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Question:
Is there a rule of thumb for setting a non-diagonal covariance matrix for your Metropolis-Hastings proposal distribution? References are appreciated.
Background:
Say I have some posterior distribution I am interested in obtaining samples from $p(\theta|y)$. I choose an initial proposal distribution for a Metr... |
You are not right, Le Châtelier's principle plays a very important role.
Let's have a look at the reactions involving disodium monohydrogen phosphate, as it is an amphoteric substance and therefore a buffer on its own:\begin{align}\ce{Na2HPO4 + H2O &<=> 2Na+ + H3+O + PO4^3- \\Na2HPO4 + H2O &<=> 2Na+ + {}^{-}OH + H2PO4^... |
For an Alexandrov space M with curvature bounded from below, the isoperimetric profile $v \to I_M(v)$ defined for every $v\in (0,V(M))$ (the volume of M might be infinite), is given by $$ I_M(v)=inf\{A(\partial D): V(D)=v, D \subset \subset M\}, $$ where D varies over relatively compact open subset of M.
Then given any... |
I want to write the following constraint: If A=1 and B <= m then C=1 ( where A and C are binary, m is a constant and B is continuous).
My solution requires some kind of hack in the model, a
Big-$M$ value, which is pretty common, but also a tolerance $\varepsilon$, which is not very desirable. I hope that I do not miss ... |
I) In this answer we would like to relax the conventional definition of a
conservative force to include e.g. the Lorentz force.
II) The standard definition of a conservative force is given on Wikipedia (October 2013) roughly as follows:
A force field ${\bf F}={\bf F}({\bf r})$ is called a
conservative force if it meets... |
For $N$ samples of normally distributed data $X_i \sim \mathcal{N}(\mu,\sigma^2)$, the $1-\alpha$ confidence interval for the sample mean $\bar{X}$ is $$ \left[\bar{X} - z_{\alpha/2}\frac{\sigma}{\sqrt{N}}, \bar{X} + z_{\alpha/2}\frac{\sigma}{\sqrt{N}}\right], $$ where $ z_{\alpha/2}$ is the $(1-\alpha/2)$ quantile for... |
Find all positive integers $m$ and $n$ with $m\ne n$ that satisfy the equation
$~~~~~~~\displaystyle \sqrt[m]{m} ~=~ \sqrt[n]{n}$
Puzzling Stack Exchange is a question and answer site for those who create, solve, and study puzzles. It only takes a minute to sign up.Sign up to join this community
Find all positive integ... |
Let $n>2$ be even. Consider a compact Riemannian manifold $(M^n,g)$ and denote with $P_g$ the critical GJMS operator.
Recall that $P_g$ is conformally invariant, i.e. $$P_{\tilde g}=e^{-nu}P_g$$ if $\tilde g=e^{2u}g$ for some $u$.
Let $H$ be given by the following expression $$H(x,y)=c_n \log(\frac{1}{r})f(r)$$ where $... |
Summations and Series are an important part of discrete probability theory. We provide a brief review of some of the series used in STAT 414. While it is important to recall these special series, you should also take the time to practice. For more in depth review, there are links to Khan Academy.
Summations
First, it i... |
Main Page The Problem
Let [math][3]^n[/math] be the set of all length [math]n[/math] strings over the alphabet [math]1, 2, 3[/math]. A
combinatorial line is a set of three points in [math][3]^n[/math], formed by taking a string with one or more wildcards [math]x[/math] in it, e.g., [math]112x1xx3\ldots[/math], and repl... |
RANT - I hate problems that don't use significant figures properly. So is the answer supposed to be +/- 1 ml, +/- 0.1 ml, or +/- 0.01 ml?
First your overall approach is right. There are three parts to solving the problem:
(1) Calculate pHs
(2) Calculate how many moles NaOH
(3) Calculate how many ml of 0.1 molar solutio... |
I'm looking at Lakens' (2017) primer and he tests the hypothesis that there is a difference between two groups $X_1$and $X_2$of magnitude $\Delta=E[X_1]-E[X_2] \neq0$ by subtracting $\Delta$ from the difference between the sample means $d=M_1-M_2$ and then he computes the $t$ value and $p$ value based on this differenc... |
kidzsearch.com > wiki Explore:images videos games
List of readability tests Contents Overview The Dale–Chall formula Edgar Dale, a professor of education at Ohio State University, was one of the first critics of Thorndike's vocabulary-frequency lists. He claimed that they did not distinguish between the different meani... |
The CRC Handbook of Chemistry and Physics [1] provides data for the solubility of $CO_2$ in $H_2O$ originally from reference [2]. The reported data are mole ratio solubilities $\chi$ of the gas at a partial pressure of one atmosphere (101.325 kPa), but can readily be converted into Henry's law solubility in other units... |
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Mon, 24 Sep 2018
A long time ago, I wrote up a blog article about how to derive the linear regression formulas fro first principles. Then I decided it was not of general interest, so I didn't publish it. (Sometime later I posted it to math stack exchange, so the effort wasn't waste... |
A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.
bidibangboom Posts: 34 Joined: May 10th, 2019, 6:38 pm
triple poster
Code: Select all
#C A... |
While writing array index in an algorithm $a[i]\gets v$ is conventionally used. Is the notation $a_{i}\gets v$ also used ?
If the algorithm uses
struct or equivalent, some notation is required for property access. In some occasions $p(s)$ is used where $p$ is the property. Using $s \rightarrow p$ messes up with the ass... |
In lambda calculus there are three types of reduction,
$\alpha$-renaming
$\beta$-reduction
$\eta$-conversion
The use of $\eta$ in $\eta$-conversion seems rather strange to me. Since they already used $\alpha$ and $\beta$ I would expect the pattern to be continued with $\gamma$ the third Greek letter, but $\eta$ is used... |
Suppose $X$ is an infinite set and let $\mathcal{T}_{cf} = \{ U\subset X\ |\ X\setminus U\ \mathrm{is\ finite\ or}\ U=\emptyset\}$. Let $p$ be an element that is not in $X$ and let $Y=X\cup \{p\}$.
Topologize $Y$ by declaring a set $U$ in $Y$ to be open if and only if $U\subset X$ or if $p \in U$, then $X\setminus U$ m... |
The corrections made to the measurements described in step 16 of the Frequency Discriminator test setup procedure
are somewhat inscrutable. For those who wish to understand the rationale behind them, I provide the mathematical justification in this message. Those who don't like or can't be bothered with math are encour... |
Learning Objectives
To get a simple overview of the origin of color and magnetism in complex ions.
Electromagnetic radiation is a form of energy that is produced by oscillating electric and magnetic disturbance, or by the movement of electrically charged particles traveling through a vacuum or matter.
Electron radiatio... |
Question
Bradley (2005, Section 3.1) states:
Theorem 3.1Suppose $X := (X_k; k \in Z)$ is a strictly stationary, finite state Markov chain. Then the following five statements are equivalent: X is irreducible and aperiodic. X is mixing (in the ergodic-theoretic sense). $\alpha(n) \rightarrow 0$ as $n \rightarrow \infty$.... |
You still need to show that:
$\oplus_S$ has a neutral element.
$\oplus_S$ is associative.
If $0_S$ is the aforementioned additive neutral element, that $\oplus_S$ has opposites, id est, that for all $a$ there is $b$ such that $a\oplus_S b= 0_S$ and $b\oplus_S a=0_S$.
If your definition of ring requires it (most of them... |
Generating networks with a desired second order motif frequency
One way to add structure beyond the Erdös-Rényi random network (ER random network) is to generate ensembles of networks with a prescribed degree distribution. Here we describe another approach: modulating the frequencies of small network motifs in directed... |
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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 ... |
I'm trying to determine whether this matrix is diagonalizable:
$$A = \pmatrix{\sqrt3&0&-1\\0&-1&0\\1&0&0}$$
The characteristic polynomial is:
$$-\lambda^3 + (\sqrt3-1)\lambda^2 + (\sqrt3-1)\lambda -1 = 0$$
And so we get eigenvalues: $$\lambda_1=-1,$$ $$\lambda_2=\frac{\sqrt3}{2}+\frac{i}{2},$$ $$\lambda_3=\frac{\sqrt3}... |
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Now showing items 1-2 of 2
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 ... |
The climb rate depends on the excess power which is available after drag has been subtracted from net thrust. If the airplane stays at the same polar point while climbing, it needs to accelerate in order to compensate for the decrease in air density. Therefore, besides drag also this acceleration work needs to be subtr... |
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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 ... |
Result Number Material Type Add to My Shelf Action Record Details and Options 11
Material Type:Article
Measurement of the production and lepton charge asymmetry of $\textit{W}$ bosons in Pb+Pb collisions at $\sqrt{s_{\mathrm{\mathbf{NN}}}}=$ 2.76 TeV with the ATLAS detectorEuropean Physical Journal C: Particles and Fie... |
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Thu, 26 Jul 2018
There are well-known tests if a number (represented as a base-10 numeral) is divisible by 2, 3, 5, 9, or 11. What about 7?
Let's look at where the divisibility-by-9 test comes from. We add up the digits of our number !!n!!. The sum !!s(n)!! is divisible by !!9!! if... |
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math-ph
Change to browse by: References & Citations Bookmark(what is this?) Mathematics > Probability Title: Some properties of non-linear fractional stochastic heat equations on bounded domains
(Submitted on 4 May 2016 (v1), last revised 16 Dec 2016 (this version, v2))
Abstract: Consider the fo... |
Difference between revisions of "De Bruijn-Newman constant"
(→Bibliography)
(→Threads)
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* [https://terrytao.wordpress.com/2018/01/27/polymath15-first-thread-computing-h_t-asymptotics-and-dynamics-of-zeroes/ Polymath15, first thread: computing H_t, asymptotics, and dynamics of zeroes], Terence Tao, Jan ... |
As is well known, Dirac introduced the creation and annihilation operators for the quantum harmonic oscillator ($\hat{a}^\dagger$ and $\hat{a}$ respectively), which are now part of every first course in quantum mechanics due to their far-reaching importance and simplicity.
$$\hat{a}^\dagger=\sqrt{\frac{m\omega}{2\hbar}... |
Klaus Warzecha's answer pretty much answers your question. But I know that this subject is easier to understand if supported by some pictures. That's why I will take the same route as Klaus at explaining the concept behind why the absorption in conjugated systems is shifted to higher wavelengths but I will provide some... |
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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 ... |
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NUCLEAR PHYSICS B, ISSN 0550-3213, 05/1998, Volume 519, Issue 1-2, pp. 19 - 36
Using a sample of 10(8) triggered events, produced in pi(-)-Cu interactions at 350 GeV/c, w... |
Recall the following properties of the Fourier transform:
If $x(t)$ is an even function, then its Fourier transform $X(\omega)$ is purely real.
If $x(t)$ is an odd function, then its Fourier transform $X(\omega)$ is purely imaginary.
Thus, we can think of the real and imaginary parts of the Fourier transform of a zero-... |
I have a sphere or radius r that has a small point like object moving at a constant velocity inside it. Each time it hits the side it bounces in a random direction but always away from the tangent plane at the contact point. The longest distance it can travel is through the center to the other side $2r$ if it bounces a... |
While it's apparently some form of time series, if there are multiple observations at a single point, it might be a little unusual to call it
a time series.
One difficulty I see is how do I relate (say) 2 observations at time $\tau$ to 3 observations at time $\tau-s$? What's the model? Does the expectation at time $\ta... |
Let's assume that we have $X_1,...,X_n\sim^{iid} Exp(\theta)$.
The LRT is of the form $\Lambda(X,\theta_0,\theta_1)=e^{\left(\frac{1}{\theta_0}-\frac{1}{\theta_0}\right)\sum X_i}$. When $\theta_0<\theta_1$, the LRT is increasing in the sufficient statistic $T(X)=\sum X_i$.
Why the focus on the monotonicity of the LRT w... |
Search for dissertations about: "renewal processes"
Showing result
1 - 5 of 64 swedish dissertations containing the words renewal processes. University dissertation from Västerås : Mälardalen University
Abstract : In this thesis we investigate a model of nonlinearly perturbed continuous-time renewal equation. Some char... |
Sometimes, especially in introductory courses the instructor will try to keep things "focused" in order to promote learning. Still, it's unfortunate that the instructor couldn't respond in a more positive and stimulating way to your question.
These reactions do occur at $\ce{sp^2}$ hybridized carbon atoms, they are oft... |
Let me combine all the ideas I find to prove that $\forall k \ge 1. H_m < \log(2*m+1)$. As noted by @mihaild this is sufficient for the proof of the theorem. We can proceed by induction.
For $k = 1$ , we have $1 < \log(3) = 1.09\ldots$ which holds.
For $k > 1$, we assume $H_m < \log(2*m+1)$ and would like to show $H_{m... |
Remember that, in an ideal gas, there are no interactions between the particles, hence, the particles do not exert forces on each other. However, particles do experience a force when they collide with the walls of the container. Let us assume that each collision with a wall is elastic. Let us assume that the gas is in ... |
This article describes the scoring system in Arcaea in detail, as well as various other mechanics.
Timing
Like other rhythm games, point are given depending on how accurate and precise your timing is when hitting notes. There are names given to different levels of judgement for the timing:
The points per note of a song... |
Calculate the pH at the equivalence point for the titration of $\pu{0.130 M}$ methylamine ($\ce{CH3NH2}$) with $\pu{0.130 M}$ $\ce{HCl}$. The $K_\mathrm{b}$ of methylamine is ${5.0 \cdot 10^{–4}}$.
So I started with the equation:
$$\ce{HCl + CH3NH2 <=> CH3NH3+ + Cl-}$$
and then I knew that
$$\mathrm{pH} = \mathrm{p}K_\... |
Difference between revisions of "Main Page"
(Fixing location.)
(Collected background materials)
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'''<math>k=3</math> Density Hales-Jewett (DHJ(3)) theorem:''' <math>\lim_{n \rightarrow \infty} c_n/3^n = 0</math>
'''<math>k=3</math> Density Hales-Jewett (DHJ(3)) theorem:''' <math>\lim_{n \rightarrow \inft... |
Consider the following axiomatic definition of a field:
A
fieldis a set $F$ together with two binary operations $+$ and $\cdot$ on $F$ such that $(F,+)$ is an Abelian group with identity $0$ and $(F\setminus\{0\},\cdot)$ is an Abelian group with identity $1$, and the following left-distributive law holds: $$a\cdot(b+c)... |
I am doing some research into the movement of robots executing a given algorithm, and have come up with the following recursive equations that describe the movement of the robots at each iteration:
\begin{equation} \theta_i = \frac{3}{4}\theta_{i-1} \end{equation}
\begin{equation} L_i=\frac{1}{2}\sqrt{L_{i-1}^2+A_{i-1}... |
Coloring.tex
\section{The coloring Hales-Jewett problem}\label{coloring-sec}
The Hales-Jewett theorem states that for every $k$ and every $r$ there exists an $n = HJ(k,r)$ such that if you colour the elements of $[k]{}^n$ with $r$ colours, then there must be a combinatorial line with all its points of the same colour.
... |
I fit a binary logistic regression model with a single categorical variable, for which I received a coefficient. When I added further categorical predictor variables, the coefficient of the original categorical variable changed. What is the reason for this? That is, why is the coefficient of a predictor variable sensit... |
The following quote is from the book "The art of computer programming":
(..) sentence would presumably be used only if either $j$ or $k$ (not both) has exterior significance.
In most cases we will use notation (2) only when the sum is
finite- that is, when only a finite number of values $j$ satisfy $R(j)$ and have $a_j... |
Cohomology is a stronger invariant than homology because it can be equipped with a ring structure. To be precise, if one starts with the singular cohomology groups $H^\bullet(-; R)$ with coefficients in a ring $R$, then there is a map $$H^n(X; R) \times H^m(X; R) \stackrel{\smile}{\to} H^{m+n}(X; R)$$ which is graded c... |
$\Phi$, or the
golden ratio, is basically $\frac{a+b}{a}=\frac{a}{b}$. The silver ratio corresponds to a similar idea of: $\frac{2a+b}{a}=\frac{a}{b}$. I've read on Wikipedia that both of these ratios are well known and have some appearance in nature (not the mystical hogwash stuff). In addition, there is the relation ... |
The simplest answer I can think of: because we can make a finite look-up table for answers.In other words, if you have a finite language $L = \{w_0, \ldots, w_{k-1}\}$,consider the following algorithm:
Input: $x$
$L \leftarrow [w_0, \ldots, w_{k_1}]$ for $i$ from 0 to k-1 do $~~$ if $x = L[i]$ $~~$$~~$ accept reject
No... |
I am learning about the binomial coefficient and counting. We define: $$ (1+x)^m = \sum^m_{n=0} \begin{pmatrix} m \\ n \end{pmatrix} x^n $$ the coefficients of the powers of $x^n$ represent the number of ways of choosing $n$ objects from a set of $m$. Is there a way to convert this into a probability distribution by di... |
This scenario is explicitly handled by Gordan's theorem, which states$$\text{either} \quad\exists x \in \mathbb{R}_+^m\setminus\{0\} \centerdot Ax = 0,\quad\text{or}\quad\exists y\in\mathbb{R}^n\centerdot A^\top y > 0,$$
where $\mathbb{R}_+$ denotes nonnegative reals.(Like Farkas's Lemma, this is a "Theorem of Alternat... |
Range of a matrix
The
rangeof m× nmatrix A, is the span of the ncolumns of A. In other words, for
\[ A = [ a_1 a_2 a_3 \ldots a_n ] \]
where \(a_1 , a_2 , a_3 , \ldots ,a_n\) are
m-dimensional vectors,
\[ range(A) = R(A) = span(\{a_1, a_2, \ldots , a_n \} ) = \{ v| v= \sum_{i = 1}^{n} c_i a_i , c_i \in \mathbb{R} \} \]... |
Math Contents Introduction
TeX was designed for ease of typesetting books that contained mathematics. As ConTeXt is built on top of TeX, it inherits all those features. In addition to these, ConTeXt adds lot of macros to make the typesetting of mathematics easier.
For typesetting of mathematics follows different rules ... |
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Tue, 25 Jun 2019
I don't have a good catalog in my head of basic theorems of category theory. Every time I try to think about category theory, I get stuck on really basic lemmas like “can I assume that a product !!1×A!! is canonically isomorphic to !!A!!?” Or “Supp... |
Difference between revisions of "Degree of irreducible representation divides order of group"
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bigger = order|
bigger = order|
biggerof = group}}
biggerof = group}}
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==Statement==
==Statement==
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* [[Degree of irredu... |
Difference between revisions of "Moser-lower.tex"
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\subsection{Higher k values}
\subsection{Higher k values}
−
One can consider subsets of $[k]{}^n$ that contain no geometric lines.
+
One can consider subsets of $[k]{}^n$ that contain no geometric lines. has considered the case $k=3$. Let $c'_{n,k}$ ... |
What constitutes a proof in a system like this is a
derivation which is a tree of rule applications. The above translation function is defined by (structural) recursion over that tree. Note, this is why it labels the premises in the rules with $\delta$. This is intended to be mnemonic for "derivation".
I'm guessing but... |
This category contains definitions related to Power Series.
Related results can be found in Category:Power Series.
Let $\xi \in \R$ be a real number.
Let $\sequence {a_n}$ be a sequence in $\R$.
The series $\displaystyle \sum_{n \mathop = 0}^\infty a_n \paren {x - \xi}^n$, where $x \in \R$ is a variable, is called a po... |
I like to know if we can model binary outcome with time series predictors. For example lets say Y is binary. $X_1, X_2, X_3,...,X_n$ is the same predictor variable but is a historical snapshot over time period $1,...,n$. I am interested in predicting $Y$ but include the auto correlation among $X_1,...,X_n$ and seasonal... |
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Is the usual \(\leq\) ordering on the set \(\mathbb{R}\) of real numbers a total order?
So, yes.
1. Reflexivity holds
2. For any \\( a, b, c \in \tt{R} \\) \\( a \le b \\) and \\( b \le c \\) implies \\( a \le c \\)
3. For any \\( a... |
I apologize if this question is well-known, but I was unable to find it mentioned anywhere.
There exists a bug which moves around in $r$-space. The bug begins at the origin of this $r$-space. If the bug is at the center of a regular $r$-simplex (all of which are oriented the exact same direction) with radial length of ... |
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Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
Quasirandomness
Quasirandomness is a central concept in extremal combinatorics, and is likely to play an important role in any combinatorial proof of the density Hales-Jewett theorem. This will be particularly true if that proof is based on the density increment method or on some kind of generalization of Szemerédi's r... |
Bohr's theory of the atom precedes quantum theory but does describe the Balmer and other lines in atomic hydrogen. I've outlined the calculation so that you can see where the Bohr radius comes from.
He assumed that the electron orbits the nucleus in a circle with a radius
r and is determined by the balance of centripet... |
Let $X_k$ be $\mathbb{P}^2$ blown up at $k$ points (where $k$ is $0$ to $8$). Let $\beta \in H_2(X_k, \mathbb{Z})$ be the homology class given by $$ \beta := n L + m_1 E_1 + \ldots + m_k E_k $$ where $L$ is the homology class of a line and $E_i$ are the exceptional divisors. Also, define $$ \delta_{\beta} := < c_1(TX_k... |
Is it wrong to say that
Density Functional means that Electron Density is a function of the orbitals (wave function) of all electrons in 3 dimensions, if so, why ?
In general, a
functional $F$ is a mapping from an arbitrary set $\mathcal{X}$ of functions to the set of complex numbers $\mathbb{C}$ or the set of real num... |
I think that the OP is asking a more specific question than whether or not a surface has a connection that is not metric or not torsion free. It seems that the OP is assuming that the surface $M$ comes equipped with an immersion $\mathbf{r}:M\to\mathbb{E}^3$ into (oriented) Euclidean $3$-space and is asking whether,
us... |
With holiday season coming up I decided to make some cinnamon stars. That was fun (and the result tasty), but my inner nerd cringed when I put the first tray of stars in the box and they would not fit in one layer:
Almost! Is there a way they could have fit? How well can we tile stars, anyway? Given that these are regu... |
My university is participating in the implementation of a library borrowing managing system at Richelieu National Library in France.
I received the order to formulate the query: "find all users having borrowed every book" in relational Algebra, in relational Calculus and in SQL (which would probably not happen, probabl... |
What is the median of the non-central t distribution with non-centrality parameter $\delta \ne 0$? This may be a hopeless question because the CDF appears to be expressed as an infinite sum, and I cannot find any information about the inverse CDF function.
You can approximate it.
For example, I made the following nonli... |
It's well known that chain complexes are an abelian category, and in particular we can consider chain complexes of chain complexes, i.e.
double complexes. Given a double complex $A^{\bullet\bullet} \in \mathrm{Kom}(\mathrm{Kom}(\mathcal A))$ we can form the total complex $\newcommand{\tot}{\mathrm{Tot}}\tot(A^{\bullet\... |
Banach Journal of Mathematical Analysis Banach J. Math. Anal. Volume 8, Number 2 (2014), 93-106. Disjointness preserving linear operators between Banach algebras of vector-valued functions Abstract
We present vector-valued versions of two theorems due to A. Jimenez-Vargas, by showing that, if $B(X,E)$ and $B(Y,F)$ are ... |
ClassActivity20130325
Here are the stages that each group should get to:
1. Read in the data and plot the <math>(x_i,y_i)</math> data points, including error bars or some other graphical indication of the <math>\sigma_i</math>'s.
2. Hmm. They look kind of like a raised parabola, don't they? Try fitting a model of the f... |
Yes, you can have both as fast as possible random access and faster-than-full-rebuild insertion time.
I assume you know how dynamically growing arrays work. Also, I assume you know how to make them work in $O(1)$ worst-case. These techniques allow us to focus on the problem for lists of limited size only.
Let $n$ be th... |
If I have the following system, I am wondering how to calculate the number of valid strings it contains.
The system is something like this, which can have arbitrary variations.
Only consists of an alphabet $\Sigma$. It can't spell any words in a blacklist word list $\rho$. It can't have more than $n$ characters of the ... |
Images are essential elements in most of the scientific documents. LaTeX provides several options to handle images and make them look exactly what you need. In this article is explained how to include images in the most common formats, how to shrink, enlarge and rotate them, and how to reference them within your docume... |
Area and definite integrals
The actual
definition of ‘integral’ is as a limit of sums, whichmight easily be viewed as having to do with area. One of theoriginal issues integrals were intended to address was computation ofarea.
First we need more notation. Suppose that we have a function$f$ whose integral is another fun... |
Will a disc or cylinder (rigid body) executing pure rolling on a rough surface stop, neglecting air drag and other heat losses and rolling friction but not static and kinetic friction? If yes, due to which friction it will stop, static or kinetic and how? Assume surface has no rolling friction.
closed as unclear what y... |
I seem to be misunderstanding a claim about linear regression methods that I've seen in various places. The parameters of the problem are:
Input:
$N$ data samples of $p+1$ quantities each consisting of a "response" quantity $y_i$ and $p$ "predictor" quantities $x_{ij}$
The result desired is a "good linear fit" which pr... |
Schaefer, J., Sigeneger, F., Sperka, J. et al. (2 more authors) (2017)
Searching for order in atmospheric pressure plasma jets. Plasma Physics and Controlled Fusion, 60 (1). 014038. ISSN 0741-3335 Abstract
The self-organized discharge behaviour occurring in a non-thermal radio-frequency plasma jet in rare gases at atmo... |
I have seen at several places, incl. some notes and books, the following inference of the Holomorphic Implicit Function Theorem from the Smooth Real Function Theorem, but I believe this proof to be incorrect or rather incomplete in that it seems to be missing a non-obvious key step. I would like to know how to complete... |
Is Lebesgue's integral the only definition of integral for which the $L^1$ space is a complete vector space (for a natural norm on it)?
I'm mostly interested on integrals of functions $f:\Bbb R^n \to \Bbb R$, and where the integral is an
explicit operator (it must have a "practical utility", and we should be able to co... |
Solve the equation: $$2^x=1-x$$
I know this is extremely easy and I know the solution using graphical approach. Basically, I can see the solution, but I can't work it out algebraically.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It... |
Given a set of points $(x_i, y_i)$, least-squares linear regression finds the linear function $L$ such that $$\sum \varepsilon(y_i, L(x_i))$$ is minimized, where $\varepsilon(y, y') = (y-y')^2$ is the squared error between the actual $y_i$ value and the one predicted by $L$ from $x_i$.
Suppose I want to do the same, bu... |
Let $T$ be a bounded operator on a Hilbert space with the property that $T^*(T-I)= 0$. I'd like to show that $T$ is an orthogonal projection.
I'm not really sure how to show that an operator is an orthogonal projection. If $A:X\rightarrow U$ is a projection onto a closed subspace of X, then $\langle x- Ax, u_i\rangle =... |
The Lazy Laser Physicist is quite shocked about what happened to his setup over night:
Almost all of his mirrors were taken away, but some other things have been put on his table. Besides these there is also a message:
Your setup was a total mess! I don't know how you could work there, but weren't all these unused mirr... |
Considering the problem
There were n couples attending a ceremony. Out of the 2n people, exactly m of them ate pizza, chosen randomly over all subsets of 2n people. Let X be the number of couples that didn’t eat pizza. Find an explicit expression for the mean of X.
There seems to an easy and correct solution by taking ... |
A lot of the stuff I've written in the past couple of years has beenon math.StackExchange. Some of it is pretty mundane, but some isinteresting. My summary of April's interesting posts waswell-received, so here are the noteworthy posts I made in May 2015.
What matrix transforms !!(1,0)!! into !!(2,6)!! and tranforms!!(... |
Formula Macro
Inserts a mathematical formula
Type JAR Developed by Active Installs 1 Rating License GNU Lesser General Public License 2.1
Bundled With
XWiki Enterprise
Table of contents
Description
The formula needs is written in TeX markup and rendered as an image.
Usage
Examples of formula syntax can be seen on the.
... |
Question:
Calculate the molar sulfate concentration in a solution that is $0.200$ M in $\ce{Ag+}$ and saturated with $\ce{Ag2SO4}$.
My attempt:
Looking through old notes and googling lead me to this webpage. Example #2 looked similar to my problem, and my notes from general chemistry involved something called an ICE ta... |
Topological Methods in Nonlinear Analysis
Approximate controllability for abstract semilinear impulsive functional differential inclusions based on Hausdorff product measures
Lipschitz Retractions onto Sphere VS Spherical Cup in a Hilbert space
Finite-time blow-up in a quasilinear chemotaxis system with an external sig... |
Ghatak, Chandana and Ayappa, KG (2004)
Solvation force, structure and thermodynamics of fluids confined in geometrically rough pores. In: Journal of Chemical Physics, 120 (20). 9703 -9714.
PDF
Solvation_force.pdf
Download (870kB)
Abstract
The effect of periodic surface roughness on the behavior of confined soft sphere ... |
This question already has an answer here:
I want to prove (or disprove) that
$$\sum_{i=1}^n\log_2 i = \Theta(n\log_2 n)\,,$$
but I totally get stuck with this example. May someone help me with that.
Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer sci... |
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