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I think that a good way to understand the Levi-Civita connection is to say that is is the Ehresmann connection in $TTM$ obtained from the linearization of the geodesic flow by a natural geometric construction.
I described this construction in my answer to this MO question, but I'll do so again with some improvements.
D... |
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 ... |
So I am simulating stock prices with what I believe to be geometric Brownian motion using parameters from the usual Black-Scholes framework (Please correct me if I am wrong) with the following formula:
$$S_{t} = S_{0}e^{(r-\delta -\frac{1}{2}\sigma^{2})t +z\sigma \sqrt{t}} ,$$
where St is the stock price at time t, r i... |
I'm trying to work through a self-made exercise, which may be ill formed as a question. Any general advice in dealing with these types of problems is also much appreciated!
I'm looking at a quantum gate $U_f$ for a function $f$, that has the effect $$\sum_x \alpha_x \vert x\rangle\vert 0\rangle \mapsto \sum_x \alpha_x\... |
Suppose that $\{\theta^1,\ldots,\theta^M\}$ is a $2\delta$-separated set contained in the space $\theta(\cP)$. Generate a r.v. $Z$ by the following procedure:
Sample $J$ uniformly from the index set $[M]={1,\ldots,M}$.
Given $J=j$, sample $Z\sim \bbP_{\theta^j}$.
Let $\bbQ$ denote the joint distribution of the pair $(Z... |
Yes, it has a lot to do with mass. Since deuterium has a higher mass than protium, simple Bohr theory tells us that the deuterium 1s electron will have a smaller orbital radius than the 1s electron orbiting the protium nucleus (see "Note" below for more detail on this point). The smaller orbital radius for the deuteriu... |
Dielectrophoretic Separation
How can you use an electric field to control the movement of electrically neutral particles? This may sound impossible, but in this blog entry, we will see that the phenomenon of dielectrophoresis (DEP) can do the trick. We will learn how DEP can be applied to particle separation and demons... |
Successor Ordinal A successor ordinal, by definition, is an ordinal $\alpha$ that is equal to $\beta + 1$ for some ordinal $\beta$.
The successor function, denoted as $\beta+1$, $\operatorname{suc} \beta$, or $\beta ^+$ is defined on the ordinals as $\beta \cup \{ \beta \}$
Properties of the successor
There are no ordi... |
I guess this is true, because log is a strictly increasing function, but how do I prove it formally?
I tried something like:
Let $f(n)$ and $g(n)$ be monotonically increasing functions, $c \in \mathbb{R}$ and $n_0 \in \mathbb{N}$, such that $0 \leq f(n) \leq c g(n)$, for all $n \geq n_0$. We must find $c'$ and $n_0'$ s... |
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Test (
Test
36% of 175g \(=36 \div 100 \times 175\) \(=63\)
\( 2. \frac {4} {9} - \frac {5} {12} \)
Times the left fraction by the right fractions denominator and then visa versa \( = \frac {48} {108} - \frac {45} {108} \) 150L increasedby 43 \(... |
$E = - \frac{\Delta V}{d}$ is derived from the definition of electric potential difference $\Delta V$. Pay careful attention to the negative signs in the derivation, as that is probably the source of most errors by beginning students.
Briefly, we imagine some distribution of fixed charged particles that produce a net e... |
26 0
Greetings helpful gentlemen and gentle women!
The following is a problem I ran into during my internship. The background of my problem is biological/chemical in nature, so I’ll try to bother you as little as possible with the details.
Thanks in advance for any help given.
I have a point p0 on a 2-dimensional surfa... |
Equivalence of Definitions of Factorial Contents Theorem
The
factorial of $n$ is defined inductively as: $n! = \begin{cases} 1 & : n = 0 \\ n \left({n - 1}\right)! & : n > 0 \end{cases}$
The
factorial of $n$ is defined as:
\(\displaystyle n!\) \(=\) \(\displaystyle \prod_{k \mathop = 1}^n k\) \(\displaystyle \) \(=\) \... |
The Nonparaxial Gaussian Beam Formula for Simulating Wave Optics
In a previous blog post, we discussed the paraxial Gaussian beam formula. Today, we’ll talk about a more accurate formulation for Gaussian beams, available as of version 5.3a of the COMSOL® software. This formulation based on a plane wave expansion can ha... |
Difference between revisions of "SageMath"
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=== Starting Sage Notebook Server throws an ImportError ===
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+ +
The Sage Not... |
This question already has an answer here:
Explanation: Simple Harmonic Motion 9 answers
How can you check whether the given expression shows simple harmonic motion or not?And also how to calculate angular frequency of the given equation?
Physics Stack Exchange is a question and answer site for active researchers, acade... |
It is proved that $\Pi^1_1$ -indescribability in $P_{\kappa}\lambda$ can be characterized by combinatorial properties without taking care of cofinality of $\lambda$ . We extend Carr's theorem proving that the hypothesis $\kappa$ is $2^{\lambda^{<\kappa}}$ -Shelah is rather stronger than $\kappa$ is $\lambda$ -supercomp... |
In the paper A Duality Web in 2+1 Dimensions and Condensed Matter Physics by Seiberg, Senthil, Wang, and Witten, they studied the particle-vortex dualities in $2+1$ dimensions.
On page 20, section 3.1, they considered phase transitions of the $2+1$ dimensional theory
$$\mathcal{L}=-\frac{1}{4e^{2}}f_{\mu\nu}f^{\mu\nu}+... |
Let me tell you about a fascinating paradox arising in certain infinitary two-player games of perfect information. The paradox, namely, is that there are games for which our judgement of who has a winning strategy or not depends on whether we insist that the players play according to a deterministic computable procedur... |
Learning Objectives
Systems manipulate signals. There are a few simple systems which will perform simple functions upon signals. Examples include amplification (or attenuation), time-reversal, delay, and differentiation/integration.
Systems manipulate signals, creating output signals derived from their inputs. Why the ... |
Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/125167
Title: Linearització conforme de punts fixos el·líptics Author: Camps Pallarès, Joan Maria Director/Tutor: Fagella Rabionet, Núria Keywords: Funcions holomorfes
Treballs de fi de grau
Sistemes dinàmics diferenciables
Teoria del p... |
The de Broglie wavelength is the wavelength, \(\lambda\), associated with a object and is related to its momentum and mass.
Introduction
In 1923, Louis de Broglie, a French physicist, proposed a hypothesis to explain the theory of the atomic structure. By using a series of substitution de Broglie hypothesizes particles... |
I propose a small modification of the parametrization for the torus that addresses issues with conformality. Try
F[t_, u_, r_] := {Cos[t] (r + Cos[u + Sin[u]/r]),
Sin[t] (r + Cos[u + Sin[u]/r]),
Sin[u + Sin[u]/r]}
instead. Next, we wish to choose suitable values for $m, n$ for a given $r$ such that the mapping of the r... |
N. Barton, A. E. Caicedo, G. Fuchs, J. D. Hamkins, and J. Reitz, “Inner-model reflection principles,” ArXiv e-prints, 2017. (manuscript under review)
@ARTICLE{BartonCaicedoFuchsHamkinsReitz:Inner-model-reflection-principles, author = {Neil Barton and Andr\'es Eduardo Caicedo and Gunter Fuchs and Joel David Hamkins and ... |
Rendezvous with Geostationary Destinations
Geostationary orbits are nontrivial to maintain. They are perturbed by non-round-earth forces represented by the J_{22} term in the spherical harmonics of the gravity field, forming attractors at 75 degrees east (above a point slightly east of the Maldives and south of India) ... |
Your question seems not well-posed to me. User reuns seems to interpret it as:
Let $K$ be
one fixed finite extension of $\Bbb Q_p$. If $f: K \rightarrow K$ is continuous, is there a continuous map $\hat{f}: \Bbb C_p \rightarrow K$ such that $\hat{f}_{\vert K} = f$?
and in his answer simultaneously restricts to the spec... |
Rendezvous with Geostationary Destinations
Geostationary orbits are nontrivial to maintain. They are perturbed by non-round-earth forces represented by the J_{22} term in the spherical harmonics of the gravity field, forming attractors at 75 degrees east (above a point slightly east of the Maldives and south of India) ... |
Given solely the first $n$ moments $m_1,\dots,m_n$ of a random variables $X\in\mathbb{R}$, I was wondering whether there exists a direct methodology to approximate $X$ with a Gaussian Mixture ?
The method of moments can always be used; I assume its properties for Gaussian mixture have been studied but I don’t know any ... |
Unitary constraints on charged pion photoproduction at large p⊥ Abstract
Around $$\theta_{\pi}=$$90$$^\circ$$, the coupling to the $$\rho^\circ N$$ channel leads to a good accounting of the charged pion exclusive photoproduction cross section in the energy range 3 < E
γ < 10 GeV, where experimental data exist. Starting... |
Rendezvous with Geostationary Destinations
Geostationary orbits are nontrivial to maintain. They are perturbed by non-round-earth forces represented by the J_{22} term in the spherical harmonics of the gravity field, forming attractors at 75 degrees east (above a point slightly east of the Maldives and south of India) ... |
We should find the Cauchy principal value integral of the form $$ I=\oint \frac{dz}{(z-z_1)(z-z_2)}~, $$ where both roots $z_1$ and $z_2$ lie on the contour path. My answer is: $$ I=a \left(-\oint \frac{dz}{z-z_1}+\oint \frac{dz}{z-z_2}\right)=a(-i\pi+i\pi)=0~, $$ where $a=1/(z_2-z_1)$. However, in a book, they do not ... |
This is a question in Treves.
Suppose $a>1$ and $\tau \in \mathbb R $,
(i) show that for all $(\tau, \xi) \in \mathbb R^{n+1}$, $|(\tau-ia)^2 - |\xi|^2| \ge(\tau ^2+|\xi|^2+a^2)^{1/2}$
(ii) show that if $k>n/2$,
$\iint [(\tau-ia)^2-|\xi|^2]^{-1}(1+a^2+(\tau-ia)^2+|\xi|^2)^{-k}\,d {\tau}\, d {\xi}\quad$
is bounded by a ... |
Prove or disprove the following statement: There exists a function whose Maclaurin series converges at only one point.
The best solution was submitted by Kook, Yun Bum (국윤범, 수리과학과 2015학번). Congratulations!
Here is his solution of problem 2017-21.
Alternative solutions were submitted by 민찬홍 (중앙대학교사범대학부속고등학교 3학년, +3), 채지... |
Joint work with Øystein Linnebo, University of Oslo.
J. D. Hamkins and Ø. Linnebo, “The modal logic of set-theoretic potentialism and the potentialist maximality principles,” to appear in Review of Symbolic Logic, 2018.
@ARTICLE{HamkinsLinnebo:Modal-logic-of-set-theoretic-potentialism, author = {Hamkins, Joel David and... |
Rendezvous with Geostationary Destinations
Geostationary orbits are nontrivial to maintain. They are perturbed by non-round-earth forces represented by the J_{22} term in the spherical harmonics of the gravity field, forming attractors at 75 degrees east (above a point slightly east of the Maldives and south of India) ... |
№ 9
All Issues Estimates for the best asymmetric approximations of asymmetric classes of functions Abstract
Asymptotically sharp estimates are obtained for the best $(\alpha, \beta)$ -approximations of the classes $W^r_{1; \gamma, \delta}$ with natural $r$ by algebraic polynomials in the mean.
English version (Springer... |
So in RBC and Ramsey-derived utility function, the following is usually the form of utility:
$$u(c,l) = c^{1-\sigma}(1 + \omega(l))$$
where $\omega(l)$ is arbitrary function of $l$, labor, that satisfies $u_c>0$, $u_l <0$, $u_{ll} \leq 0$ and $u_{cc} < 0$. $c$ is consumption.
In Mankiw/Rotemberg/Summers paper Intertemp... |
Rendezvous with Geostationary Destinations
Geostationary orbits are nontrivial to maintain. They are perturbed by non-round-earth forces represented by the J_{22} term in the spherical harmonics of the gravity field, forming attractors at 75 degrees east (above a point slightly east of the Maldives and south of India) ... |
Learning Outcomes Calculate and interpret the correlation coefficient
The correlation coefficient,
r, tells us about the strength and direction of the linear relationship between x and y. However, the reliability of the linear model also depends on how many observed data points are in the sample. We need to look at bot... |
Subramanian, CR and Furer, Martin and Madhavan, Veni CE (1998)
Algorithms for Coloring Semi-random Graphs. In: Random Structures and Algorithms, 13 (2). pp. 125-158.
PDF
page163.pdf
Restricted to Registered users only
Download (382kB) | Request a copy
Abstract
The graph coloring problem is to color a given graph with t... |
Rendezvous with Geostationary Destinations
Geostationary orbits are nontrivial to maintain. They are perturbed by non-round-earth forces represented by the J_{22} term in the spherical harmonics of the gravity field, forming attractors at 75 degrees east (above a point slightly east of the Maldives and south of India) ... |
I want it to be stable near $f(0) = 1$. Is there a nice function that does this already, like maybe a hyperbolic trig function or something like expm1, or should I just check if $x$ is near zero and then use a polynomial approximation?
Consider the Bernoulli numbers, defined by the recursive formula:
$$B_0=1$$
$$\sum_{... |
I have the following family of polynomials
$$ (p-1)(1-x^{2(n+1)}) - x(1-x^{2n}) = 0 $$
where $p\in\mathbb{R}$. By construction this polynomial has roots on the unit circle, and this is reflected in the fact that it is anti-palindromic. I can divide out two roots, $x=1,-1$ and get the following polynomial
$$ (p-1)x^{2n}... |
Let $\Phi: G \times M \rightarrow M$ be a group action on a symplectic manifold $M$ and $G$ be a Lie group. Furthermore, $x$ is a solution of the Hamilton equation $\dot{x}(t) = X_H(x(t))$ and for a any $t$ there is a $g(t) \in G_x:=\{g \in G; Ad^*_h(x)=x\}$ (here $x \in \mathfrak{g}^*$) such that $x(t) = \Phi(g(t),d(t... |
Euclid's proof is typically regarded as very weak, because it produces a density which is extremely thin. My question is how far the most obvious generalizations of Euclid's algorithms (for definiteness, algorithm E2) partially fix this problem. In particular, does E2 produce a smooth monotone $\pi(n)$ which asymptotic... |
kidzsearch.com > wiki Explore:images videos games
Function (mathematics)
In mathematics, a
function is a prescription that assigns to every object of one set an object of another (or the same) set. In many cases the objects are numbers. A function may be seen as producing an output - the assigned object -, when given a... |
Contents
There is very few documents on the Web and few books that explain the Perlin noise method in an intuitive way; but finding information on how to compute Perlin noise derivatives (especially in an analytical way) is even harder. Though, for those of you who don't know what these derivatives are and why they are... |
Rendezvous with Geostationary Destinations
Geostationary orbits are nontrivial to maintain. They are perturbed by non-round-earth forces represented by the J_{22} term in the spherical harmonics of the gravity field, forming attractors at 75 degrees east (above a point slightly east of the Maldives and south of India) ... |
Rendezvous with Geostationary Destinations
Geostationary orbits are nontrivial to maintain. They are perturbed by non-round-earth forces represented by the J_{22} term in the spherical harmonics of the gravity field, forming attractors at 75 degrees east (above a point slightly east of the Maldives and south of India) ... |
Difference between revisions of "Antenna Position"
(Created page with "== Obtaining ''u,v,w'' From An Antenna Array == A synthesis imaging radio instrument consists of a number of radio elements (radio dishes, dipoles, or other collectors of ra...")
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This vector difference in positions can point in a... |
I'll write $\longrightarrow$ for some standard iterations and $\implies$ for some possibly non-standard iterations. The relaxed Collatz conjecture is that for all $x$, $x \implies 1$. I'll call counterexamples to the conjecture
escapees.
First of all, since it's a good example of the notation, a lemma: for all $a$, $4 ... |
This situation pose a simple mathematical problem while the physical situation occurs in cases where a specific flow rate is required with a given pressure ratio (range) (this problem was considered by some to be somewhat complicated). The specific flow rate can be converted to entrance Mach number and this simplifies ... |
Notre Dame Journal of Formal Logic Notre Dame J. Formal Logic Volume 46, Number 1 (2005), 19-50. Definable Types Over Banach Spaces Abstract
We study connections between asymptotic structure in a Banach space and model theoretic properties of the space. We show that, in an asymptotic sense, a sequence $(x_n)$ in a Bana... |
If we have two sets $A$ and $B$ such that these two sets contain the same number of elements (the same
cardinal number or cardinality), then both these sets are equivalent. The order of listing is not important, e.g. $$\{a, b, c\} = \{b, a, c\}.$$ Nevertheless, they are not necessarily equal. A multiple of sets are equ... |
Elyase İskender posted in his blog an interesting plot correlating Professors Salary and Alumni Earnings Relation in US Universities. Is there a good way to establish causality here?Did the highest ...
Suppose I have a set of units $n_i, i = 1,...,N$. One unit was receiving a treatment $n_j = 1$ at times $t=1$ to $t=\t... |
Analyzing the Viscous and Thermal Damping of a MEMS Micromirror
Micromirrors have two key benefits: low power consumption and low manufacturing costs. For this reason, many industries use micromirrors for a wide range of MEMS applications. To save time and money when designing micromirrors, engineers can accurately acc... |
A regular hexagon inscribed in a circle has an area of $$54*3^\frac{1}{3} \text{sq.in}$$ Prove that the circumference of a circle is $$25\pi$$
closed as off-topic by Lord Shark the Unknown, Ewan Delanoy, WaveX, postmortes, Hans Lundmark Jun 24 at 6:18
This question appears to be off-topic. The users who voted to close ... |
Differentiable Function is Continuous
Jump to navigation Jump to search
Theorem
Let $x_0 \in I$ such that $f$ is differentiable at $x_0$.
Then $f$ is continuous at $x_0$. Proof
By hypothesis, $f' \left({x_0}\right)$ exists.
We have:
\(\displaystyle f \left({x}\right) - f \left({x_0}\right)\) \(=\) \(\displaystyle \frac... |
Is there an injective lattice homomorphism $\varphi: \text{Top}(\kappa)\to \text{Top}^{T_1}(\kappa)$?
The answer is Yes, there is such an embedding.
I will argue that if $\kappa$ is aninfinite cardinal, then there is a complete lattice embedding$\varphi: \text{Top}(\kappa)\to \text{Top}^{T_1}(\kappa\times\kappa)$.This ... |
Definition:Multiplication/Natural Numbers Contents Definition
Let $\N$ be the natural numbers.
Multiplication on $\N$ is the basic operation $\times$ everyone is familiar with.
For example:
$3 \times 4 = 12$ $13 \times 7 = 91$
The same holds for any construction of $\N$ in an ambient theory.
Let $+$ denote addition.
$\... |
Let me tell you about a fascinating paradox arising in certain infinitary two-player games of perfect information. The paradox, namely, is that there are games for which our judgement of who has a winning strategy or not depends on whether we insist that the players play according to a deterministic computable procedur... |
Compute $$\int_0^{\infty} \frac{e^{-ax}}{1+x^2}\,\,dx,\;\; a>0$$ using complex analysis.
but with no luck.
Edit The answers are great but lets keep this question open until someone maybe finds a way to solve this integral using complex analysis.
Mathematics Stack Exchange is a question and answer site for people studyi... |
Science Advisor
Gold Member
2,216 1,247 Summary Wigner's friend seems to lead to certainty in two complimentary contexts Summary:Wigner's friend seems to lead to certainty in two complimentary contexts
This is probably pretty dumb, but I was just thinking about Wigner's friend and wondering about the two contexts invol... |
If I have two functions in a convolution like
$$X*Y=1$$
$$X*Z=1$$
then it means (trivially) $Y=Z$.
Is this correct or are there subtleties in the convolution theorem where $Y=Z$ isn't always true?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related... |
The general trick to calculating such odds is that the probability of rolling a result that matches some criterion equals the number of possible matching rolls, divided by the total number of possible rolls.
(By "roll", here, we mean a sequence of numbers obtained by rolling a certain number (e.g. 6) of a certain kind ... |
A
rooted binary tree is a type of graph that is particularly ofinterest in some areas of computer science. A typical rooted binarytree is shown in figure 3.5.1.The root is the topmost vertex. The vertices below a vertex andconnected to it by an edge are the children of the vertex. It is abinary tree because all vertice... |
Bubble tower solutions of slightly supercritical elliptic equations and application in symmetric domains
1.
Laboratoire d’Analyse et de Mathématiques Appliquées, CNRS UMR 8050, Département de Mathématiques, Université Paris XII-Val de Marne, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France, France
2.
Departm... |
Problem:
There was a typo in the original statement. I fixed it now!!
Two runners start running (from the same point) in opposite directions along a circular path of radius $100\ m$ at a speed of $5\ m/s$. At what rate is the shortest distance between these two runners growing after $10$ seconds?
\
Here is my attempt:
... |
I see often that people have troubles with the rule of product in combinatorics. I also see often that people who claim to not have troubles with it and try to explain it to the aforementioned clueless people just end up saying "it's just a formula, don't worry about where it came from and why we do it, just memorize i... |
Why not look at Stasheff's original paper? He does give a point-set model (where $K_{n+2}$ is a compact convex semialgebraic subset of $\mathbb{R}^n$) and describes explicitly the substitution maps $\text{sub}_i: K_m \times K_n \to K_{m+n-1}$ which are collectively tantamount to the operad structure.
James Dillon Stash... |
Variable Importance in Random Forests can suffer from severe overfitting Predictive vs. interpretational overfitting
There appears to be broad consenus that random forests rarely suffer from “overfitting” which plagues many other models. (We define
overfitting as choosing a model flexibility which is too high for the d... |
I recently stumbled across the following statement:
If $G$ and $H$ are groups and $\phi : H \rightarrow G$ and $\psi : G \rightarrow H$ are homomorphisms with $\psi \circ \phi = Id_{H}$, then $G \approx H \oplus \ker \psi$. I believe I have a proof, but my proof relies on $G$ being Abelian. In the context I encountered... |
In the problem set 2 of Rubinsteins Microeconomics (btw is there a comparably nice written book on macroeconomics?) there is the following question: Let $\succ_n$ be the preference relations defined on $\mathbb{R}^2_+$ by the utility $x_1^n + x_2^n$. Let the preference relations $\succ$ be defined by the utility $\max\... |
How can I plot: $$\sum_{n=1}^{400}\frac1{n^3\sin^2(n)}$$ without using the Table function? I am looking for a plot similar to the discrete plot in
Mathematica. I am new to this software, I was able to complete the job with Maple and MATLAB but can't figure out how to do so in Mathematica. Thank you for any help!
$\text... |
Let $G$ be a complex affine reductive algebraic group, $B\subseteq G$ a Borel with maximal torus $T$ and unipotent radical $U$. Let $w\in\operatorname N_G(T)$ be a representative of the longest Weyl element. I am wondering whether the big open Bruhat cell $BwB\subseteq G$ is a principal open set, i.e. whether there is ... |
I have this very simple ODE-contrained optimization problem:
$h(x,x',p,t) = x'-A(p)x-b(p) = 0$, the constraint $g(x(0)) = x_0$, the initial condition with no parameters involved $F = \int (X-X_{obs})^2 dt$, the objective equation
According to adjoint method, I need to
Integrate constraint equation: $$x'=A(p)x+b(p)$$
In... |
First, you're taking the question backwards. Inertia is the default position. You shouldn't be looking for reasons not to switch, but for reasons to switch. If there are no strong reasons to switch, nobody will switch.Security is not a reason. Between SHA-2 and SHA3, there is no reason to believe that one is more secur... |
Introduction
The College Board releases a list of topics on the AP Physics Exam. In this study guide, I will be going over each one, including a potential problem that could come up.
Electrostatics Charge and Coulomb's Law Possible Problem
Three charges in a line. What's the force on the first one? When doing this, kee... |
Here are two interesting questions involving derivatives:
1. Suppose two different functions have the same derivative; what can you say about the relationship between the two functions?
2. Suppose you drive a car from toll booth on a toll road to another toll booth at an average speed of 70 miles per hour. What can be ... |
This is the third in a series of posts I’ve made recently concerning what I call the universal algorithm, which is a program that can in principle compute any function, if only you should run it in the right universe. Earlier, I had presented a few elementary proofs of this surprising theorem: see Every function can be... |
also, if you are in the US, the next time anything important publishing-related comes up, you can let your representatives know that you care about this and that you think the existing situation is appalling
@heather well, there's a spectrum
so, there's things like New Journal of Physics and Physical Review X
which are... |
Outline
Introduction
Derivation Example Conclusion References
Introduction
Hello! My name is Ryan Johnson! You might be wondering what a slecture is! A slecture is a student lecture that gives a brief overview about a particular topic! In this slecture, I will discuss the relationship between an original signal, x(t), ... |
The following equations are taken from Ravenna, walsh: "Optimal Monetary Policy with Unemployment and Sticky Prices" (2011).
(i)$$\frac{Z_{t}}{\mu_{t}} = w_t + \frac{\kappa}{q_{t}} - (1-\rho)E_{t}(\frac{1}{R_{t}})(\frac{\kappa}{q_{t+1}}) $$
(ii) $$ w_{t} = w^u + (\frac{b_t}{1-b_t})(\frac{\kappa}{q_t}) - (1-\rho)E_t(\fr... |
NP by definition is the class of decision problems solvable in polynomial-time on a non-deterministic Turing machine. So, by definition, NP is your $A$ set. NP can't also be $B$ for superficial reasons: NP is a subset of functions $2^*\to 2$, and so it simply doesn't contain any functions $2^*\to2^*$ whose output isn't... |
Introduction to the Classical Discrete Fourier transform:
The DFT transforms a sequence of $N$ complex numbers $\{\mathbf{x}_n\}:=x_0,x_1,x_2,...,x_{N-1}$ into another sequence of complex numbers $\{\mathbf{X}_k\}:=X_0,X_1,X_2,...$ which is defined by $$X_k=\sum_{n=0}^{N-1}x_n.e^{\pm\frac{2\pi i k n}{N}}$$ We might mul... |
tl;dr- Quantum computers can't really help us to simulate the whole universe as the universe is likely vastly more complex than even quantum mechanics can capture, plus we can't even begin to guess how big it is or many other basic fundamental features. In short, simulating the whole universe is beyond sci-fi.We can't ... |
The binomial coefficients count the subsets of a given set; the sets themselves are worth looking at. First some convenient notation:
Definition 1.7.1 Let $[n]=\{1,2,3,\ldots,n\}$. Then $\ds 2^{[n]}$ denotes the set of all subsets of $[n]$, and $\sbs{n}{k}$ denotes the set of subsets of $[n]$ of size $k$.
Example 1.7.2... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
I have an existing integration based on CSOM, which I need to move from one .NET solution to another. In the process, I was made aware that Microsoft now has a graph API. I’ve tried to research recommendations about whether to use the Graph API or CSOM, but I haven’t found documentation that I’d thought was quite defin... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
You’ve done some nice work in finding the Cartesian equation for the parabola, but it think it might be easier overall to work with the parametric form $\mathbf r:t\mapsto(x(t),y(t))$. (I’ve omitted most of the tedious details of the algebraic manipulations in the following.)
The first order of business is to find the ... |
If the degree $d=1$, then it's not true for $K_2$. Otherwise the graph is disconnected. Now assume $d \geq 2$.
If there is a bipartite graph with $\geq 2$ biconnected components then there is a bridge $e$. If we delete $e$, then we separate the graph into two disjoint components. Take one of these components and call i... |
What does it mean when the price elasticity of demand %Qd/%P is greater than one? Typically I hear that it means the demand is elastic since if, say, the price decreases by 1% the demand for the good increases by more than 1%. But what happens if %P is +1% and %Qd still increases by more? Sure, this is elastic, but doe... |
Answer
$-0.25$
Work Step by Step
The denominator can be expanded to 100... and the fraction is easily written as a decimal number $-\displaystyle \frac{1}{4}=-\frac{1\times 25}{4\times 25}=-\frac{25}{100}=-0.25$
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After you claim an an... |
Contents Ray-Tracing a Polygon Mesh
As we suggested before, ray-tracing a polygon mesh which has been triangulated is really simple. We already have a routine to compute the intersection of rays and triangles. Therefore, to test if a ray intersects a polygon mesh, all we need to do is loop over all the triangles in the... |
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The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
We have defined and used the concept of limit, primarily in our development of the derivative. Recall that $\ds \lim_{x\to a}f(x)=L$ is true if, in a precise sense, $f(x)$ gets closer and closer to $L$ as $x$ gets closer and closer to $a$. While some limits are easy to see, others take some ingenuity; in particular, th... |
Definition 3.3.1 A
partition of a positive integer $n$ is amultiset of positive integers that sum to $n$. We denote the number ofpartitions of $n$ by $p_n$.
Typically a partition is written as a sum, not explicitly as a multiset. Using the usual convention that an empty sum is 0, we say that $p_0=1$.
Example 3.3.2 The ... |
Suppose $\{ p_{k} \}$ is a collection of real numbers with the following properties:
1) $p_k \in (0,1)$ $~~~~$(i.e. $0$ and $1$ are not allowed values)
2) $\sum_{k=1}^{\infty} p_k =1$
An example of such a collection is $p_k := \frac{6}{\pi^2 k^2}$. You are free to choose any such collection in order to answer the follo... |
I would like to graphically show Bendixson’s criterion.
The Bendixson Criterion:
If $f_1$ and $f_2$ are continuous in a region $R$ which is simply-connected (i.e., without holes), and
$$\frac{\partial f_1}{\partial x_1}+\frac{\partial f_2}{\partial x_2}\ne0$$ at any point of $R$,
then the system
$$x_1' = f_1(x_1, x_2)$... |
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