text stringlengths 256 16.4k |
|---|
In Bishop's Pattern Recognition and Machine Learning, he states that exponential family distributions over $\mathbf{x}$ given parameters $\boldsymbol{\eta}$ can be written as $p(\mathbf{x} | \boldsymbol{\eta}) = h(\mathbf{x})g(\boldsymbol{\eta})\exp\{\boldsymbol{\eta}^\top\mathbf{u}(\mathbf{x})\}$.
He gives the natural... |
I find the Frobenius Method quite beautiful, and I would like to be able to apply it. In particular there are three questions in my text book that I have attempted. In each question my limited understanding has stopped me. Only one of these questions (the last) is assigned homework. The rest are examples I found intere... |
2019-09-04 12:06
Soft QCD and Central Exclusive Production at LHCb / Kucharczyk, Marcin (Polish Academy of Sciences (PL)) The LHCb detector, owing to its unique acceptance coverage $(2 < \eta < 5)$ and a precise track and vertex reconstruction, is a universal tool allowing the study of various aspects of electroweak an... |
Here are some thoughts about this question - but not a definitive answer: I don't believe a definitive answer exists.
In general, error propagation is founded on the assumption that the distribution of the errors is Gaussian, and that the error is small compared to the value of the quantity. In that case, a simple prop... |
No, it is not possible. In particular, consider that, were we to number the stakes from $0$ through $2015$ going evenly around the circle, then a string going from $a$ to $b$ is parallel to one going from $c$ to $d$ if and only if $a+b\equiv c+d\pmod{2016}$. This may be seen as there is a reflection taking stake $a$ to... |
2019-05-20 15:18 Detailed record - Similar records 2019-01-23 09:13
nuSTORM at CERN: Feasibility Study / Long, Kenneth Richard (Imperial College (GB)) The Neutrinos from Stored Muons, nuSTORM, facility has been designed to deliver a definitive neutrino-nucleus scattering programme using beams of $\bar{\nu}_e$ and $\bar... |
I'm want to do a recursive least square algorithm but I can't get it to work. If you don't know what recursive least square algorithm is. Well, it just ordinary least square, but it's an algorithm which works as online estimator for estimating a mathematical model, every iteration.
So let's say what we have a process $... |
Search
Now showing items 1-1 of 1
Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
When we go swimming, we feel a little weightless in the water. The reason for this is that liquids exert an upward force to objects submerged in them. This is known as thrust and is a consequence of the difference in pressure a liquid exerts at different heights. As we submerge an object (considering it is fully submer... |
Let us define the compound Poisson process $$Y_{N_t}=a+\sum_{n=1}^{N_t}X_n$$ where $X_n \sim f(x)$ such that $\langle X_n \rangle > 0$ $\forall n$ and $N_t$ is an independent Poisson random variable of parameter $\lambda t$. I want to study the survival probability above $0$ at infinite time $\mathbb{P}(Y_{N_t}\geq0, \... |
Answer
$W=135\ J$
Work Step by Step
We know that $W=\int \vec{F}\cdot d\vec{r}$. Thus, we find: $W = \int_0^3 cxydx+\int_0^6d dy$ $W = \int_0^3 cx(ax^2-bx)dx+6\times15$ $W=135\ J$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have
24 hours to sen... |
This question is cross-posted from math.stackexchange.com, where it did not (yet?) get any answers despite a +100 bounty.
Consider a wave equation $$\frac{\partial^2 u}{\partial t^2} = c(x)^2 \frac{\partial^2 u}{\partial x^2} \tag{1}$$ In frequency domain this becomes an ODE: $$-\omega^2 u = c(x)^2 \frac{\partial^2 u}{... |
Search
At this week's labs we will implement the AdaBoost algorithm. The AdaBoost algorithm takes a class of “weak” classifiers and boosts their performance by combining them together to a “strong” classifier with adaptive weights assigned to each of the weak classifiers (AdaBoost stands for “adaptive boosting”). This ... |
It looks like you're new here. If you want to get involved, click one of these buttons!
Isomorphisms are very important in mathematics, and we can no longer put off talking about them. Intuitively, two objects are 'isomorphic' if they look the same. Category theory makes this precise and shifts the emphasis to the 'iso... |
It looks like you're new here. If you want to get involved, click one of these buttons!
In this chapter we learned about left and right adjoints, and about joins and meets. At first they seemed like two rather different pairs of concepts. But then we learned some deep relationships between them. Briefly:
Left adjoints ... |
There are many words and sentences in mathematics that I basically completely don't understand, including the words "Koszul" and "derived". But rather than ask for a complete description of such words, I will ask about a particular example, and hope that an MOer can spell out concretely what's going on. (Of course, lin... |
Hello MO World
I'm working on a paper involving embedding your favourite measure-preserving transformation into a topological model (think Krieger generator theorem: embedding in a full shift) and have run into a question about entropy and Bowen balls.
Setup: $T$ is a homeomorphism from a compact metric space $X$ to it... |
Your clicks are coming from two sources. The wavetable and the hardware.
If you are looking to create a simple little instrument that produces tones by playing back a wavetable, then there is no way to fix the size of the "playback window" to reproduce tones without clicks.
The frequencies that compose the chromatic sc... |
In both cases, there appears to be a confusion of terminology between common and technical uses.
We commonly use methane and propane for cooking (and home heating), but not ethane. I would expect ethane to be suitable for this, being in between the two, but I've never heard of anyone using it for this purpose. Why is t... |
There exists a number of robust estimators of scale. A notable example is the median absolute deviation which relates to the standard deviation as $\sigma = \mathrm{MAD}\cdot1.4826$. In a Bayesian framework there exist a number of ways to robustly estimate the
location of a roughly normal distribution (say a Normal con... |
2019-09-20 08:41
Search for the $^{73}\mathrm{Ga}$ ground-state doublet splitting in the $\beta$ decay of $^{73}\mathrm{Zn}$ / Vedia, V (UCM, Madrid, Dept. Phys.) ; Paziy, V (UCM, Madrid, Dept. Phys.) ; Fraile, L M (UCM, Madrid, Dept. Phys.) ; Mach, H (UCM, Madrid, Dept. Phys. ; NCBJ, Swierk) ; Walters, W B (Maryland U... |
So we are calculating the loss
$$J(\theta) = -\frac{1}{T}\sum_{t=1}^T\sum_{-m \leq j \leq m} \log P(w_{t+j}|w_t;\theta)$$
and to do this we need to calculate
$$P(o|c) = \frac{\exp(u_o^Tv_c)}{\sum \exp(u_w^Tv_c)},$$
which is computationally inefficient. To solve this we could use the hierarchical softmax and construct a... |
$\newcommand{\real}{\mathbb R}\newcommand{\field}{\mathbb F}\newcommand{\cx}{\mathbb C}\newcommand{\ip}[2]{\left< #1,#2\right>}$We need to dive into mathematics of vector spaces and inner products in order to understand what a vector means and what is it mean to take a scalar product of two vectors. There is a long pos... |
There is a book of Byckling and Kajantie, "Particle kinematics", discussing in particular (Chapter V) the kinematics of the $2\to 3$ cross-sections. It can be easily found in internet. I just want to ask those who read it about the phase space evaluation.
I follow their idea of representing of the phase space $$ d\Phi_... |
So in your proposal, the balloons themselves provide only tensile strength. The resistance to compression comes from the pressure of the air inside the chambers. Let $R$ be the inside radius of the balloon shell, and let $a$ be the thickness of the shell. (So the outside radius is $R+a$.)
Now consider what happens when... |
I try to find a solution for this Problem: We should compare circular motion with uniform acceleration.
The Task is to find out whether it is better to make a turn if you face a wall in front of your car or to brake.Turn would mean a 90° turns so that you do not hit the wall. Another important information is that the v... |
Nice question/homework!
Stated in another way: $\mathsf{NP}$ is not closed under Cook reductions (assuming $\mathsf{P}\neq \mathsf{NP}$).
How about $\mathsf{NP}\cap\mathsf{coNP}$? Is $\mathsf{NP}\cap\mathsf{coNP}$ closed under Cook reductions? Is the only reason that $\mathsf{NP}$ is not closed under Cook reductions is... |
Category:Metric Subspaces
This category contains results about Metric Subspaces.
Let $\left({A, d}\right)$ be a metric space.
Let $H \subseteq A$.
Let $d_H: H \times H \to \R$ be the restriction $d \restriction_{H \times H}$ of $d$ to $H$.
That is, let $\forall x, y \in H: d_H \left({x, y}\right) = d \left({x, y}\right... |
Timeline of prime gap bounds
Date [math]\varpi[/math] or [math](\varpi,\delta)[/math] [math]k_0[/math] [math]H[/math] Comments Aug 10 2005 6 [EH] 16 [EH] ([Goldston-Pintz-Yildirim]) First bounded prime gap result (conditional on Elliott-Halberstam) May 14 2013 1/1,168 (Zhang) 3,500,000 (Zhang) 70,000,000 (Zhang) All su... |
I was going to post a comment(especially since it's an old question), but it became too long.That Application Note National AN-1852 (Which it located at TI now), describes in large detail the reasons for the inclusion of the op-amp to begin with.It provides two totally different services to the circuit.First it provide... |
Search
Now showing items 1-10 of 15
A free-floating planet candidate from the OGLE and KMTNet surveys
(2017)
Current microlensing surveys are sensitive to free-floating planets down to Earth-mass objects. All published microlensing events attributed to unbound planets were identified based on their short timescale (bel... |
Review Questions Review Questions User-defined functions
Q07.01 Write a function called
ft_to_in() which converts feet to inches. Note the conversion factor is 1 foot = 12 inches. Convert 6 feet into inches using your function.
Q07.02 Write a function called
m_to_ft() which converts meters to feet. Note the conversion ... |
Because you are dealing with normal-normal model, its not to hard to work out analytically whats going on. Now the standard argument for "diffuse" priors is usually $\frac{1}{\sigma}$ for variance parameters ("jeffreys" prior). But you will be able to see that if you were to use jeffreys prior for both parameters, you ... |
You look at ACF and PACFs of the differenced series. This is because these are tools for looking at
stationary processes. You mention that the undifferenced values have a mean increasing over time...right off the bat that process can't be stationary.
Looking at the ACF and PACF will help you distinguish between some so... |
To do this analysis, one needs data up to 20000 psi (1400 bars) on either enthalpy vs temperature and pressure (a graph) or compressibility factor Z vs temperature and pressure. The only graphs I have found of the former type go up to only 100 bars, which is a factor of 14 too low. However, I have found data on the com... |
Achieving desired tolerance of a Taylor polynomial on desired interval
This third question is usually the most difficult, since it requiresboth
estimates and adjustment of number of terms in theTaylor expansion: Given a function, given a fixed point, givenan interval around that fixed point, and given a required tolera... |
Your notation is pretty standard. The sign bit is obvious to anyone, so I won't address that further. The mantissa is in hidden-bit notation (the "1." is assumed, except in the unique case of an exact zero, which you didn't discuss.) The exponent is in the usual "excess" notation (some bias is added, so that a stored/p... |
It looks like you're new here. If you want to get involved, click one of these buttons!
Prove that the poset of upper sets on a discrete poset (see Example 1.25) on a set \(X\) is simply the power set \(P(X)\).
An upper set in P is a subset U of P satisfying the condition that if p ∈ U and p ≤ q, then q ∈ U.
Because in... |
Given two free semicirculars X_1 and X_2 and a projection h in the von-Neumann algebra generated by X_1, how does one show that the von-Neumann algebra generated by {X_1, hX_2(1-h)} is a factor? It is easy to show that the two elements in the generating set are free. But I am unable to see what kind of an object hX_2(1... |
I am interested in showing continuity/boundedness of the weak solution to the following problem pde:
\begin{align*} 0 &= \mathbf{q} + \mathbf{\nabla}u && \quad x\in \Omega,\\ 0 &= \mathbf{\nabla} \cdot \mathbf{q} && \quad x\in \Omega,\\ 0 &= u && \quad x\in \partial \Omega_D,\\ g &= \mathbf{q}\cdot \mathbf{\eta} &&\qua... |
Let's say we have a GARCH($1,1$) process specified as follows:
$y_t = \epsilon_t \sqrt h_t, \quad \epsilon_t \sim N(0,1) \quad \text{i.i.d.}$
$h_t = a_0 + a_1 y^2_{t-1} + b_1 h_{t-1}.$
If we were trying to estimate the parameters $\Theta = (a_0, a_1, b_1)$, and we have a sample $\{y_k\}^n_{k=1}$, would it make a differ... |
One thing to watch for, since you didn't clearly indicate it: the MLE is the maximum of the absolute values $|X_k|$, not simply the maximum of the $X_k$.
Taking the derivative of the log of this likelihood function isn't valid since it would lead to the conclusion that $\frac{-n}{2\theta} = 0$, which isn't helpful in f... |
I'm trying to calculate the probability current for a scattering problem. The potential is $V = V_0 > 0$ in $x>0$, with $E>V_0$
So I have in the region $x \le 0$:
$$\psi = \exp(ikx) + R \exp(-ikx)$$
And in $x>0$
$$\psi = T \exp(i \kappa x)$$
I am trying to calculate the probability current, $j = \frac{-ih}{2m} (\bar{\p... |
Let $f : \mathbb{S}^n \to \mathbb{S}^n$ be a continuous function.
From homology, the degree $\deg_1(f)$ of $f$ can be defined as the integer $n$ such that $f_* : x \mapsto n \cdot x$, where $f$ induces the morphism $f_* : \mathbb{Z} \simeq H_n(\mathbb{S}^n) \to \mathbb{Z} \simeq H_n(\mathbb{S}^n)$.
From topological deg... |
in nearly all code examples I've seen of a VAE, the loss functions are defined as follows (this is tensorflow code, but I've seen similar for theano, torch etc. It's also for a convnet, but that's also not too relevant, just affects the axes the sums are taken over):
# latent space loss. KL divergence between latent sp... |
I'm analysing classroom interaction data. I'm using a simple quantitative index counting the number of interactions of a certain kind. I want to know if it significantly changed between years 1 and 2, where I used method A to teach, and year 3, where I used method B.
I thus have $x_1$ and $x_2$ from the first two years... |
I need to understand a passage from a paper which I don't quite understand.
Let $M$ be a module over the ring $\mathbb C\{t\}$ of convergent power series. We want to show that $M$ is torsion-free, i.e., if $\psi(t)\cdot m = 0$ for some non-zero $\psi \in \mathbb C\{t\}$ then $m = 0$.
What the author is actually showing... |
Archive:
Subtopics:
Comments disabled
Wed, 18 Sep 2019
Suppose you have a bottle that contains !!N!! whole pills. Each day you select a pill at random from the bottle. If it is a whole pill you eat half and put the other half back in the bottle. If it is a half pill, you eat it. How many half-pills can you expect to ha... |
It looks like you're new here. If you want to get involved, click one of these buttons!
Isomorphisms are very important in mathematics, and we can no longer put off talking about them. Intuitively, two objects are 'isomorphic' if they look the same. Category theory makes this precise and shifts the emphasis to the 'iso... |
In this review, we present a couple of the more important Multivariable Calculus methods commonly used in STAT 414, mainly for Exam 4 and the Final Exam. While this is not a complete review, you should use this to refresh your memory and guide you to where you need to spend time reviewing. As always, practice is key!
F... |
Section 3.5.2 in
The Elements of Statistical Learning is useful because it puts PLS regression in the right context (of other regularization methods), but is indeed very brief, and leaves some important statements as exercises. In addition, it only considers a case of a univariate dependent variable $\mathbf y$.
The li... |
Here's a problem I need some help with:
Let $ f $ be a twice differentiable function in the closed interval $ [-1, 1] $ and $ f''(x) \geq 0 $ for all $ x \in [-1, 1] $. Show that $$ \int^1 _{-1} f(x)dx \geq 2f(0)$$
When does the equality hold?
There was a small hint given to apply the Mean Value Theorem and the fact th... |
Say $A$ is a square matrix over an algebraically closed field. Say $m$ is the minimal polynomial and $p$ is the characteristic polynomial.
Of course C-H implies that $m|p$. Conversely, if we can show $m|p$ then C-H follows; the question is whether one can give a "simple", "elementary" or "straightforward" proof that $m... |
Although the OP did not respond, I am answering this to showcase the method I proposed (and indicate what statistical intuition it may contain).
First, it is important to distinguish
on which entity is the constraint imposed. In a deterministic optimization setting, there is no such issue : there is no "true value", an... |
Gold Member
16 0
I'm reading through Lancaster & Blundell's
It seems to me that the energy of the harmonic oscillator in its "one-particle" state is ##\omega_0##, and the general energy (off the mass shell) is given by ##\omega## so that the position-space propagator would be given by $$G\left(x,y\right)=\int\frac{d^{4... |
Institute of Mathematical Statistics Lecture Notes - Monograph Series Multivariate sequential analysis with linear boundaries Abstract
Let $\{S_n=(X_n,W_n)\}_{n\ge0}$ be a random walk with $X_n\in\R$ and $W_n\in\R^m$. Let $\tau=\tau_a=\inf\{n:X_n>a\}$. The main results presented are two term asymptotic expansions for t... |
Math.SE report 2015-06
[ This page originally held the report for April2015, which has moved. It now containsthe report for June 2015. ]
Is “smarter than” a transitiverelationship?concerns a hypothetical "is smarter than" relation with thefollowing paradoxical-seeming property:
most X's are smarter than most Y's, but m... |
We know that $2^4 = 4^2$ and $(-2)^{-4} = (-4)^{-2}$. Is there another pair of integers $x, y$ ($x\neq y$) which satisfies the equality $x^y = y^x$?
This is a classic (and well known problem).
The general solution of $x^y = y^x$ is given by
$$\begin{align*}x &= (1+1/u)^u \\ y &= (1+1/u)^{u+1}\end{align*}$$
It can be sh... |
I know that this seems to be a pretty easy question but for some reason I can’t find any explanation for the following equation in any high school text book or on the internet.
So according to my answers sheet this equation is valid for the state of equilibrium of an object with the mass $m$ hanging on a metal spring.
... |
Some remarks on boundary operators of Bessel extensions
1.
Department of Statistics, University of Auckland, Private Bag 92019, Victoria Street West, Auckland 1142, New Zealand
2.
Department of Applied Mathematics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan
3.
National Center for Theoretical Sc... |
I tried to approach it from Leibniz formula for determinants
$$\det(A) = \sum_{\sigma \in S_n} \operatorname{sgn}(\sigma) \prod_{i=1}^n A_{i,\sigma_i}.$$
There are $n!$ factorial terms in this sum. Alice will have $\frac{n^2+1}{2}$ moves whereas Bob has $\frac{n^2-1}{2}$ moves. There are $n^2$ variables (matrix entries... |
Abel problem
To find, in a vertical plane $(s,\tau)$, a curve such that a material point moving along it under gravity from rest, starting from a point with ordinate $x$, will meet the $\tau$-axis after a time $T=f(x)$, where the function $f(x)$ is given in advance. The problem was posed by N.H. Abel in 1823, and its s... |
My question is as follows.
Do the Chern classes as defined by Grothendieck for smooth projective varieties coincide with the Chern classes as defined with the aid of invariant polynomials and connections on complex vector bundles (when the ground field is $\mathbf{C}$)?
I suppose GAGA is involved here. Could anybody gi... |
In the theory of electromagnetism (EM), why is the principle of superposition true? Can we read it off from Maxwell's equations directly?
Does it have any limit of applicability or is it a fundamental property of nature?
The principle of superposition comes from the fact that equations you solve most of the time are ma... |
My variable is alpha, \( \alpha \), but I defined it as
al_phasince Maxima doesn't like variables that are already defined and many of those are Greek variables. I just broke it up phonetically. I set alpha to be a constant by
al_pha: 30*%pi/180
(I think using just "pi" works too. It does, it just leaves it in symbolic... |
Archive:
Subtopics:
Comments disabled
Wed, 15 Nov 2017
[ Credit where it is due: This was entirely Darius Bacon's idea. ]
In connection with “Recognizing when two arithmetic expressions are essentially the same”, I had several conversations with people about ways to normalize numeric expressions. In that article I obse... |
so I found out that SR-71 Blackbird is using what's called "turboramjet" and I find the idea a bit appealing since they say with such engine, the Blackbird is more fuel efficient at it's top speed. I know that the mechanism for such engine is extremely complicated, but what's on my mind is not making an engine like Bla... |
Partial Answer
The trick that usually solves this type of challenging problems is finding an invariant.
First, let us say $(i,j)$ represents the $j$th space in the $i$th row. We say the $i$th row is the one with $i-1$ spots.
We should label each cell with a number. For any given position, we can sum the values of each ... |
Question:
When $\pu{60 g}$ of $\ce{C60}$ is combusted in a bomb calorimeter that has a water jacket containing $\pu{300.0 g}$ of water, the temperature of the water increases by $\pu{10 ^\circ C}$. Assuming that the specific heat of water is $\pu{4.18 J g^{-1} K^{-1}}$, estimate $\Delta E$ of combustion per mole of $\c... |
My textbook, Gettys's
Physics (Italian language edition), says that the Lorenz gauge choice uses the magnetic vector potential $$\mathbf{A}(\mathbf{x},t):=\frac{\mu_0}{4\pi}\int \frac{\mathbf{J}(\mathbf{y},t-c^{-1}\|\mathbf{x}-\mathbf{y}\|)}{\|\mathbf{x}-\mathbf{y}\|}d^3y $$ which is said to be such that$$\nabla^2\math... |
Orthogonal Vectors
Two vectors,
xand y, are orthogonalif their dot product is zero.
For example
\[ e \cdot f = \begin{pmatrix} 2 & 5 & 4 \end{pmatrix} * \begin{pmatrix} 4 \\ -2 \\ 5 \end{pmatrix} = 2*4 + (5)*(-2) + 4*5 = 8-10+20 = 22\]
Vectors
e and f are not orthogonal.
\[ g \cdot h = \begin{pmatrix} 2 & 3 & -2 \end{p... |
Definition:Cardinality Contents 1 Definition 2 Cardinality of Natural Numbers 3 Also defined as 4 Also known as 5 Examples 6 Also see 7 Sources Definition
The
cardinality of a set $S$ is written $\card S$.
Let $S$ be a finite set.
The
cardinality $\card S$ of $S$ is the number of elements in $S$.
That is, if:
$S \sim \... |
User talk:WikiSysop Contents 1 Test external Link 29th January 2015 2 Test Copy&Paste HTML 3 Test Asymptote 3.1 Test January 12th 2015 3.2 Tests November 1th 3.3 Tests November 17th 3.4 Tests November 4th 3.5 Tests October 27th 3.6 Previous tests 4 Test Cite Extension 5 Test MathJax 6 Pages A-Z 7 Recent Changes Test ex... |
Search
Now showing items 1-10 of 24
Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
Search
Now showing items 1-1 of 1
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 ... |
We have SampleLeft function in lattice trapdoors as
Algorithm $\textbf{SampleLeft}(A,M_1,T_A,u,\sigma)$:
$\textbf{Input}$: a rank $n$ matrix $A$ in $\mathbb{Z}^{n×m}_q$ and a matrix $M_1$ in $\mathbb{Z}^{n×m_1}_q$ , a “short” basis $T_A$ of $\Lambda^{\perp}_q(A)$ and a vector $u \in \mathbb{Z}^n_q$, a gaussian paramete... |
Let $(X, \mathcal{A}, \mu)$ be a measurable space, $(f_n)$ a sequence of integrable functions that converges in measure to some integrable function $f$. Assume further that there is some $g : X \rightarrow [0,\infty]$ integrable such that $|f_n|\leq g$ and $|f|\leq g$. Then $(f_n) \rightarrow f$ in mean.
I am not sure ... |
I'm trying to implement an equation into a programming language which doesn't have functions for integrals. However as it's many years since I've had any math exercise I'm having some trouble understanding how I can simplify the following equation.
$$\mathrm{erf}(x) = \frac{1}{\sqrt{\pi}} \int_{-x}^x e^{-t^2} dt.$$
As ... |
I am reading thorugh some topological definitions, in my book it is stated that $id_M:(M,\tau_d)\rightarrow(M,\tau_h),x\rightarrow x$ is a Homeomorphism where
$(M,d)$ is a metric space, $h(x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric $h$ on $M$.
A Homeomorphism between topological spaces is a map which is bijective, conti... |
In a recent research paper, I formalised some of my theorems in the proof assistant Isabelle, but left some of them as just proved 'by hand'. I found it helpful to use a different 'QED' symbol depending on which method I had used. Below is an enlarged version of the 'three cubes' symbol in the snippet… Continue reading... |
We know thatif $\lim\limits_{x\rightarrow a}{y(x)}=a$ and $\lim\limits_{x\rightarrow a}{w(x)}=b$ then $\lim\limits_{x\rightarrow a}{\left(y(x)\times w(x)\right)}=ab$
Now $\lim\limits_{x\rightarrow \infty}{\dfrac1{f(x)}}=m$ (as $m$ is non-zero)
Consider functions $y(x)=\dfrac{1}{f(x)}$ and $w(x)=f(x)\times g(x)$. Now as... |
The conditional variational principle for maps with the pseudo-orbit tracing property
1.
School of Mathematical Sciences, Anhui University, Hefei 230601, Anhui, China
2.
School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210023, Jiangsu, China
3.
Center of Nonlinear Science... |
what does it mean by becoming extensional in the first place?
The axiom of extensionality relates to what it means for two functions to be equal. Specifically, extensionality says:
$f = g \iff \forall x \ldotp f(x) = g(x)$
That is, functions are equal if they map equal inputs to equal outputs. By this definition, quick... |
This question is based on two answers I saw. I want to know if my reasoning is correct in each case. For me, $A$ is always a commutative ring with $1 \ne 0$.
In the first answer this proposition was given:
Let $f_1,\dots,f_t\in A[X]$ be nonzero. If there is $0 \ne g\in A[X]$ such that $gf_1=\cdots=gf_t=0$, then there i... |
Using Green's theorem to find area
Typically we use Green's theorem as an alternative way to calculate a line integral $\dlint$. If, for example, we are in two dimension, $\dlc$ is a simple closed curve, and $\dlvf(x,y)$ is defined everywhere inside $\dlc$, we can use Green's theorem to convert the line integral into t... |
Basic integration formulas
The fundamental
use of integration is as a continuousversion of summing. But, paradoxically, often integrals are computed by viewing integration as essentially an inverse operation to differentiation. (That fact is the so-called Fundamental Theorem of Calculus.)
The notation, which we're stuc... |
I'm currently looking into survival analysis regression models and can't quite wrap my head around the following:
Say I want to model time to occurrence of a cardiovascular event and use age (as opposed to follow-up time) as the underlying time scale. It seems clear to me that it doesn't make sense to include age as a ... |
Population and Parameters Section Population A populationis any large collection of objects or individuals, such as Americans, students, or trees about which information is desired. Parameter A parameteris any summary number, like an average or percentage, that describes the entire population.
The population mean \(\mu... |
If we idealize the scenario enough, this is a simple exercise in differential equations, so let's get to work. First, we know that it's
initial speed is $150 \text{ m/s}$, but that is by no means its final speed - obviously, the bb slows down as it travels through air! Let's suppose that the moment the bb exits the bar... |
Living in the world today requires giving up a lot of control. We give up control of our financial lives to banks and unaccountable credit bureaus. We give up control of our most intimate data to use online services like Facebook, Amazon, and Google. We give up control of our elections to voting-system companies who ru... |
A "field of sets" is a collection $\mathcal{F}$ of subsets of a given set $X$ which is closed under binary unions, intersections, and under complementation. Alas, it is not an "field" in the sense of abstract algebra.
It
is a "subalgebra" of the Boolean algebra of the power set of $X$. Alas, here as well, "Boolean alge... |
Interferometers Big telescopes are expensive, and doubling the size of a telescope increases the cost by a much bigger factor. In addition, bigger telescopes suffer from deforming under their own weight, so there is a limit to the useful size of a single telescope. There is however, a way to combine telescopes so that ... |
What does 1/k represent regarding Newtons Law of Cooling?
I know k represents the cooling constant. I think the inverse of k is the time taken for the liquid to cool from its maximum temperture to surrounding temperature. Any clarification would be most appreciated.
What does 1/k represent regarding Newtons Law of Cool... |
Math.SE report 2015-04
[ Notice: I originally published this report at the wrong URL. Imoved it so that I could publish the June 2015report at that URL instead. If you'reseeing this for the second time, you might want to read the Junearticle instead. ]
A lot of the stuff I've written in the past couple of years has bee... |
Cherry-picking? [Study Assessment]
»
3. The within-subject standard deviation of test and reference products will be compared, and the upper limit of the 90% confidence interval for the test-to-reference ratio of the within-subject variability should be ≤ 2.5.
» […] 90% confidence interval for the test-to-reference rat... |
In geometry, you come across different types of figures which properties that set them apart from one another. One common figure among them is a triangle. A triangle is a closed figure, a polygon, with three sides. It has 3 vertices and its 3 sides enclose 3 interior angles of the triangle. The sum of the three interio... |
I have a problem understanding how phasors work and I'll use a problem from a recent exam to illustrate the misunderstanding.
Note: Underlined variables such as \$\underline{V}\$ are considered here to be complex numbers, while non-underlined are considered to be magnitudes of the complex numbers.
Here's the text:
We h... |
Let $f\in L^2\mathbb{R}^d$ such that $\nabla f$ (in the distributional sense) coincides with an $L^2$-function outside of $0$. In which dimensions $d$ do we automatically have that $\nabla f\in (L^2\mathbb{R}^d)^d$?
For $d=1$ it is wrong, e.g. the Heaviside functions provides a counterexample.
For $d\ge3$, I can prove ... |
I know that a constant current doesn't create induced emf, however, I do not know why a changing one does. Are there any ways to understand it briefly/easily, or is it just the way it is?
You can understand this through the Faraday Law:
$$ \varepsilon = - \frac{\Delta \Phi_B}{\Delta t}$$
Here $\varepsilon$ is the EMF, ... |
Search
Now showing items 1-10 of 21
Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.