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Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
"Abstract: We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, insta... |
8.3.3.1 - Example: SAT Scores Example: SAT Scores Section
This example uses the dataset from Lesson 8.3.3 to walk through the five-step hypothesis testing procedure using the Minitab Express output.
Research question: Do students score differently on the SAT-Math and SAT-Verbal tests?
Because the sample size is large (... |
Munapo (2016, American Journal of Operations Research, http://dx.doi.org/10.4236/ajor.2016.61001) purports to have a proof that binary linear programming is solvable in polynomial time, and hence that P=NP.
Unsurprisingly, it does not really show this.
Its results are based on a convex quadratic approximation to the pr... |
Globally, there is Lakner and Milanovik (2015)'s elephant graph:Hellebrandt and Mauro (2015)Thus, the two previous distributions look like bimodal log-normal distributions.or CDFs, as in MacAskill's book Doing Good BetterDid not find something strictly related to wages. For most of people, income may be a good proxy of... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
In the comments, Charles Hudgins was kind enough to link me to Ying, J.H. Arch. Math (1973) 24: 561. This was a paper leading up to John Hsiao Ying's 1973 PhD thesis,
Relations between subgroups and quotient groups of finite groups. As far as I can tell, the thesis is not available online anywhere; however, I was recen... |
Please kindly refer to page 88 in the link below
$\oint_{S}\vec{E}\cdot d\vec{a}=\frac{Q_{enc}}{\epsilon_{0} }=\frac{\sigma A}{\epsilon _{0}}$
The pill box has an area vector $\vec{A}=\pm \hat{z}A$: "-" if the area A is facing in the negative z direction and "+" if the area A is facing in the positive z direction.
We k... |
Today we will advance our coverage toward quantum mechanics by looking at an unusual feature of daily life. We’ll be looking at an aspect of the world which doesn’t quite behave as expected; though it won’t be as counterintuitive as, say, the Heisenberg uncertainty relations, it does tend to make people blink a few tim... |
Sometimes it is possible to express a value of the $\Gamma$-function at a rational point through values of the $\Gamma$-function at rational points with smaller denominators, e.g. $$\Gamma\!\left(\tfrac{1}{10}\right)=\frac{\sqrt{5+\sqrt{5}}}{2^{7/10}\sqrt{\pi}}\Gamma\!\left(\tfrac{1}{5}\right)\Gamma\!\left(\tfrac{2}{5}... |
Simplify expression
Hi, I need to simplify the following.
\(\cos\left(3π+α\right) \)
I am unsure of the steps to take to do this.
Thanks
Quote:
$\displaystyle \cos(x+y)=\cos{x}\cos{y}-\sin{x}\sin{y}$
Sorry, I'm still unsure what you mean.
Do you mean...
\(\cos\left(3π+α\right)= \cos\left(3π\right)\cos\left(α\right)-\si... |
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 ... |
ä is in the extended latin block and n is in the basic latin block so there is a transition there, but you would have hoped \setTransitionsForLatin would have not inserted any code at that point as both those blocks are listed as part of the latin block, but apparently not.... — David Carlisle12 secs ago
@egreg you are... |
An electron has angular momentum. Shouldn't it also have angular velocity?
Ignoring the g-factor (just for the order of magnitude approximation) and the fact that an electron is not a sphere the electron's angular velocity should be around:
$$ \omega \approx \frac{\mu}{er^2} $$
or about 0.01 to 10^17 rad/s depending on... |
8.3.2 - Hypothesis Testing
Below are the procedures for conducting a hypothesis test for two paired means. This is often referred to as a "paired means \(t\) test," "dependent means \(t\) test," or "matched pairs \(t\) test."
Data must be paired. The difference between the two groups must be normally distributed in the... |
Study Radiofrequency Tissue Ablation Using Simulation
Radiofrequency tissue ablation is a medical procedure that uses targeted heat for a variety of medical purposes, including killing cancerous cells, shrinking collagen, and alleviating pain. The process involves applying mid- to high-frequency alternating current dir... |
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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... |
Hello,
I've a problem to calculate the Position of a pendulum as a function of theta.
For example: $\theta (t)$ is a function of time which returns the angle made by the pendulum at a particular instant wrt it's equilibrium Position.
So,
$$ T = \dfrac 12 m l^2 \dot \theta^2 $$$$ U = - mgl \cos \theta $$ $$ L(\theta, \d... |
last week in chemistry 43new preprints about chemistry in the last week chemRxivmost active server in chemistry in the last week most popular topics mentioned by preprints
How to Stay out of Trouble in RIXS Calculations Within the Equation-of-Motion
Coupled- Cluster Damped Response Theory Framework? Safe Hitchhiking in... |
When to Use the D86 Beam Width Measurement Method Introduction
Although the clip level method and the second moment method are the most popular methods of beam width measurement, other beam width measurement techniques such as the D86 method can be used with beam profiling cameras. Rather than using the 1D or 2D profile... |
The strings do not attach to the space-time manifold, they move around on it as a background. Option 1 is not right.
Option 2 is more like it, except that you are assuming that string theory as it is formulated in the string way builds up space-time from something more fundamental. This is not exactly true in the Polya... |
Given a 2D-curve arc $\mathscr{C}$, I would like to be able to easily compute a subset of $n$ points belonging to $\mathscr{C}$, so that the points are separated by equal-length curve arcs.
For that purpose, I'm trying to find a
convenient parametric representation of the curve $f : t \mapsto (x(t),y(t))$ (for my purpo... |
Disclaimer: I have no idea what is the state of the art in the environmental map sampling. In fact, I have very little knowledge about this topic. So this will not be complete answer but I will formulate the problem mathematically and analyze it. I do this mainly for myself, so I make it clear for my self but I hope th... |
It seems to me exaggerated to use the DCT here, because this is a deep theorem and the example is completely elementary.
To be more precise, I would say that it is, of course, a perfect solution
mathematically speaking, but perhaps not pedagogically speaking ...
Indeed, we have :
$$\forall x\in[0,1],\lim_{n\to\infty}f_... |
This is part of an old qual problem at my school.
Assume $\{f_n\}$ is a sequence of nonnegative continuous functions on $[0,1]$ such that $\lim_{n\to\infty}\int_0^1 f_n(x)dx=0$. Is it necessarily true that there are points $x_0\in[0,1]$ such that $\lim_{n\to\infty}f_n(x_0)=0$?
I think that there should be some $x_0$. M... |
If you’re looking for a high-quality essay then you found the right person to write it. I’ve been working as an essay writer for 4 years now, which places me in the best position to handle your project. I look forward to working with you on not just this project but on future projects too; so you can totally rely on wh... |
Uniqueness for the solution of semi-linear elliptic Neumann problems in $\mathbb R^3$
1.
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China, China
$\Delta_0 u-\lambda u+f(u)=0, u>0,\ $ in $\Omega,\quad \frac{\partial u}{\partial\nu}=0\ $ on $\partial\Omega$
where $\Omega$ is convex and $f(u)$ 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 ... |
The notation
Producer=Actor=Director is wrong. Besides that, neither
Π nor Actor(Film) Π has an attribute Producer(Produce)
Director. The first projection has only an attribute
Actor, the second projection has only an attribute
Producer.
In the second answer what is meant if you divide two relations that have the same ... |
A plank of length $L$ and mass $M$ is placed on the ground such that there is no friction between the plank and the ground. A small block with mass $m$ is placed on one side of the plank. Friction between block and plank is $\mu$. At point $t=0$ block has some velocity $v_0$. What is the minimal $v_0$ such that block c... |
In flat space we have $$\hat{p}_\mu=-i\hbar \partial_\mu . $$ Does this still hold in a curved spacetime (particularly Schwarzschild space)?
A short-ish answer to this : $\hat{p}_a = -i\hbar \partial_a$ is not appropriate for the momentum operator due to the fact that it is not self-adjoint. As a reminder, $\hat{p}$ is... |
Consider a set $S \subseteq \Sigma^n$ where $\Sigma$ is a finite alphabet and $p : \Sigma \rightarrow [0,1]$ is a probability function. Let $T$ be a tree leaf-labeled by the elements of $S$. Consider the following random process which labels the nodes of $T$ in a bottom-up order. Given an unlabeled node $x$ whose child... |
What you're getting at is the difference between a
vector space and an algebra over a field (see https://en.wikipedia.org/wiki/Algebra_over_a_field). I'll just assume our field is $\mathbb{R}$, the real numbers.
The set of vectors of length $n$ with entries in $\mathbb{R}$, which we might also think about as $n \times ... |
So the question states, Let $B = \{x = (x_1,x_2,x_3) \in \mathbb{R}^3: x_1^2 +x_2^2 +x_3^2 \leq 1 \}$ be the unit ball in $\mathbb{R}^3$. Compute the diameter of $B$ for each of the following metrics.
note: $diam(B) = \sup\{d(x,y): x,y \in B\}$
I know the diameter is 2 but I want to be able to do this in general for an... |
Let $F$ be a field of characteristic zero, $\overline{F}$ be the algebraic closure of $F$. Let $\zeta_n$ be a primitive $n$-th root of unity in $\overline{F}$. Then it is well-known that $F(\zeta_n)$ is a finite Galois extension of $F$.
Q. If $\sigma:F\rightarrow F$ is a field automorphism, then is it always possible t... |
Let $M$ be a smooth manifold.
(1) A subset $S$ of $M$ that with the subspace topology is a topological manifold (with or without boundary), together with a differential structure that makes the inclusion $\iota:S\rightarrow M$ a smooth embedding (that is, a smooth map with constant rank equal to the dimension of $S$), ... |
I've translated the following from my German textbook, so please correct me if there is something wrong or strange.
Definitions
Let $X$ be a set and $\mathfrak{T} \subseteq \mathcal{P}(X)$ with fits the following restrictions:
(i) $\emptyset, X \in \mathfrak{T}$
(ii) $\forall U_1, U_2 \in \mathfrak{T}: U_1 \cap U_2 \in... |
I usually need to draw graphs with multiple edges. I would really appreciate if someone can tell me how to write a multiple edge command which will allow me to write one line instead of repeatedly many. Say the name of my edge command is
\myedge[m] meaning that I will draw m edges between two nodes.
I want to use somet... |
Arithmetic Sequences
3, 7, 11, 15, 19
is an arithmetic sequence with 4 being added to each term to get the next term.
Given any arithmetic sequence we can find an expression for the
\[n\]th term. If
\[d\]is the number that is added each time (called the common difference) and
\[a\]is the first term, then the
\[n\]th te... |
I swear this was supposed to be Silly proofs three, but obviously my memories of having done two silly proofs are misleading.
This proof isn’t actually that silly. It’s a proof of the [tex]L^2[/tex] version of the Fourier inversion theorem.
We start by noting the following important result:
[tex]\int_{-\infty}^{\infty}... |
Indeed, you have lost some sort of uniqueness of dimension, but not between the vector and the spinor representation: The vector representation of $\mathrm{SO}(1,3)$ is irreducible, while the four-dimensional Dirac-spinor representation is not - it is the sum of a left-chiral and a right-chiral Weyl representation.
In ... |
Alpha
1. INTRODUCTION
Evaluating the return of an investment without proper accounting for risks taken does not make a lot of sense. Thus in asset management we take a
relative performance perspective comparing the return on investment to return on investment with similar risk. Alpha is the average return in excess of ... |
An easy calculation is to start with the solar constant, the power (energy per unit time) produced by solar radiation at a distance of one astronomical unit. This is 1.361 kilowatts per square meter. The surface area of the Earth is $4\pi R^2$, where $R$ is the radius of the Earth, while the cross section of the Earth ... |
Some useful discussion and links can be found on projectrho.com, I mentioned these in comments before the question was migrated but they were deleted in the migration, so I'll repost here. First of all, in the Space War page, at the top there are various links to posts on the "rocketpunk manifesto" blog which have good... |
I’ve had the following question for a while: How do I create a mapping of keys to values where the keys are regular expressions, and two regular expressions are considered equivalent if they correspond to the same language?
An example of why you might want to do this is e.g. when constructing a minimal deterministic fi... |
Let $N = {q^k}{n^2}$ be an odd perfect number given in Eulerian form (i.e., $q$ is prime with $\gcd(q,n)=1$ and $q \equiv k \equiv 1 \pmod 4$). (That is, $2N=\sigma(N)$ where $\sigma$ is the classical sum-of-divisors function.)
Since $\gcd(q^k,\sigma(q^k))=1$, it follows that $q \mid \sigma(n^2)$.
My question is this:
... |
Using the Ratio Test, I have to find whether $$ \sum_{n=1}^\infty \frac{\cos(n\pi/3)}{n!} $$ converges or diverges. The back of the book says that the sum is absolutely convergent.
My work:
$a_n = \dfrac{\cos(n\pi/3)}{n!}$, $a_{n+1} = \dfrac{\cos((n+1)\pi/3)}{(n+1)!}$
\begin{align} &\lim_{n\rightarrow \infty} \left|\fr... |
I have a two dimensional function represented by 3 data set
$f_i(\omega_i,\beta_i)=\psi_i$ such that $i \in [1,N]$
How can I do the following:
First interpolate to larger data points using Radial Basis Function but want to increase the interpolating points such $ g_k \equiv f_i $ with $ k \in [1,M] ; M > N $ Approximat... |
This is Velleman's exercise 3.5.4:
Suppose $A \cap C \subseteq B \cap C$ and $A \cup C\subseteq B \cup C$. Prove that $A \subseteq B$
This is the proof given by the book (which I understand completely):
Proof. Suppose x ∈ A. We now consider two cases:
Case 1. $x \in C$. Then $x ∈ A \cap C$, so since $A \cap C\subseteq ... |
CLAIM : Prove that LCM$(n/a , n/b) = n$ if $(a,b)=1$
let us assume the factorization of $n = p_1^{\alpha_1} p_2^{\alpha_2} \cdots p_k^{\alpha_k}$ and $a=q_1^{\beta_1} q_2^{\beta_2} \cdots q_k^{\beta_k}$$ and $ $b = r_1^{\gamma_1} r_2^{\gamma_2} \cdots p_k^{\gamma_k}$
Please note that both $a$ and $b$ divides $n$.
case ... |
Bayes’ Rule Section
Consider any two events
A and B. To find \(P(B|A)\), the probability that B occurs given that A has occurred, Bayes’ Rule states the following:
\(P(B|A) = \dfrac{P(A \text{ and } B)}{P(A)}\)
This says that the conditional probability is the probability that both
A and B occur divided by the uncondit... |
How to Use the Beam Envelopes Method for Wave Optics Simulations
In the wave optics field, it is difficult to simulate large optical systems in a way that rigorously solves Maxwell’s equation. This is because the waves that appear in the system need to be resolved by a sufficiently fine mesh. The beam envelopes method ... |
Discriminant analysis is a 7-step procedure.
Step 1: Collect training data T raining data are data with known group memberships. Here, we actually know which population contains each subject. For example, in the Swiss Bank Notes, we actually know which of these are genuine notes and which others are counterfeit example... |
Definition:Galois Connection Definition
Let $\left({S, \preceq}\right)$, $\left({T, \precsim}\right)$ be ordered sets.
Let $g: S \to T$, $d: T \to S$ be mappings.
Then $\left({g, d}\right)$ is Galois connection if and only if: $g$ and $d$ are increasing mappings and $\forall s \in S, t \in T: t \precsim g\left({s}\righ... |
I'm not strong with electrical engineering and I have prototyped a circuit which works; however, to my chagrin, I don't understand why.
I'm using an Arduino digital out pin to power a relay. I have an NPN transistor to switch 5 volts through the relay coil that's 125 ohm. At first, I just connected the base to the outp... |
hfe of a npn bjt transistor is given by collector current / base current so to calculate hfe you need to know the collector current and base current (which can be set using resistors) . I have to ask , what is the point of doing this ? You can simply calculate the emitter current using Kirchhoff current rule . This is ... |
We assume that in population \(\pi_{i}\) the probability density function of \(\boldsymbol{x}\) is multivariate normal with mean vector \(\boldsymbol{\mu}_{i}\) and variance-covariance matrix \(\Sigma\) (same for all populations). As a formula, this is...
\(f(\mathbf{x}|\pi_i) = \dfrac{1}{(2\pi)^{p/2}|\mathbf{\Sigma}|^... |
When an unknown specimen is classified according to any decision rule, there is always a possibility that the specimen is wrongly classified. This is unavoidable. This is part of the inherent uncertainty in any statistical procedure. One procedure to evaluate the discriminant rule is to classify the
training data accor... |
In order to compare $T$ and $W$, one needs to express one in terms of the other. As explained in the diagram itself, since the block is in translational equilibrium, we have:
$$\vec{T_1}+\vec{T_2}=\vec{W_b}$$
Projecting this relation onto the $Oy$ axis, the components of the tensions are both $T\sin\theta$ (because the... |
ok, suppose we have the set $U_1=[a,\frac{a+b}{2}) \cup (\frac{a+2}{2},b]$ where $a,b$ are rational. It is easy to see that there exists a countable cover which consists of intervals that converges towards, a,b and $\frac{a+b}{2}$. Therefore $U_1$ is not compact. Now we can construct $U_2$ by taking the midpoint of eac... |
Finite Subgroup Test/Proof 2 Theorem
Let $\struct {G, \circ}$ be a group.
Then: $H$ is a subgroup of $G$ $\forall a, b \in H: a \circ b \in H$ Proof Sufficient Condition
Let $H$ be a subgroup of $G$.
Then:
$\forall a, b \in H: a \circ b \in H$
by definition of subgroup.
$\Box$
Necessary Condition $\forall a, b \in H: a... |
Definition 28.35.1.reference Let f : X \to SWish Jersey Lakers Lakers Jersey be a morphism of schemes. Let \mathcal{L} be an invertible \mathcal{O}_ X-module. We say \mathcal{L} is
relatively ample, or f-relatively ample, or ample on X/S, or f-ample if f : X \to S is quasi-compact, and if for every affine open V \subse... |
Students T Processes
Student T Processes (STP) can be viewed as a generalization of Gaussian Processes, in GP models we use the multivariate normal distribution to model noisy observations of an unknown function. Likewise for STP models, we employ the multivariate student t distribution. Formally a student t process is... |
Pseudo-prime
Traditionally, a composite natural number $n$ is called a pseudo-prime if $2^{n-1} \equiv 1$ modulo $n$, for it has long been known that primes have this property: this is Fermat's little theorem. (The term is apparently due to D.H. Lehmer.) There are infinitely many such $n$, the first five being $$ 341,\... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
It would seem that one way of proving this would be to show the existence of non-algebraic numbers. Is there a simpler way to show this?
As Steve D. noted, a finite dimensional vector space over a countable field is necessarily countable: if $v_1,\ldots,v_n$ is a basis, then every vector in $V$ can be written uniquely ... |
The question is a little hard to define because, as pointed out in the comments, it's not clear what the "outside volume" is, or how to define it in curved space to compare it to regular space. Still, I think there is a sense in which the answer is "yes".
A regular sphere has area $A = 4 \pi R^2$ and volume $V = 4 \pi ... |
8.2.2.1 - Formulas
Earlier in this lesson we considered confidence intervals for proportions and the multiplier in our intervals was a value from the standard normal (i.e., \(z\)) distribution. But, what if our variable of interest is a quantitative variable and we want to estimate a population mean?
We apply similar t... |
Let's step back and ask what the determinant is and why it is useful. Then we'll get to this particular property.
Permit me to introduce a new product of vectors, called the
wedge product. If $a, b$ are vectors, then their wedge product is $a \wedge b$. The result is not a vector, but instead, we interpret it geometric... |
Suppose $1<p<\infty$ and $\Omega$ is an open bounded set in $\mathbb R^n$ with nice boundary (say Lipschitz or even better). Let $(f_j)_j \subset W^{1,p}(\Omega)$ s.t. $f_j \rightharpoonup f$ weakly in $W^{1,p}(\Omega)$.
Is it true that $f_j \to f$
stronglyin $L^p(\Omega)$?
For sure it is true that $f_j \rightharpoonup... |
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Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
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Now showing items 1-10 of 27
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 ... |
I am trying to understand proof of Prop. 5.1(page 64) from Fulton and Harris representation theory. I am unable to prove one statement in the proof. Which is
Let $V$ be an irreducible representation of a finite group $G$. Let $W$ be restriction of $V$ to a normal subgroup $H$ with index $2$. Now $W = W' \oplus W''$, wh... |
As pointed out in the comments, you certainly can't do this for
any dense linear order of cardinality $\kappa$. However, if $D$ is a dense linear order of cardinality $\kappa$ in which every interval has cardinality $\kappa$ (i.e. for all $a,b\in D$, $(a,b) = \{c\in D\mid a < c < b\}$ has cardinality $\kappa$), you can... |
Probably not.
After some more consideration, I'm less confident that the proposal could work. There are two reasons: No guarantee of focusing at any one point, and an inability to control the parameters of the lens.
1. A gravitational lens has no focal point.
The analogy to a traditional lens does eventually break down... |
Ratio of Densities of Planet Core and Mantle Problem
\[M\]and radius
\[R\]consists of two layers of material, each with a constant density. The core contains 60% of the planets mass, but has radius equal to 30% of the planets radius. The mantle constitutes the rest of the mass.
What is the ratio Density of Core: Densit... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
Keep in mind that existential and universal types are rather different.It is constructive logic, not classical logic andin constructive logic $\forall$ and $\exists$ are not as related as they are in classical logic.
$\forall x:A. B(x)$ is the type of programs that receive an object of type $A$ and return an object of ... |
I am using the definition in "Introduction to Smooth Manifolds" by Lee
Defn: Suppose $M$ is a smooth manifold. An embedded smooth manifold of $M$ is a subset $S\subset M$ which is a manifold in the subspace topology, endowed with a smooth structure with respect to which the inclusion map $i:S\to M$ is a smooth embeddin... |
Yesterday, I got a math problem as follows.
Determine with proof whether $\tan 1^\circ$ is an irrational or a rational number?
My solution (method A)
I solved it with the following ways.
I can prove that $\tan 3^\circ$ is an irrational, the proof will be given later because it takes much time to type.
Let's assume that... |
Where $\phi$ is the natural isomorphism yielding the adjunction and $\epsilon_A$ is the counit.
Could anyone explain why this diagram commutes?
Thanks very much!
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to ... |
Let $(X,d)$ be a compact, connected metric space. For every $\epsilon>0$ define an equivalence relation on $X$ by $x\sim_{\epsilon}y$ if and only if there exists a finite sequence $(x=x_0,x_1,\dots,x_n=y)$ such that $d(x_i,x_{i+1})<\epsilon$.
Note that the space is connected if and only if for every $\epsilon>0$, the $... |
While designing another problem I came up with the following question:
My guess is that the problem is not solvable (in the sense that one can construct multiple $h$ with the same $\alpha,\beta$ and $x$), but cannot see how to show this.
So far I gave the problem a try by splitting the angle and combining some trigonom... |
Central Tendency: The Mean Vector Section
Throughout this course, we’ll use the ordinary notations for the mean of a variable. That is, the symbol \(\mu\) is used to represent a (theoretical) population mean and the symbol \(\bar{x}\) is used to represent a sample mean computed from observed data. In the multivariate s... |
Dispersion: Variance, Standard Deviation Section Variance A variancemeasures the degree of spread (dispersion) in a variable’s values.
Theoretically, a
population variance is the average squared difference between a variable’s values and the mean for that variable. The population variance for variable \(X_j\) is Popula... |
A test statistic which has an F-distribution under the null hypothesis is called an F test. It is used to compare statistical models as per the data set provided or available. George W. Snedecor, in honour of Sir Ronald A. Fisher, termed this formula as F-test Formula.
F \; Value
\[\LARGE F \; Value \; = \; \frac{varia... |
I'm trying to prove the following theorem.
Theorem (Zero free region):
There exists $C>0$ such that $\sigma > 1-\frac{C}{log(\vert t \vert +4)}\Rightarrow \zeta(\sigma + i t)\neq 0$.
In the proof I have a problem with one of the arguments, namely:
If $0<\delta\leq 2$ then $\frac{-\zeta'}{\zeta}(1+\delta) = \frac{1}{1+\... |
Measures of Association: Covariance, Correlation Section
Association is concerned with how each variable is related to the other variable(s). In this case, the first measure that we will consider is the covariance between two variables
j and k.
The
population covariance is a measure of the association between pairs of ... |
Old Neural Net API
Warning
This API is deprecated since v1.4.2, users are advised to use the new neural stack API.
Feed-forward Network¶
To create a feedforward network we need three entities.
The training data (type parameter
D)
A data pipe which transforms the original data into a data structure that understood by th... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
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 ... |
* Make .ps file as normal
* Make a dummy .tex file doing the psfrag replacements, e.g.
Code: Select all
\documentclass{article}\usepackage{epsfig,psfrag}\pagestyle{empty}\begin{document}\begin{figure}\begin{center}\psfrag{CT}[][][1.2]{$l(l+1) C_l / 2\pi \mu K^2$}\psfrag{l}[][][1.2]{$l$}\psfig{figure=series_contribs.ps,... |
The following formula gives the critical coupling (more precisely the ratio of the spin-spin coupling over the temperature) for $O(n)$ models on a triangular lattice:
$$\text{e}^{-2K}=\frac{1}{\sqrt{2+\sqrt{2-n}}}$$
with $K=\beta J$
Numerically, it says that:
Ising model (n = 1) has $K \approx 0.27$
XY model (n=2) has ... |
tl;dr
The single particle density matrix is directly related to NEGF as shown here, I wish to find a way to relate NEGF also to density matrices which describe probability distribution of many body
states, such as those encountered by solving Liouville Von Neumann based equations for many body problems. General questio... |
I'm swimming in the ocean and there's a thunderstorm. Lightning bolts hit ships around me. Should I get out of the water?
In fresh water what makes lightening so dangerous to a swimmer is that most of the current travels on the surface of the water, so rather then getting a $1/r^2$ falloff in current density, you see a... |
Following this thread "Does a univariate random variable's mean always equal the integral of its quantile function?" I tried to do a similar thing for a conditional expectation. It seems like my stochastic skills are a bit rusty. For a continuous r.v. with support on the real line I think that it holds
$ E[X|X<q_\theta... |
The second matrix translates the eye [...]
You don't do that in a projection matrix. You do that with your view matrix:
Model (/Object) Matrix transforms an object into World Space View Matrix transforms all objects from world space to Eye (/Camera) Space (no projection so far!) Projection Matrix transforms from Eye Sp... |
This question comes from Georgi,
Lie Alegbras in Particle Physics. Consider the algebra generated by $\sigma_a\otimes1$ and $\sigma_a\otimes \eta_1$ where $\sigma_a$ and $\eta_1$ are Pauli matrices (so $a=1,2,3$). He claims this is "semisimple, but not simple". To me, that means we should look for an invariant subalgeb... |
Consider the stage game:
Let $\delta\in(0,1)$ be the discount factor. Let $G$ be the symmetric grim trigger strategy profile. The payoffs are then
$$E_{A}(G) = E_{B}(G) = \sum_{i=0}^{\infty}3\delta^{i} = \frac{3}{1-\delta}. $$
If a player were to defect from $G$ at time $n$, they would be playing $N$ at time $n$ and ev... |
I have the following question:
For the passive RC low pass filter shown below: $$V_S(t)=\cos(t)+\cos(100t)$$ $$V_0(t)=\alpha\cos(t+\theta)+\beta\cos(100t+\phi)$$
(where \$\alpha\$, \$\beta\$, \$\theta\$ and \$\phi\$ are constants)
The value of \$\displaystyle \left|\frac{\alpha}{\beta}\right|\$ is?
The answer is \$10\$... |
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