as its temperature changes. The most visible example is the expansion of hot air. When air is heated, it expands and becomes less dense than the surroundin... |
I am struggling with question about possible outcomes of momentum measurement and their probability. I know I can calculate it with momentum operator, but a wavefunction is of form
$$\psi (x)=3\cos\pi x+\cos3\pi x$$
and I am unsure how to deal with it, as the derivative consists of sines.
I know that $\cos{kx}=\frac{e^... |
$$ q \propto \Delta{T} $$
Heat is energy transferred due to a difference in temperature:
There are three modes of heat transfer:
In a general heating process, all modes of heat transfer may occur at the same time. A good example is the heating of a tin can of water by using a Bunsen burner:
The heat transferred by cond... |
Update: I went over this answer and clarified some parts. Most importantly I expanded the Forces section to connect better with the question.
I like your reasoning and you actually come to the right conclusions, so congratulations on that! But understanding the relation between forces and particles isn't that simple an... |
Here is a problem I don't even know how to approach: For arbitrary integers a,b,c which satisfy $(a,b)=(b,c)=1$ and $b>1$ there exist infinitely many integers n such that $ab^n+c$ is not prime. Any help with this problem will be appreciated.
closed as off-topic by Matthew Conroy, C. Falcon, Juniven, user91500, user2233... |
A
closed-loop transfer function in control theory is a mathematical expression ( algorithm) describing the net result of the effects of a closed ( feedback) loop on the input signal to the circuits enclosed by the loop. Overview [ edit ]
The closed-loop
transfer function is measured at the output. The output signal wav... |
So, this curiosity has arisen for a fun project I thought I'd tackle, where I'm attempting create a crude simulation of an internal combustion cylinder.
I wanted to explore the particle level interactions of a 4 step methane reaction, and see how they effect macroscopic properties like cylinder wall and force on the pi... |
I have a question regarding capacitor values within a power distribution system. Unfortunately I believe that I have to give a bit of background before I can ask this question.
As stated in both the forum post and the app note the physical geometry of a capacitor dictates the self-inductance. In the case of decoupling ... |
Let F be a field of characteristic $p > 0$. Let $g$ be a linear lie algebra, that is there exists a natural number $n$ such that $g \subset M_n(F)$. Does there exist a condition involving $n$ and $p$ such that $g$ is semisimple if and only if its killing form is non-degenerate?
The short answer is no. In prime characte... |
Learning Objectives
By the end of this section, you will be able to:
Calculate the Reynolds number for an object moving through a fluid. Explain whether the Reynolds number indicates laminar or turbulent flow. Describe the conditions under which an object has a terminal speed.
A moving object in a viscous fluid is equi... |
I was studying Pascal's Law which states(According to Wikipedia):-
Pascal's law is a principle in fluid mechanics that states that a pressure change occurring anywhere in a confined
"incompressible" fluid is transmitted throughout the fluid such that the same change occurs everywhere.
This principle is stated mathemati... |
The most elegant way I've seen to describe this is described in the paper The river model of black holes. If we write the Schwarzschild metric in Gullstrand-Painlevé coordinates we get (in units where $c = G = 1$):
$$ ds^2 = -dt_{ff}^2 + \left(dr + \beta dt_{ff} \right)^2 + r^2 d\Omega^2 $$
where:
$$ \beta = \sqrt{\fra... |
It seems me that there is a "difference" (at least apparently) in how the Belinfante-Rosenfeld tensor is thought of in section 7.4 of Volume 1 of Weinberg's QFT book and in section 2.5.1 of the conformal field theory book by di Francesco et. al.
I would be glad if someone can help reconcile the issue.
Schematically the... |
2-manifolds and inverse limits of set-valued functions on intervals
1.
University of Auckland, Private Bag 92019, Auckland, New Zealand
2.
University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom
Suppose for each $n\in\mathbb{N}$, $f_n \colon [0,1] \to ... |
Meshing Considerations for Linear Static Problems
In this blog entry, we introduce meshing considerations for linear static finite element problems. This is the first in a series of postings on meshing techniques that is meant to provide guidance on how to approach the meshing of your finite element model with confiden... |
Quadratic irrationality A root of a quadratic trinomial with rational coefficients which is irreducible over the field of rational numbers. A quadratic irrationality is representable in the form $a+b\sqrt{d}$, where $a$ and $b$ are rational numbers, $b\ne 0$, and $d$ is an integer which is not a perfect square. A real ... |
Please assume that this graph is a highly magnified section of the derivative of some function, say $F(x)$. Let's denote the derivative by $f(x)$.Let's denote the width of a sample by $h$ where $$h\rightarrow0$$Now, for finding the area under the curve between the bounds $a ~\& ~b $ we can a...
@Ultradark You can try d... |
I have a counting experiment:
Let's say I have N identical bees. I take one of them, expose it to $\gamma$-radiation and look if it has died or survives. If it survives, I count it as 1 count. If it dies, - 0 counts. I do that N times, until I run out of bees. I calculate the probability of death as:
$p=\frac{\sum_{i=1... |
In statistic, the Coefficient of variation formula or known as CV, also known as relative standard deviation (RSD) is a standardized measure of dispersion of a probability distribution or frequency distribution. When the value of coefficient of variation is lower, it means the data has less variability and high stabili... |
[This is the 6th post in the current series about Wythoff’s game: see posts #1, #2, #3, #4, and #5.
Caveat lector: this post is a bit more difficult than usual. Let me know what you think in the comments!]
Our only remaining task from last week was to prove the mysterious Covering Theorem: we must show that there is ex... |
Solving for Acceleration In Terms of Displacement
\[a= \frac{d^2 x}{dt^2}\]so it might appear that we have to integrate twice and require two condition or cannot solve.{/jatex}. How can we find an expression for the velocity?
If the acceleration is given in terms of the displacement, there is a way forward. We can use ... |
Today was another day of parallel talks. There was again six streams of talks where again the topics in each stream varied throughout the day. I would have loved to spend the day in the Higgs stream, listening to the new ATLAS, CMS, CDF and D0 results, however, I spent the day in the heavy flavour physics stream. This ... |
Last week we saw how to compute the area of a circle from first principles. What about spheres?
To compute the volume of a sphere, let’s show that a hemisphere (with radius \(r\)) has the same volume as the
vase shown in the figure below, formed by carving a cone from the circular cylinder with radius and height \(r\).... |
I'm making a 12V power distribution box, and it's my first time I work with high currents. This is for a boat, and the idea is to run low-power up to the switch panel and having the high-power cables as short as possible.
Simplified schematic:
Input on X1-1, F1 is a 25A fast acting fuse, K1 is a relay switch and finall... |
Informally, a signature scheme with message recovery is one where some or all of the message is embedded in the signature, allowing to conserve bandwidth when transmitting a signed message, compared to a signature scheme with appendix.
Total message recovery
A
[some sources make signature scheme with total message reco... |
FLoC 2018 Selected Talks Dependency Quantified Boolean Formulas
QBF PSPACE-complete DQBF Dependencies explicitly specified NEXPTIME-complete
Every \(\exists\) depends on all \(\forall\) before it.
Dependency Quantified Boolean Formulas
\(\forall x_1...\forall x_n \exists y_1(D_{y1}).. y_n(D_{yn}) : \phi \)
with \(D_{yi... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
Correcting an Important Goertzel Filter Misconception
Recently I was on the Signal Processing Stack Exchange web site (a question and answer site for DSP people) and I read a posted question regarding Goertzel filters [1]. One of the subscribers posted a reply to the question by pointing interested readers to a Wikiped... |
I am currently working on problem that I think could be expressed as an integer lattice problem.
Given $u \in \mathbb{R}^n$ and a
bounded integer lattice $L = \mathbb{Z}^n \cap [-M,M]^n$ I would like to find an integer vector $v \in L$ that minimizes the angle between $u$ and $v$. That is, I would like $$v \in \text{ar... |
Exponential Smoothing with a Wrinkle
Introduction
This is an article to hopefully give a better understanding to the Discrete Fourier Transform (DFT) by providing a set of preprocessing filters to improve the resolution of the DFT. Because of the exponential nature of sinusoidal functions, they have special mathematica... |
Event detail Analysis and PDE Seminar: Fredholm theory and the resolvent of the Laplacian near zero energy on asymptotically conic spaces
Seminar | February 5 | 4-5 p.m. | 740 Evans Hall
András Vasy, Stanford University
We consider geometric generalizations of Euclidean low energy resolvent estimates, such as estimates... |
I would like to generate correlated data draws across two unrelated distributions (or across two empirical datasets that are from unknown distributions). The correct way to do this is to use a copula. I'm not a copula expert.
Mechanically, my steps are as follows:
Do multivariate normal draws with a fixed correlated st... |
Attempted answers:
MD 1. \\(\Delta\\) is monotonic, because \\(a \leq b \to (a,a) \leq (b,b)\\), by definition of \\(\leq_{A\times A}\\)
MD 2. By the method in lecture 6, r(y,z) = least upper bound of X = \\(\\{x : \Delta (x) \leq (y,z) \\}\\). Since X is the set of elements of A less than min(y,z), r(y,z) is min(y,z).... |
For a continuous signal (function), we have Bernstein inequality : $$ |{df(t)}/dt| \le 2AB\pi $$ where $A=\sup|f(t)|$ and $B$ is the bandwidth of $f(t)$. The question is: is there a relationship for a discrete function $x[n]$ like this? $$ |x[n] -x[n-1] | \le\ \mu\ W $$ where $$ X[k] = \sum\limits_{n = 0}^{N - 1} {x[n]... |
There's a subtle issue here that is not mentioned in the question regarding estimation of the standard deviation of $\overline{x}$'s sampling distribution.
Suppose you have a sample from a population with mean $\mu$ and variance $\sigma^2$. When $\sigma^2$ is known, $${\rm SE}(\overline{x}) = \sigma/\sqrt{n}$$ is exact... |
With a similar reasoning as here, I might be able to give an answer to your question under certain conditions.
Let $x_{i}$ be your true value for the $i^{th}$ data point and $\hat{x}_{i}$ the estimated value. If we assume that the differences between the estimated and true values have
mean zero (i.e. the $\hat{x}_{i}$ ... |
It looks like the pivot is slightly displaced from the beam's center of mass. If the center of mass of the beam is displaced slightly below the pivot by some distance $D$, then just pick the pivot as the center of mass and calculate the torque from that small displacement as the angle of the beam changes. The force $g\... |
I am trying to Plot an integral equation that involves exponential function. My code is as follow,
L[\[Alpha]_] := NIntegrate[ 1/(k + I*0.1) ( Exp[I*k*x] (Exp[Sqrt[k^2 + \[Alpha]/w^2]*w] - 1) (Exp[k*w] - 1 + I*0.1) Sqrt[ k^2 + \[Alpha]/ w^2])/((Sqrt[k^2 + \[Alpha]/w^2] + k) (Exp[ Sqrt[k^2 + \[Alpha]/w^2]*w - Exp[k*w]])... |
This is a quite simple question: quarks do mix (through the CKM matrix), neutrinos do mix (through the PMNS matrix).
Then
why do charged leptons not mix?
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up.Sign up to join this... |
When we talk about the present-day number density of photons ($n_\gamma\approx 10^8 \:\mathrm m^{-3}$) in the universe do we mean the number density of CMB photons? I mean there are other sources of photons, for example, stellar or galactic sources. Are these photons included in $n_\gamma$ ?
Is it the same $n_\gamma$ w... |
Even before quantization, charged bosonic fields exhibit a certain "self-interaction". The body of this post demonstrates this fact, and the last paragraph asks the question.
Notation/ Lagrangians
Let me first provide the respective Lagrangians and elucidate the notation.
I am talking about complex scalar QED with the ... |
Please assume that this graph is a highly magnified section of the derivative of some function, say $F(x)$. Let's denote the derivative by $f(x)$.Let's denote the width of a sample by $h$ where $$h\rightarrow0$$Now, for finding the area under the curve between the bounds $a ~\& ~b $ we can a...
@Ultradark You can try d... |
Previous
abstract Next
abstract
Session 58 - Future of Antarctic Astrophysics.
Display session, Wednesday, June 10
Atlas Ballroom,
We report observations of the ^3P_1\rightarrow^3P_0 fine structure transition of neutral carbon ([C I], \lambda=609\ \mum) and the J=4\rightarrow3 rotational transition of CO (\lambda=652\ ... |
How many ways are there to fill a bag (maximum of weight $N$) with watermelons, apples, and grapes, where the number of apples has to be at least the number of watermelons? The weights are given as follows:
$\omega(watermelon) = 10$
$\omega(apple) = 2$
$\omega(grapes) = 1$
So far, I've tried creating the series for eac... |
What is the ratio of $\ce{MbO2/Mb}$ if the solution is saturated with air?
Details of the question: $$ \begin{align} \ce{Mb + O2 (aq) &-> MbO2}\\ \Delta G' &= -30.3~\mathrm{kJ/mol}\\ T &= 298~\mathrm{K}\\ \ce{pH} &= 7\\ \text{Henry's Constant for }\ce{O2} &= 42 \cdot 10^3~\mathrm{bar}\\ \text{Content of }\ce{O2}\text{ ... |
Part of your question is to find the threshold price of a crafted item that covers exactly its cost of production, especially when production is random. Once you know this threshold, the price you will ask to a buyer has to be greater than this threshold. Otherwise, you make losses.
Consider the craft of a precise item... |
Geometry is basically the study of different properties of point, line and plane.
Angles: Right angle: An angle of 90° is called a right angle. Acute angle: An angle of less than 90° is called an acute angle. Obtuse angle: An angle of greater than 90° is called an obtuse angle. Reflex angle: An angle of greater than 18... |
Assuming that you have a infinite long conducting cylindrical wire: Is it possible to let the magnetic field be constant inside the cavity and why?
Using Ampere's law
$$\nabla \times \mathbf H = \mathbf{J} + \frac{\partial \mathbf D}{\partial t}$$
and assuming to have steady-state condition ($\partial \over \partial t$... |
Well, let's try it, and see how hard it is to forge a message.Let's say for illustrative purposes that each character is a block, and that numbers represent the length indicator section. And let's start by putting the length indicator at the end. So,XXXXXXX7represents a 7-block message, with the '7' indicator at the en... |
Article
Keywords: Cesàro mean; Abel mean; growth order; uniformly continuous operator semi-group and cosine function
Summary: It will be proved that if $N$ is a bounded nilpotent operator on a Banach space $X$ of order $k+1$, where $k\geq 1$ is an integer, then the $\gamma$-th order Cesàro mean $C_{t}^{\gamma}:=\gamma ... |
I have an equation like this
$$-K(y)-\frac{\pi J}{2 \sqrt{\lambda }}+\frac{E(y)}{1-y}=0$$
1/(1 - y) EllipticE[y] - EllipticK[y] - (J π /(2 Sqrt[λ])) == 0
Where $E(y)$ and $K(y)$ are the Elliptic integrals in the Mathematica notation and $y$ is Real. I want to solve the equation numerically for $y$ for different values ... |
Power Series Expansion for Exponential Function Theorem
Let $\exp x$ be the exponential function.
Then:
\(\displaystyle \forall x \in \R: \ \ \) \(\displaystyle \exp x\) \(=\) \(\displaystyle \sum_{n \mathop = 0}^\infty \frac {x^n} {n!}\) \(\displaystyle \) \(=\) \(\displaystyle 1 + x + \frac {x^2} {2!} + \frac {x^3} {... |
Here is one solution:
Clearly Double-SAT belongs to ${\sf NP}$, since a NTM can decide Double-SAT as follows: On a Boolean input formula $\phi(x_1,\ldots,x_n)$, nondeterministically guess 2 assignments and verify whether both satisfy $\phi$.
To show that Double-SAT is ${\sf NP}$-Complete, we give a reduction from SAT t... |
Search
Now showing items 1-10 of 26
Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
Babbys first HoTT Note Curry-Howard correspondence and geometric semantics
syntax computation logic geometry $P$ type proposition space $x$ with $x:P$ term $x$ of type $P$ argument $x$ for proposition $P$ point $x$ of $P$ $\bf{0}$ empty type false proposition empty set ${\bf 1}$ type which does have one unique term tru... |
Does anyone here understand why he set the Velocity of Center Mass = 0 here? He keeps setting the Velocity of center mass , and acceleration of center mass(on other questions) to zero which i dont comprehend why?
@amanuel2 Yes, this is a conservation of momentum question. The initial momentum is zero, and since there a... |
The MathJax Processing Model¶
The purpose of MathJax is to bring the ability to include mathematics easily in web pages to as wide a range of browsers as possible. Authors can specify mathematics in a variety of formats (e.g., MathML or LaTeX), and MathJax provides high-quality mathematical typesetting even in those br... |
Given a forward rate, for example:$ F(t, T, T+\delta)$The instantaneous forward rate $f(t,T)$ fixed in $t$ is the limit when $\delta \rightarrow 0$ of your forward rate.If the relation between forward rate and zero coupon bond is:$F(t,T,T+\delta) = \frac{p(t,T) - p(t,T+\delta)}{\delta p(t,T+\delta)}$We have,\begin{equa... |
Typesetting and Converting Mathematics¶
There are two main uses for MathJax:
Typesetting all the mathematics within a web page, and Converting a string containing mathematics into another form.
In version 2, MathJax could perform the first function very well, but it was much harder to do the second. MathJax version 3 m... |
Terms sourced from: http://iupac.org/publications/pac/62/11/2167/
"Glossary of atmospheric chemistry terms (Recommendations 1990)", Calvert, J.G.,
Pure and Applied Chemistry 1990, 62(11), 2167
abatement absorbance \(A\)absorber absorption absorption coefficient absorption cross-section \(\sigma\)absorption line absorpt... |
The two biggest challenges of ACT Math are the time crunch—the math test has 60 questions in 60 minutes!—and the fact that the test doesn’t provide you with any formulas.
All the formulas and math knowledge for the ACT comes from what you’ve learned and memorized.
In this complete list of critical formulas you'll need ... |
In last week’s discussion of proofs by contradiction and nonconstructive proofs, we showed:
Theorem: There exist irrational numbers \(x\) and \(y\) with the property that \(x^y\) is rational.
However, our proof was
nonconstructive: it did not pinpoint explicit values for \(x\) and \(y\) that satisfy the condition, inst... |
Much in the fashion of a few problems already answered on Mathematica.SE
(1, 2), I am trying to solve the Laplace equation in velocity potential $\phi$ to simulate irrotational, inviscid flow over a cylinder (in Cartesian coordinates).
I find that my pressure field is flipped. i.e., at the front ($\theta$=0) the stagna... |
Let $E=\{A,B\}$ be a set and $X_{1,t}, X_{2,t}, X_{3,t}$ three independent Markov chains on the set $E$ with respective transition probability $P^{(1)}, P^{(2)}, P^{(3)}$ where $$P^{(i)}=\begin{bmatrix}p^{(i)} & 1-p^{(i)}\\ 1-p^{(i)} & p^{(i)} \end{bmatrix}$$
Let $P = P^{(1)}\otimes P^{(2)}\otimes P^{(3)}$ where $\otim... |
The following is adapted from an answer I gave to a similar but not identical question.
Let the position of the (unmoving) sun be $(S_x,S_y)$.
Drag this position to the origin. Let the current position of the planet be $(A_x,A_y)$. Our dragging procedure drags $(A_x,A_y)$ to $(A_x-S_x,A_y-S_y)$.
For simplicity of notat... |
The first cohomology of parabolic actions for some higher-rank abelian groups and representation theory
1.
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States
parabolicoperators. First, let $N$ be the upper-triangular group of $SL(2,\mathbb{C})$, $\Gamma$ any lattice a... |
1.Kathy buys a watch for Rs.500 and sells it to Jake for Rs.600. Find the profit percent.
a. 20%
b. 25%
c. 30%
d. 35%
Answer: A
Explanation:
Profit percent = $\dfrac{{sp - cp}}{{cp}} \times 100 = \dfrac{{600 - 500}}{{500}} \times 100$ = 20%
Profit percent = $\dfrac{{sp - cp}}{{cp}} \times 100
= \dfrac{{600 - 500}}{{500... |
Setting
The (sub-)circuit in question looks like this:
(Both OP amps can be considered as ideal.)
– Schematic created using CircuitLab
It's part of a larger question about an Ackerberg-Mossberg biquad (which looks like this) where one is asked to calculate
a) this subcircuits DC voltage gain \$A_{v,DC}=\frac{V_{out}}{V... |
Taken from Chapter 17 of Mas Colell "Microeconomic Theory"
Consider an exchange economy with two commodities and two consumers. Both consumers have homothetic preferences of the constant elasticity variety. Morover, the elasticity of substitution is the same for both consumers and is small (i.e. goods are close to perf... |
April 2010
"To a factor près": Cayley’s Partial Anticipation of the Weierstrass P-Function By: Adrian Rice arice4@rmc.edu Although Arthur Cayley is perhaps best remembered for his contributions to matrix algebra and group theory, one of his prime interests was the subject of elliptic functions, among the most vibrant a... |
This question already has an answer here:
\begin{equation*} U(x, y) = (ax^{-c} + by^{-c})^{-\frac{1}{c}} \end{equation*}
I ask this mainly because after logging both sides of the Utility equation (the first step to proving the assertion, I assume), I am left with:
\begin{equation*} \lim_{c \rightarrow 0} \dfrac{-\ln(ax... |
I'm basically just going to copy Matthew Doty's puzzles but with lexicographical order:
**Definiton.** The **lexicographical order** of two posets \\((A,\leq_A)\\) and \\((B,\leq_B)\\) is \\((A \times B, \leq^{lex})\\) where
$$
(a_1,b_1) \leq^{lex} (a_2,b_2) \Longleftrightarrow a_1 \lt_A a_2 \text{ or } (a_1 =_A a_2 \t... |
I have a question about the contents of this paper*, which links a building energy model and a utility-maximization component. In it, the author tests several electricity prices using a Cobb-Douglas utility function. As I understand, the C-D function ($U=X^\alpha*Y^\beta$) stipulates that $X=\frac{\alpha}{\alpha+\beta}... |
Inhalt des Dokuments Berliner Kolloquium Wahrscheinlichkeitstheorie und Seminar RTG 1845 Sommerstemester 2015
Datum Sprecher GK-Seminar 17:15-18:00 Sprecher Kolloquium (18:00-19:00) Ort 22. 4. 2015 (keiner, Ausstellung) Herbert Spohn (München) 17:15-18:15 U Potsdam Haus 8, Raum 0.58 6.5.2015 Maite Wilke Berenguer (TUB)... |
Fix an integer $k$. Let $X=G/P$ be a complex rational homogeneous variety. I assume here $G$ is a simply connected semi simple complex Lie group and $P=P_k$ is a maximal parabolic subgroup defined by dropping the $k$-th simple root (Assume we have chosen and fixed a Borel subgroup to avoid ambiguity, and we use Bourbak... |
Is it ever valid to include a two-way interaction in a model without including the main effects? What if your hypothesis is only about the interaction, do you still need to include the main effects?
In my experience, not only is it necessary to have all lower order effects in the model when they are connected to higher... |
Existence and non-existence results for variational higher order elliptic systems
Università degli Studi dell'Insubria, Dipartimento di Scienza e Alta Tecnologia, Via Valleggio 11, Como, 22100, Italy
$α ∈ \mathbb{N}$
$α ≥ 1$
$(-Δ)^{α} = -Δ((-Δ)^{α-1})$
$\begin{cases}\begin{aligned}(-Δ)^{α} u = H_v(u, v) \\(-Δ)^{α} v = ... |
Why does one consider the dual of the Steenrod algebra?
There are really two reasons, both of which are already alluded to in Eric Peterson's answer and in Pierre's answer.
Formally one can think about mod p cohomology as being a functor to the category of modules over the Steenrod Algebra. Similarly one can think abou... |
Difference between revisions of "Stiffened equation of state"
m (Added some internal links)
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The '''Stiffened equation of state''' is a simplified form of the Grüneisen equation of state <ref>[http://catalog.lanl.gov/F/
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The '''Stiffened equation of sta... |
I am teaching a Calculus class and we are finishing up power/Taylor series this week. The last section of the chapter is on applications, but the only ones listed there are approximating non-rational numbers like $\sqrt{1.02}$ and computing limits like $\lim_{x\to 0}\frac{\sin x}{x}$. I would like to find better exampl... |
as stated: why other assets' value can be determined by taking into consideration their expected cash flow (CF)? I read an argument which refers to arbitrage, but I wonder is there an additional simple argument from a theoretical point of view. thanks,
closed as unclear what you're asking by chollida, Bob Jansen♦ Apr 5... |
Difference between revisions of "Pole (of a function)"
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Revision as of 00:02, 30 April 2012
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An isolated singular point $a$ of single-... |
In the Hamilton-Jacobi equation, we take the partial time derivative of the action. But the action comes from integrating the Lagrangian over time, so time seems to just be a dummy variable here and hence I do not understand how we can partial differentiate $S$ with respect to time? A simple example would also be helpf... |
Every geometry textbook has formulas for the circumference (\(C = 2 \pi r\)) and area (\(A = \pi r^2\)) of a circle. But where do these come from? How can we prove them?
Well, the first is more a definition than a theorem: the number \(\pi\) is usually
defined as the ratio of a circle’s circumference to its diameter: \... |
Assume the amount of evidence against a defendant in a criminal trial is an exponential random variable $X$. If the defendant is innocent, then $X$ has mean $1$, and if the defendant is guilty, then $X$ has mean $2$. The defendant will be ruled guilty if $X>c$, where $c$ is a suitably chosen constant.
If the judge want... |
Typesetting and Converting Mathematics¶
There are two main uses for MathJax:
Typesetting all the mathematics within a web page, and Converting a string containing mathematics into another form.
In version 2, MathJax could perform the first function very well, but it was much harder to do the second. MathJax version 3 m... |
I am new in the field of signal processing. What's the different between Hamming and Hanning window? When we use the former and latter?
Max is right that the difference between Hamming and Hann windows are small. (BTW, I am a proponent of the movement to totally do away with them term
"Hanning". There is no Dr. Hanning... |
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