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Let $a \in \Bbb{R}$. Let $\Bbb{Z}$ act on $S^1$ via $(n,z) \mapsto ze^{2 \pi i \cdot an}$. Claim: The is action is not free if and only if $a \Bbb{Q}$. Here's an attempt at the forward direction: If the action is not free, there is some nonzero $n$ and $z \in S^1$ such that $ze^{2 \pi i \cdot an} = 1$. Note $z = e^{2 \... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
1 - Eugenio Calabi affirms that every closed non singular 1-forms in closed manifolds are intrinsecally harmonic ("An instrinsic characterization of harmonic 1-forms", 1969). This is easy proved observing first that such forms are transitive. The dual case is a open problem, but I believe that is true. A closed $(n-1)$... |
EXAMPLE:A 7-segment display shows any number from 0 to 9 at random (equalprobabilities).
Let $X$ be the indicator random variable ofwhether the blue segment is on. Similarly, $Y$ is theindicator for the red segment. Find the conditional distributionof $Y$ given $X.$SOLUTION:Here $X,Y$ both take values in $\{0,1\}.$We n... |
PCTeX Talk Discussions on TeX, LaTeX, fonts, and typesetting
Author Message zedler Joined: 03 Mar 2006 Posts: 15
Posted: Thu Mar 09, 2006 9:20 am Post subject: spacing Hello,
Please have a look at the spacing of these equations
- $[]_{\langle n\times m\rangle}$ (the brackets touch)
- $Z_{F1}$ (F and 1 spacing)
- $\frac... |
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Now showing items 1-10 of 17
J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
There were a number of upsets in the NBA this past Christmas week. Here, we offer no explanation, but do attempt to quantify just how bad those upsets were, taken in aggregate. Short answer: real bad! To argue this point, we review and then apply a very simple predictive model for sporting event outcomes — python code ... |
The answer is... it is not so simple. Some quantum mechanics follow, but the
TL;DR version is that while $m_l=0$ corresponds to $p_z$, the orbitals for $m_l=+1$ and $m_l=-1$ lie in the $xy$-plane, but not on the axes. The reason for this outcome is that the wavefunctions are usually formulated in spherical coordinates ... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
It sounds like you could simply use the Cost Minimization Problem:$$\underset{z_1,...z_N}{min}\sum_{i=1}^N q_iz_i$$$$s.t.\quad f(z_1,...,z_N)\geq \bar{y}$$$$z_1,...z_n\geq0$$Where $z_i$ and $q_i$ are the quantity and price of input $i$, respectively, $\bar{y}$ is some predetermined level of output, and $f(\frac{}{})$ i... |
As you have already pointed out in your question, it is not possible (without using optimization methods) to compute an exact L2 solution for the frequency domain design problem of IIR filters due to the non-linear relationship between the filter coefficients and the error function. There is, however, a method which ca... |
In Wikipedia's QHO page there is a moment when the following is stated:
I don't know why "the ground state in the
position representation is determined by $a|0\rangle=0$". I would say that the position representation of the ground state is rather $\langle x|0\rangle$, isn't it?
However, there are other things that I'm ... |
Ananthanarayan, B and Rindani, Saurabh D (2004)
CP violation at a linear collider with transverse polarization. In: Physical Review D, 70 (3). 036005/1-6. This is the latest version of this item.
PDF
A25anantnaryanab.pdf
Download (225kB)
Abstract
We show how transverse beam polarization at $e^+e^-$ colliders can provid... |
Here is a detailed explanation of Jech's proof.
Let $D$ be a normal measure on $\kappa$. Suppose, towards a contradiction, that $\kappa$ is not Mahlo. Then there is some club $C \subseteq \kappa$ such that$$C \cap \{ \alpha < \kappa \mid \mathrm{cof}(\alpha) = \alpha \} = \emptyset.$$
Since $D$ is normal, it contains a... |
I got a simple modulating signal $x(t)=\sin(2\pi\alpha t)\sin(2 \pi \beta t)$ with carrier frequency $\alpha$ and modulation frequency $\beta$. The spectral correlation will obviously have components ...
some days ago I asked here parseval for a continuos but limited signal if the Parseval can be applied for limited si... |
I'm going through the article in the following link lately and one point confuses me a lot. https://arxiv.org/pdf/1509.05001.pdf
So, the goal of this paper is to solve the following constrained binary quadratic programming. Here the parameters $A$, $Q$ and $b$ are all of integer values.
max $x^{T}Qx$ $s.t.,$ $Ax\leq b$... |
Let's say you want to estimate a quantity $\mu$, but you have only access to unbiased estimates of its logarithm, i.e., $\log\mu$. Can you obtain an unbiased estimate of $\mu$?
2019/06/14 2016/10/26
Say that you have a dynamical process of interest $X_1,\ldots,X_n$ and you can only observe the process with some noise, ... |
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... |
Starting with a finite set of 3D points, Plotly can generate a
Mesh3d object, that depending on a key value can be the convex hull of that set, its Delaunay triangulation or an alpha set.
This notebook is devoted to the presentation of the alpha shape as a computational geometric object, its interpretation, and visuali... |
Why don't people discuss the eigenstate of the field operator? For example, the real scalar field the field operator is Hermitian, so its eigenstate is an observable quantity.
The answer is simple. They are not realized in nature too often. And more, they are not stationary states, so such a state evolves in time to a ... |
Digital electronics is based on the ancient philosophy of
logic.
Logical variables are two-valued, or
binary—either true or false.
Logic variables are combined with a short list of
operators—AND, OR, and NOT.
We represent logic several ways—with equations, symbols, and truth tables.
Written by Willy McAllister.
Content... |
Difference between revisions of "The Erdos-Rado sunflower lemma"
(→Variants and notation: added weak sunflower section)
(→Variants and notation: cleared up DES part)
Line 53: Line 53:
<B>Disproven for <math>k=3,r=3</math></B>: set <math>|V_1|=|V_2|=|V_3|=3</math> and use ijk to denote the 3-set consisting of the i^th e... |
Since the Goldbach conjecture is in $\Pi_1^0$, if it were proven to be independent of Peano Arithmetic, it would follow that the Goldbach conjecture is
true (i.e. true in the standard model), since informally speaking, if it were indeed false, we would have a counterexample of the Goldbach conjecture, contradicting the... |
I have area
A and length of the base s. I need to describe a triangle minimal perimeter using this information. from given equation I can find height. and final equation will look like this Since my perimeter is equal to $ s + \sqrt{x^2 + h^2} + \sqrt{(x - s)^2 + h^2} $ problem is to change orthocenter of h (x) in orde... |
There are many factors to be considered such as covalent character and electron-electron interactions in ionic solids. But for simplicity, let us consider the ionic solids as a collection of positive and negative ions. In this simple view, appropriate number of cations and anions come together to form a solid. The posi... |
I am calculating the Gibbs energy of dissolving one mole of solid glucose in pure water such that the final solution has a volume of one liter and a concentration of one mole per liter. I have three different ways of calculating it, and I get two different answers.
The Gibbs energy is a state function, so it should not... |
Uniformly Accelerated Motion
Objects on the earth surface are accelerated towards the centre of the earth at a rate of 9.8 m/ sec². If we raise an object above the surface of the earth and then drop it and the object will start from rest, its velocity will be increased by 9.8 m/ sec². For each second it is falling towa... |
If $0 \rightarrow X \xrightarrow{i} Y \xrightarrow{\pi} Z \rightarrow 0$ is a short exact sequence and $W$ is a vector space, then the sequence $$0 \rightarrow X \otimes W \xrightarrow{i\otimes \text{id}_W}Y \otimes W\xrightarrow{\pi \otimes \text{id}_W}Z \otimes W \rightarrow 0 $$ is also exact. In particular,if $X \s... |
What you have is a
MultinormalDistribution. The quadratic and linear forms in the exponential can be rewritten in terms of $-\frac12(\vec{x}-\vec{\mu})^\top\Sigma^{-1}(\vec{x}-\vec{\mu})$ where $\vec{\mu}$ represents the mean and $\Sigma$ the covariance matrix, see the documentation.
With this, you can do integrals of ... |
Let $f: A\rightarrow B$ be a function and consider a subset $Y\subseteq B$.
,is $f(f^{-1}(Y)) = Y$ always true?
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 sign up.Sign up to join this community
Yes, there ... |
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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 ... |
If the natural density of $A = \{a_i\}$ exists, then we can show that it must be zero.
Let $\displaystyle S_{n} = \frac{|A \cup [1,n]|}{n}$
Now $\displaystyle \{\frac{n}{a_n}\}$ is a subsequence of $S_{n}$ and so if the limit is $\displaystyle 2\delta > 0 $ then we have that for all $\displaystyle n > N_0$, $\displayst... |
Here, we introduce — and outline a solution to — a generalized SIR model for infectious disease. This is referenced in our following post on measles and vaccination rates. Our generalized SIR model differs from the original SIR model of Kermack and McKendrick in that we allow for two susceptible sub-populations, one va... |
The key here is that the potential comes from the fact that there are losses. Consider a circuit element like a resistor; If instead this was an ideal wire, then the work needed to move a charge (neglecting external fields such as gravity) is 0 because there is no force applied to the charge. Now if we replace this ide... |
I have asked this question before in the sense that what does a high frequency and low frequency component signify in a image and i got satisfactory answers now i want to know that how i can get high frequency and low frequency component separately from the image.
I mean what changes i have to make in the equations of ... |
A mapping $f$ between topological spaces $(X, \mathcal I_X)$ and $(Y, \mathcal I_Y)$ is continuous in $x \in X$ if $f^{-1}(V)$ is a neighborhood of $x$ for every neighborhood of $f(x)$. I want to show that this
agree with the usual definition of continuity if $X$ and $Y$ are metric spaces and $\mathcal I_X$ and $\mathc... |
In
Classical Fourier Analysis by Loukas Grafakos we have in Proposition 2.3.25 the following definition for $\mathcal{S}_\infty(\mathbf{R}^n)$, namely that these are all the Schwartz functions $\phi$ such that for all multi-indices $\alpha$ we have that
$$\int_{\mathbf{R}^n} x^\alpha \phi(x) \, dx = 0.$$
Now I'm trying... |
The Yoneda Lemma
Welcome to our third and final installment on the Yoneda lemma! In the past couple of weeks, we've slowly unraveled the mathematics behind the Yoneda perspective, i.e. the categorical maxim that an object is completely determined by its relationships to other objects.
Last week we divided this maxim in... |
In the previous post, I discussed the function fitting view of supervised learning. It is theoretically impossible to find the best fitting function from an infinite search space. In this post, I will discuss how we can restrict the search space in function fitting with assumptions.
In the following example, we do not ... |
If I'm standing at a lat of 30.000$^\circ$ and a long of 30.000$^\circ$ and I move to a lat of 30.001$^\circ$ and a long 30.000$^\circ$, how far have I gone? Is there a relationship between decimal places and lat and long distances?
I don't understand the last sentence about decimal places, but I can tell you about the... |
Let's say that you have $n$ independent and identically distributed (real valued) random variables $(X_{1},\ldots,X_{n})$ with distribution $\mathcal{N}(\mu,\sigma^{2})$. Here, $(\mu,\sigma^{2})$ are unknown parameters which we can estimate. Note that we assume that all random varialbes $X_{i}$ have the same mean $\mu$... |
I suspect there is in general not much difference between GMRES and CG for an SPD matrix.
Let's say we are solving $ Ax = b $ with $ A $ symmetric positive definite and the starting guess $ x_0 = 0 $ and generating iterates with CG and GMRES, call them $ x_k^c $ and $ x_k^g $. Both iterative methods will be building $ ... |
In my classes, I use one "simple" situation that might help you wonder and perhaps develop a gut feeling for what a degree of freedom may mean.
It is kind of a "Forrest Gump" approach to the subject, but it is worth the try.
Consider you have 10 independent observations $X_1, X_2, \ldots, X_{10}\sim N(\mu,\sigma^2)$ th... |
In our final application of group theory, we will investigate the way in which symmetry considerations influence the interaction of light with matter. We have already used group theory to learn about the molecular orbitals in a molecule. In this section we will show that it may also be used to predict which electronic ... |
Are there any famous problems/algorithms in scientific computing that cannot be sped up by parallelisation? It seems to me whilst reading books on CUDA that most things can be.
The central issue is the length of the critical path $C$ relative to the total amount of computation $T$. If $C$ is proportional to $T$, then p... |
, where x is the unknown, and a, b, and c are known numbers, with a ≠ 0. The unknowns
\(a\)
,
\(b\)
and
\(c\)
are the coefficients of the equation and are called respectively, the quadratic coefficient, the linear coefficient and the constant term.Note that although
\(a\)
must not be zero,
\(b\)
or
\(c\)
could be. This... |
I have been using terms like underfitting/overfitting and bias-variance tradeoff for quite some while in data science discussions and I understand that underfitting is associated with high bias and over fitting is associated with high variance. But what is the reason of such association or in terms of a model what is h... |
One disadvantage of the fact that you have posted 5 identical answers (1, 2, 3, 4, 5) is that if other users have some comments about the website you created, they will post them in all these place. If you have some place online where you would like to receive feedback, you should probably also add link to that. — Mart... |
A unit of measurement is a definite amount of a physical quantity
, defined and adopted byconvention, that is used as a standard for measurement of the samephysical quantity of any amount. A unit is given a universallyrecognised symbol that represents the definite amount of thephysical quantity. For measurement, a pure... |
I have been trying to find the coefficient of $a^2x^3$, in the expansion of $(a+x+c)^2(a+x+d)^2$, without success.
I am having trouble expanding the above expression, because I can't find a way to merge them into one.
How can I solve this? Thanks
Mathematics Stack Exchange is a question and answer site for people study... |
Example 1
Question:
Prove that there is only one circle with $AB$ as its diameter.
Assumption:
Assume that there are 3 circles $C_1$, $C_2$, and $C_3$ passing through the points $A$ and $B$. $C_1$ and $C_2$ are concentric and $C_1$ and $C_3$ are not concentric. $C_1$ and $C_2$ have different radii and $C_3$ has any rad... |
I am having some problems with both the notation and the geometrical side.
1)I don't know what kind of objects $N,L$ are precisely. In Lemma 1.1 the author says that $L$ is a smooth $(1,0)$-tangent vector field on $\partial \Omega$, so I think it should be something like $$ L=\sum_{j=1}^na_j\frac{\partial}{\partial z_j... |
Consider the equations of motion
$$\begin{cases} \dot{x}(t) & = v(t) \\ \dot{v}(t) & = -\frac{\lambda}{m} v(t) + \frac{1}{m}F^{c}(x(t)) = a(x(t), v(t)) \end{cases},$$
where $x$ is the position, $v$ is the velocity, $m$ is the mass, $\lambda$ is the damping coefficient, $F^c(x(t))$ is a conservative force and $a$ is the... |
Current browse context:
q-bio.BM
Change to browse by: References & Citations Bookmark(what is this?) Quantitative Biology > Biomolecules Title: Void distributions reveal structural link between jammed packings and protein cores
(Submitted on 31 Oct 2018)
Abstract: Dense packing of hydrophobic residues in the cores of g... |
Let $\left\{ A_{n}\right\} $ be a sequence of sets that Lebesgue measurable on $\mathbb{R}$ such that $\mu\left(A_{n}\right)<\infty$ for all $n$ (integer). Let
$$A={ \bigcup_{m=1}^{\infty}}{ \left(\bigcap_{k\geq m}^{\infty}A_{k}\right)}$$
Do we have the following inequality:
$$ \mu(A) \leq \liminf_{n\to\infty} \mu(A_n)... |
One usually
starts from the CCR for the creation/annihilation operators and derives from there the commutation rules for the fields.However, one can start from either (see for example here about this).Suppose we want then to start from the equal-time anticommutation rules for a Dirac field $\psi_\alpha(x)$:$$ \tag{1} \... |
One of my data anaylsis pet peeves is false precision. Just because it is possible calculate a quantity to three decimal places doesn’t mean all of those decimal places are meaningful. This post explores how much precision is justified in the context of two common sports statistics: batting average in Major League Base... |
$$\begin{cases}&-z^{\prime\prime}(t)=\lambda(1+(N-2)t)^{\frac1{2-N}(2(N-1)+\alpha)}f(z(t)),\quad t\in(0,+\infty)\\&z(0)=z^\prime(+\infty)=0\end{cases}$$
I'm trying to solve the above differential equation. I'm using the shooting method, but for each initial guess a different solution appears. Which solution is correct?... |
Just this week I started a
Data Structures and Algorithms at my alma mater, San Jose state. And in jsut this short week I have noticed that the ones ability to properly evaluate ones code will take you a long way. Moreover, the skills developed through practiing the analysis of algortihm can go far in other discplines ... |
Visualizing high-dimensional data is a demanding task since we are restricted to our three-dimensional world. A common approach to tackle this problem is to apply some dimensionality reduction algorithm first. This maps \(n\) data points \(\fvec{x}_i \in \mathbb{R}^d\) in the feature space to \(n\) projection points \(... |
I hope this isn't a silly question. I'm learning single variable calc, and having lots of fun with optimization problems. This isn't exactly an optimization problem, but something that came up while working on one.
Let's say I have a small circular garden with a short brick border. This border is perhaps 1 foot tall, s... |
Linear Least-Squares L2-Regularized Regression Algorithm
An Linear Least-Squares L2-Regularized Regression Algorithm is a regularized regression algorithm can be implemented by a L2-Regularized Optimization System to solve an linear least-squares l2-regularized regression task)
AKA:ℓ2 Ridge Regression Method, Tikhonov ... |
Consider the functor $F: B \rightarrow Set$ where $B$ is a locally small category.
Is it true that if $F$ has a left adjoint then it is representable?
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 sign up.Sig... |
Difference between revisions of "Superstrong"
m (→Relation to other large cardinal notions: \{\})
(Super 0-huge is the same as tall)
Line 26: Line 26:
The consistency strength of $n$-superstrongness follows the [[n-fold variants|double helix pattern]] <cite>Kentaro2007:DoubleHelix</cite>. Specifically:
The consistency ... |
At a dance party there are 100 men and 20 women. Each man selects a group of women as potential dance partners, but in such a way that given any group of 20 men it is always possible to pair 20 men with 20 women, with each man paired with someone on their list. What is the smallest number L where L is the sum of the to... |
let sequence $\{a_{n}\}$ such $$a_{1}=1,a_{n+1}=1+\dfrac{n}{a_{n}}$$
show that: $$a_{n}=\sqrt{n}+\dfrac{1}{2}-\dfrac{1}{8\sqrt{n}}+o\left(\dfrac{1}{\sqrt{n}}\right)?$$
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 minu... |
A Support vector machine (SVM) is a popular choice for a classifier and radial basis functions (RBFs) are commonly used kernels to apply SVMs also to non-linearly separable problems. There are two hyperparameters in this case. First, the margin is maximized by minimizing the function\begin{equation*} \varphi(\fvec{w}, ... |
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Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
Search
Now showing items 1-1 of 1
Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
Search
Now showing items 31-40 of 155
Two- and three-pion quantum statistics correlations in Pb-Pb collisions at √sNN = 2.76 TeV at the CERN Large Hadron Collider
(American Physical Society, 2014-02-26)
Correlations induced by quantum statistics are sensitive to the spatiotemporal extent as well as dynamics of particle... |
Consider the algorithm LastMatch below, which returns the offset (shift) of the last occurrence of the pattern P in text T, or -1 if P does not occur in T:
LastMatch(T,P) for(s = T.length - P.length downto 0) j = 1 while(j =< P.length and P[j] == T[s + j]) j++ if(j == P.length + 1) return s return -1
I've been given a ... |
I want to show the following:
Let $f: \mathbb{R} \to \mathbb{R}$ be continuous.
a) If $f$ is differentiable and for $x \ne 0$ the limit $\lim_{x\to 0} f'(x) = A$ exists, then $f$ is differentiable at $x = 0$ and $f'(0) = A$.
b) Show that the inverse is false, i.e. there exists a function $f$ which is differentiable at ... |
When we have a logarithmic equation of second degree, we need to get rid of the logarithms and obtain an equivalent equation of second degree.
$$$\log(x^2+2x)-\log 8=0$$$ We can move the constant to the other side of the equation in order to eliminate the logarithms. We obtain a second degree equation that we know how ... |
PCTeX Talk Discussions on TeX, LaTeX, fonts, and typesetting
Author Message murray Joined: 07 Feb 2006 Posts: 47 Location: Amherst, MA, USA
Posted: Wed Mar 15, 2006 10:53 pm Post subject: Y&Y TeX vs. MiKTeX with MathTimePro2 fonts I used updated fonts just prior to posting of 0.98.
Initially I had different page breaks... |
Risk-neutral default probability implied from CDS is approximately $P=1-e^\frac{-S * t}{1-R}$, where $S$ is the flat CDS spread and $R$ is the recovery rate.The CDS Spread can be solved using the inverse:$$S=\ln(1-P) \frac{R-1}{t}$$$S$ is the spread expressed in percentage terms (not basis points)$t$ are the years to m... |
I really need help with this question. I am required to show that the set of odd natural numbers is closed under the operation * defined by a*b=a+b+ab, and I'm not quite sure how. Any work/help is greatly appreciated.
Let $a = 2n + 1$ and let $b = 2m + 1$ where $n, m \geq 0$.
We want to show that the set of natural odd... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
Learning Objectives
To recognize the SI base units and explain the system of prefixes used with them.
People who live in the United States measure weight in pounds, height in feet and inches, and a car’s speed in miles per hour. In contrast, chemistry and other branches of science use the International System of Units ... |
Can I be a pedant and say that if the question states that $\langle \alpha \vert A \vert \alpha \rangle = 0$ for every vector $\lvert \alpha \rangle$, that means that $A$ is everywhere defined, so there are no domain issues?
Gravitational optics is very different from quantum optics, if by the latter you mean the quant... |
I tried to figure out the MO-scheme of the tetragonal-bipyramidal complex
trans-$\ce{[Co(en)2(NCS)2]SCN}$ in which the isothiocyanate ligands are bound to the $\ce{Co^3+}$-Ion in $\eta^{1}$-mode (en = ethylenediamine). While undertaking this task I noticed that I don't know the MO-scheme of the isothiocyanate ion, whic... |
Goal
I wish to prove that it is possible to relate the Sobolev norms on an arbitrary triangle $K$ to Sobolev norms on a reference triangle $\hat{K}$.
Preliminaries
To this end: Let $F \colon \hat{K} \to K$ be an invertible affine map given by $F(\hat{x}) = B\hat{x} + c$. For a function $\hat{v} \in C^2(\hat{K})$, we de... |
I once spent far too long getting nowhere with this.
Is there a way of finding the real roots of $ax^k-bx^{k-1}+b-a=0$ where $a, b, k\in \mathbb N$ and $b\gt a$ and $k\gt 1$? I know that there is no general formula for solving polynomials of degree greater than 4, but with so few $x$s I thought it might be possible. No... |
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To send content items to your Kindle, first ensure no-rep... |
Evening All,Just enquiring as to whether someone can help me with the exact location for purchasing a 2016 Examination Response (for my younger sibling).I am on Students Online. I have done the following Go to My Details > Results Services - But can't seem to see the link to purchase...
Evening All,I'm new to completin... |
Energy changes which accompany chemical reactions are almost always expressed by
thermochemical equations, such as
\[\text{C} H_{4} (g) + 2 \text{O}_{2} (g) \rightarrow \text{C} \text{O}_{2} (g) + 2 \text{H}_{2} \text{O} (l) \text{ (25°C, 1 atm pressure)} \\ \Delta H_{m} = –890 \text{kJ} \label{1}\]
which is displayed ... |
Royden's (Real analysis, 4th edition, p.231) definition:
Let $X$ be a nonempty set and consider a collection of mapping $F=\{f_\alpha:X\rightarrow X_\alpha\}_{\alpha \in \Delta}$, where each $X_\alpha $ is a topological space. The weakest (coarsest) topology for $X$ that contains the collections of sets $\mathbb{F}=\{f... |
Good day to everyone.In my research work I came out with a function, which looks like this (it is the pdf of some random variable):$$f(x,\rho,\psi)=\frac{2}{\pi }+\sqrt{\frac{2}{\pi }} e^{-\frac{\rho ^2}{4}} \rho \sum _{k=1}^{\infty } \cos (2 k x ) \cos (2 k \psi )\left(I_{k+\frac{1}{2}}\left(\frac{\rho ^2}{4}\right)+I... |
When we are confronted with a new dataset, it is often of interest to analyse the structure of the data and search for patterns. Are the data points organized into groups? How close are the groups together? Are there any other interesting structures? These questions are addressed in the cluster analysis field. It conta... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
My question is how to evaluate Riemann's functional equation for values $\Re(s)<0$?
I know I must use the functional equation which is defined as $\zeta (s)=2^s\pi {}^{s-1}\sin \left(\frac{\pi s}{2}\right)\Gamma (1-s)\zeta (1-s)$.
Say I wanted to find $\zeta (-3+2i)$. I know how to calculate $2^s\pi {}^{s-1}\sin \left(... |
$$\int_{}^{} {{e^{ax}}dx} = \frac{{{e^{ax}}}}{a}+C$$
Unless $a=0$, in which case we're integrating $1$, and the answer is $x+C$.
This discontinuity is jarring, and seemingly odd. If we were to just substitute $a=0$ into $\frac{{{e^{ax}}}}{a}$, we don't get an indeterminate form that could possibly turn into $x$ if you ... |
We are going to try to solve the following example with the basic tools of Probabilities.
A screw factory has two machines, the M1, which is old, and does 75 % of all the screws, and the M2, newer but small, that does 25 % of the screws. The M1 does 4 % of defective screws, while the M2 just does 2 % of defective screw... |
Continuous Functions, Discontinuous Supremum
A function $f:\mathbb{R}\to\mathbb{R}$ is said to be
continuous if the preimage of any open set is open. Analogously, we might say that a function is measurable if the preimage of a measurable set is measurable. This is a generalization of the more standard defintions of a m... |
As we mentioned in the last post, there are currently over 2000 active speed loop detectors within the Bay Area highway system. The information provided by these loops is often highly redundant because speeds at neighboring sites typically differ little from one another. This observation suggests that a higher level, “... |
This is a problem known as finding 'moments of moments'.
NotationDefine the power sum $s_r$:
$$s_r=\sum _{i=1}^n X_i^r$$
Your problem only involves $s_1$.
The Problem
Let $\left(X_1,\ldots,X_n\right)$ denote a random sample of size $n$ from a population random variable $X$.
The problem is to find:
$$ E\Big [\Big (\frac... |
$$(2\sqrt 2 - 2)x^2 + \sqrt8 x + (1+\sqrt 2)=0$$
Now the discriminant of this is $0$, so it has one real repeated root. A plot on Desmos confirms this.
However, Wolfram Alpha displays the following (see image). The solution contains $i$ and doesn't agree with what it should be $= -1.707...$
What is happening?
[Solution... |
Typesetting Math
Floats
Introduction to LATEXAleksandar PetrovEUROAVIA Delft
October 8, 2015EUROAVIA
Additional resources
What is LATEX
Contents
12
What is LATEXThe Basics of the BasicsDocument LayoutSectioningLine BreaksTable of contentsBig project managementSpecial charactersTypesetting MathMath environments
Typing s... |
Thermodynamics is the study of thermal, electrical, chemical, and mechanical forms of energy. The study of thermodynamics crosses many disciplines, including physics, engineering, and chemistry. Of the various branches of thermodynamics, the most important to chemistry is the study of the change in energy during a chem... |
I am trying to compute a similarity measure between the orientation of 3D objects accounting for symmetry invariance. I have a set of 3D objects, which are defined by a center of mass, and 3 unit vectors associated to the orientation of this object such that $vec_1$ defines the orientation of the main axis, $vec_2$ the... |
Okay, so I understand that the equation is a downwards facing parabola with a y-intercept at 12. I don't understand what it means by upper vertices? I know that the answer is 32 but I don't understand how to get there. Can someone please guide me and explain to me the process of solving this problem? Thank you!
Let's $... |
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