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Consider the following 2D wave equation:
$$ \left(\frac{d^2}{dx^2}-k_y^2+\omega^2\ V(x)\right)\psi(x)=0 $$ where $V(x+L)=V(x)>0$ is a positive periodic potential, $k_y$ is the wave vector along $y$-direction, $\omega$ is the frequency, and the eigenfunction satisfies the periodic boundary condition $\psi(x+L)=\psi(x)$,... |
Perloff 3.1-4. WB 3.
You do not need to remember which Greek letter is associated with which elasticity. In questions, elasticities will always be referred to by name, not symbol.
The general formula
Suppose X increases by 1%; the “X elasticity of Y” is the percent change in Y that results (divided by 100).
Price elast... |
Author Siargey Kachanovich
Witness complex representation
Definitions
Witness complex is a simplicial complex defined on two sets of points in \(\mathbb{R}^D\):
\(W\) set of witnesses and \(L\) set of landmarks.
Even though often the set of landmarks \(L\) is a subset of the set of witnesses \( W\), it is not a require... |
It is known DLMF (25.2.8) that for $\Re s>0$ and for integers $N\geq 1$ $$\zeta(s)=\sum_{k=1}^N\frac{1}{k^s}+\frac{N^{1-s}}{s-1}-s\int_{N}^\infty \frac{x-\lfloor x \rfloor}{x^{s+1}} dx,$$
where $\zeta(s)$ is the
Riemann zeta function.
Then if I propose $\rho= \left(\frac{1}{2}+\epsilon \right)+it, $ satisfying $\zeta(\... |
(a) Let $$E_1\subset E_2\subset ... \subset E_n\subset ... \subset I_0=:[a,b]$$
be a sequence of measurable sets and let $f:[a,b]\to\mathbb{R}$ be a non-negative integrable function. Show that $$\lim_{n\to\infty}\int_{E_n}f(x)d\mu=\int_E f(x)d\mu\,\,\,\,\,\,\text{ where }E=\cup_{n=1}^\infty E_n$$
(b) Is the above state... |
I've been trying to integrate this:
$$\int_0^\infty \frac{1}{x^2 + 2x + 2} \mathrm{d} x .$$
Unfortunately I haven't found a way so far. I've been trying to factor the denominator in order to end up with partial fractions. Is there a way to factor it? If so, I can't remember any, so if you could remind me how to do it, ... |
ISSN:
1930-5311
eISSN:
1930-532X
All Issues
Journal of Modern Dynamics
October 2007 , Volume 1 , Issue 4
Select all articles
Export/Reference:
Abstract:
These notes combine an analysis of what the author considers (admittedly subjectively) as the most important trends and developments related to the notion of entropy, ... |
Perloff 6, 7; WB 12 and 13.
We examine how firms' costs are determined by two key Supply shifters — technology and input prices. This provides a foundation for the Supply curve in our model of perfect competition (it is equal to the marginal cost curve).
In this section the firm uses two inputs to reach a fixed output ... |
States of Matter: Gases and Liquids Gas Laws and Ideal Gas Equation and Kinetic Molecular Theory of Gases Gas Laws: \tt V\propto\frac{1}{P} (Boyle's Law) PV = constant
Charles' Law: V ∝ T (or) \tt \frac{V_{1}}{V_{2}}=\frac{T_{1}}{T_{2}} Gay-Lussac Law: \tt \frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}}
Avagadro's Law: V ∝ n I... |
So now let’s use the skills from the last two posts to work on mixed fractions. Consider:\[
{3}\frac{3}{8}\hspace{0.33em}{+}\hspace{0.33em}{6}\frac{7}{8}
\]
As the denominators are the same, one can do this problem by adding the whole parts first to get 9 then add the fractions together to get \[
\frac{10}{8} \] which ... |
Invited speakers
There will be four invited talks at FCT 2017. The invited speakers are:
Thomas Colcombet (CNRS, University of Paris-Diderot, France) Martin Dietzfelbinger (Technische Universität Ilmenau, Germany) Juraj Hromkovič (ETH Zürich, Switzerland) Anca Muscholl (University of Bordeaux, France) Jean-Éric Pin (CN... |
I am reading from
Degree Theory by N. Lloyd, and in one section he writes about the degree of a holomorphic map of several complex variables. I am unsure about one of the steps in a proof he gives.
The setup:
$\mathbb{C}^n$ is the vector space of complex $n$-tuples $z=(z_1,\ldots,z_n)$. $D$ is a bounded, open subset of... |
Skills to Develop
To learn the distinction between independent samples and paired samples. To learn how to construct a confidence interval for the difference in the means of two distinct populations using paired samples. To learn how to perform a test of hypotheses concerning the difference in the means of two distinct... |
Skills to Develop
To learn how to construct a confidence interval for the difference in the means of two distinct populations using small, independent samples. To learn how to perform a test of hypotheses concerning the difference between the means of two distinct populations using small, independent samples.
When one ... |
Here is my answer to a similar question posed a few days ago:
One of the most important functions in analysis is the function$$\arg:\quad \dot{\mathbb R}^2\to{\mathbb R}/(2\pi),\quad{\rm resp.},\quad \dot{\mathbb C}\to{\mathbb R}/(2\pi),$$written as $$\arg(x,y), \quad \arg(x+iy),\quad{\rm or}\quad \arg(z),$$depending o... |
I will provide an answer but from a different perspective, and hopefully convince you that there is information in a density matrix which has no classical counterpart. Furthermore this can hence be considered a quantum component, and it can be shown that this information is stored as the eigenvectors of $\rho$.
I will ... |
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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 ... |
So I will get back to roots of numbers, but let’s first look at the rules for combining exponents.
Now an integer exponent means that you are multiplying the base together as many times as the exponent indicates. That is,
\[
{3}^{5}\hspace{0.33em}{=}\hspace{0.33em}{3}\hspace{0.33em}\times\hspace{0.33em}{3}\hspace{0.33e... |
I failed to do this question on the exam and finding it very difficult, I would be glad if you can help me solve it. How shall I start?
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It only takes a minute to sign up.Sign up... |
Suppose we have two distributions given by the vectors $p=(p_1,\dots,p_n)$ and $q=(q_1,\dots,q_n)$, with $p_i,q_i\geq 0$, and $\sum_i p_i = \sum_i q_i=1$.
Now suppose that for some $\alpha\in(0,\infty)$,
$$H_{\alpha}(p)=H_{\alpha}(q),$$
where $H_{\alpha}(p)=\frac{1}{1-\alpha}\log\sum_i p_i^{\alpha}$ is the Rényi entrop... |
I had the impression that there might be proofs of the irrationality of $\sqrt{2}$ that showed that $$ \left|\frac a b - \sqrt{2} \right| \ge (\text{something possibly depending on $a$ or $b$}) >0 $$ where $a,b\in\mathbb{Z}$. But the one I saw in Wikipedia's article on the square root of $2$ spoke of whether the multip... |
How can I solve this problem without using L'Hôpital's rule?$$\lim_{x→0}\frac{(\sin(x)-x)(\cos(3x)-1)}{x(e^x -1)}$$
Thanks in advance!
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 thi... |
So, I have a book here, which has an example for context sensitive grammar, and the grammar is the famous $0^n1^n2^n$ , and it has:
$$ \begin{align} S &\rightarrow 0BS2 \mid 012 \\ B0 &\rightarrow 0B \\ B1 &\rightarrow 11 \\ \end{align} $$
I agree that the above works, but what is wrong with just saying: $S\rightarrow ... |
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 ... |
Once we have organized and summarized your sample data, the next step is to identify the underlying distribution of our random variable. Computing probabilities for continuous random variables are complicated by the fact that there are an infinite number of possible values that our random variable can take on, so the p... |
I'm reading a linear algebra book and it defines the integration operation as $T \epsilon L(P(\Bbb R), \Bbb R)$. However, it defines the differentiation operation as
T $\epsilon$ $L(P(\Bbb R), P(\Bbb R))$. Don't they both map to the vector space that contains all polynomials? Why is integration as a linear function def... |
In a recent article with Valérie Berthé [BL15], we provided a multidimensional continued fraction algorithm called Arnoux-Rauzy-Poincaré (ARP) to construct, given any vector \(v\in\mathbb{R}_+^3\), an infinite word \(w\in\{1,2,3\}^\mathbb{N}\) over a three-letter alphabet such that the frequencies of letters in \(w\) e... |
The group-algebra of an abelian group is commutative, so we can consider the spectrum of this algebra. Are there any information about the abelian group that we can obtain from such considerations? That is to say, could we study abelian groups by considering the spectrum and the scheme of its group-algebra?
Since I kno... |
A sphere is 3D or a solid shape having a completely round structure. If you rotate a circular disc along any of its diameters, the structure thus obtained can be seen as a sphere. You can also define it as a set of points which are located at a fixed distance from a fixed point in a three-dimensional space. This fixed ... |
Optimal control of the coefficient for the regional fractional $p$-Laplace equation: Approximation and convergence
1.
Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA
2.
University of Puerto Rico, Rio Piedras Campus, Department of Mathematics, College of Natural Sciences, 17 Universi... |
Models at Dynamic Stochastic General Equilibrium level must be able to replicate real economies to an acceptable degree. One of the features of real economies has been a relatively stable
growth rate (see also this post), $\dot x/x=\gamma$, where the dot above a variable denots the derivative with respect to time.
So o... |
PRZEMYSLAW DOBROWOLSKI has written a paper that (I think) can be applied to swing-twist decompositions for quaternion rotations called "SWING-TWIST DECOMPOSITION IN CLIFFORD ALGEBRA" .
I tried to apply Algorithm 1 in the paper to this simple scenario: I want to calculate the angle between the world z-axis and the body ... |
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The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
Abbreviation:
InRL
An
is a structure $\mathbf{A}=\langle A, \vee, \wedge, \cdot, 1, \sim, -\rangle$ of type $\langle 2, 2, 2, 0, 1, 1\rangle$ such that involutive residuated lattice
$\langle A, \vee, \wedge, \neg\rangle$ is an involutive lattice
$\langle A, \cdot, 1\rangle$ is a monoid
$xy\le z\iff x\le \neg(y(\neg z))... |
Does anyone have the idea to solve the global multivariate minimization problem as below?
$$\text{minimizes}\quad (x_1x_2x_3+x_1x_4x_5+x_1x_6x_7+x_2x_4x_6+x_2x_5x_7+x_3x_4x_7)-(x_1+x_2+x_4+x_7) \\ \text{subject to}\quad 1\leq x_i\leq N, \forall 1\leq i \leq 7, \text{ and }\prod_{i=1}^7 x_i=N$$
where $N>1$ is a constant... |
Wave energy converters in coastal structures: verschil tussen versies
(→Application for wave energy converters)
(→Application for wave energy converters)
Regel 78: Regel 78:
<p>
<p>
−
where
+
where
+ +
represents the spectral moment of order n. An equation similar to that describing the power of regular waves is then o... |
While reading the the book on neural network http://neuralnetworksanddeeplearning.com/chap2.html by Michael Nielson I had a problem of understanding eqn BP3. Which reads as "Change in cost wrt bias in a neuron is equals to error in that neuron". (Sorry unable to put the eqn here.)
This is just an application of the cha... |
How does one calculate fully quantum mechanical rate ($\kappa$) in the golden-rule approximation for two linear potential energy surfaces?
Attempt:
Miller (83) proposes $\kappa=\int{Tr[\exp{(-\beta\hat{H})}\hat{F}\exp{(-i\hat{H}t/\hbar)}\hat{F}\exp{(i\hat{H}t/\hbar)}]}dt$
Where integrand is simply the flux-flux correla... |
Notice:
If you happen to see a question you know the answer to, please do chime in and help your fellow community members. We encourage our fourm members to be more involved, jump in and help out your fellow researchers with their questions. GATK forum is a community forum and helping each other with using GATK tools a... |
First we must check that $T$ takes values in $W$, as the problem implies but does not prove. Consider $f \in C([-1 , 1])$. The function $T(f)$ lies in $W$ if and only if $T(f)(0) = 0$. We quickly check that it satisfies this condition:in $C([-1, 1])$ lies\[ T(f)(0) = f(0) – f(0) = 0 . \]
Now that we know $T$ takes valu... |
A few years ago, I noticed a glitch in a paper that colleagues of mine had published back in 2002. A less-than sign in an inequality should have been a less-than-or-equals. This might have been a transcription error during the typing-up of the work, or it could have entered during some other phase of the writing proces... |
[math]logit(p) = log(odds(p)) = log(\frac{p}{1-p}) \\
expit(p) = \frac{exp(p)}{1+exp(p)} = \frac{2^p}{1+2^p}
[/math]
In order to prove these are inverses, I am going to prove that
[math]\begin{eqnarray}
p &=& logit(expit(p)) \\
&=& log(\frac{expit(p)}{1-expit(p)}) \\
&=& log\Big[\frac{\frac{exp(p)}{1+exp(p)}}{1-\frac{e... |
Skills to Develop
To use Spearman rank correlation to test the association between two ranked variables, or one ranked variable and one measurement variable. You can also use Spearman rank correlation instead of linear regression/correlation for two measurement variables if you're worried about non-normality, but this ... |
2,100 16
I'm now interested in a Schrödinger's equation
[tex] \Big(-\frac{\hbar^2}{2m}\partial_x^2 + V(x)\Big)\psi(x) = E\psi(x) [/tex]
where [itex]V[/itex] does not contain infinities, and satisfies [itex]V(x+R)=V(x)[/itex] with some [itex]R[/itex]. I have almost already understood the Bloch's theorem! But I still hav... |
Answer
$128.0$ ft
Work Step by Step
Let $d$ the distance between the automobile and the person. $\sin23^{\circ}=\frac{50}{d}$ $d=\frac{50}{\sin23^{\circ}}$ $d\approx128.0$
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 send in a d... |
Answer
$\theta =60^{\circ}$
Work Step by Step
We know that the two pieces have equal velocities and equal masses, so they form the same angle with the x-axis. We find that this angle is: $cos\theta = \frac{1}{2} \\ \theta =60^{\circ}$
You can help us out by revising, improving and updating this answer.Update this answe... |
Table of Contents
A line integral is an integral of a function along a curve in space. We usually represent the curve by a parametric equation, e.g. \(\mathbf{r}(t) = [x(t), y(t), z(t)] = x(t)\mathbf{i} + y(t)\mathbf{j} + z(t)\mathbf{k}\). So, in general the curve will be a vector function, and the function we want to ... |
Some of our older headers tell stories about inverse problems and data assimilation.
Engineering the World: Ove Arup and the Philosophy of Total Design (V&A London Nov 2016). Art and science do not need to live on different planets. Today, much art needs and is based on science, and science includes elements of beauty,... |
[Top][All Lists] [Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index] [Axiom-developer] [#187 trouble with tuples] [#187 trouble with tuples]
From: William Sit Subject: [Axiom-developer] [#187 trouble with tuples] [#187 trouble with tuples] functions are objectsof type Mapping Date: Mon, 04 Jul 20... |
Answer
$19^{\circ}$
Work Step by Step
Let $\alpha$ be the angle formed by the rope and the water. $\sin\alpha=\frac{4}{12}$ $\alpha=\sin^{-1}\frac{4}{12}$ $\alpha\approx19^{\circ}$
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 se... |
Fundamentally it's mathematics. The energies of the MOs are the eigenvalues of the matrix $$\begin{pmatrix}\alpha_1 & \beta \\ \beta & \alpha_2 \end{pmatrix},$$ where $(\alpha_1,\alpha_2)$ are the energies of the two constituent orbitals and $\beta$ is (loosely speaking) the overlap between them.
For the same size of $... |
Version 6.0 [beta] of the UAH [AMSU] Temperature Dataset Released: New LT Trend = +0.11 C/decade [raw data]which is more compatible with the RSS AMSU dataset. In fact, UAH now shows a smaller (by 1/4 or so) warming trend than RSS. The trend has been exactly zero in the last 18 years. In the past, I tended to slightly p... |
Fitting Data
A common and powerful way to compare data to a theory is to search for a theoretical curve that matches the data as closely as possible. You may suspect, for example, that friction causes a uniform deceleration of a spinning disk, so you have gathered data for the angular velocity of the disk as a function... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
The earliest forms of the extended Euclidean algorithm are ancient, dating back to 5th-6th century A.D. work of Aryabhata - who described the Kuttaka ("pulverizer") algorithm for the more general problem of solving linear Diophantine equations $ ax + by = c$. It was independently rediscovered numerous times since, e.g.... |
Let $\Omega$ be a nonempty open subset of $\mathbb{R}^n$, and let $\cup_{n=1}^\infty K_n = \Omega$ be an exhaustion of $\Omega$ by compact sets. Let $\mathcal{D}(\Omega) = \mathcal{D}$ be the standard $\mathbb{C}$-vector space of smooth functions $\phi: \Omega \to \mathbb{C}$ with compact support in $\Omega$. Equip $\m... |
作者：Hariwan Zikri Ibrahim 来源：[J].Journal of Advanced Studies in Topology, 2015, Vol.6 (2), pp.61-68现代科学出版社 摘要：The purpose of this paper is to introduce the new concepts namely, α-g-closed, pre-g-closed, semi-g-closed, b-g-closed, β-g-closed, α-g-open, pre-g-open, semi-g-open, b-g-open and β-g-open sets in ditopological ... |
I understand the principle of less airflow, less control, but why is that the case?
Because moments of inertia don't change with speed
Control effectiveness means that the controls effect a change in the balance of moments which results in the desired attitude change. The smaller the control deflection for the same cha... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
I should be tarred and feathered for not knowing at least the status of the following question.
Question:Let $\Gamma$ be a discrete amenable group. If $\pi:\Gamma \rightarrow B(\mathcal{H})$ is a unitary representation of $\Gamma$ on a separable Hilbert space $\mathcal{H}$, is the von Neumann algebra $\pi(\Gamma)''$ ne... |
By Dr Adam Falkowski (Résonaances; Orsay, France)
The title of this post is purposely over-optimistic in order to increase the traffic. A more accurate statement is that a recent analysis
of X-ray spectrum of galactic clusters claims the presence of a monochromatic \(3.5\keV\) photon line which can be interpreted as a ... |
Fermi surface of the Weyl type-II metallic candidate Abstract
Weyl type-II fermions are massless quasiparticles that obey the Weyl equation and which are predicted to occur at the boundary between electron- and hole-pockets in certain semi-metals, i.e. the (W,Mo)(Te,P)$$_2$$ compounds. Here, we present a study of the F... |
Wave energy converters in coastal structures: verschil tussen versies
(→Environmental impact)
(→See also)
Regel 283: Regel 283:
* [[Seawall]]
* [[Seawall]]
* [[Seawalls and revetments]]
* [[Seawalls and revetments]]
−
* [[Coastal defense techniques]]
+
* [[Coastal defense techniques]]
* [[Wave energy converters]]
* [[W... |
Happy New Year and welcome to my first post of 2019!
My last post introduced the idea of modelling physical things with math equations. To do this from scratch, requires calculus but seeing the final result is very interesting. So in my last post, I modelled the simple physical event of a ball thrown into the air. Anot... |
ISSN:
1556-1801
eISSN:
1556-181X
All Issues
Networks & Heterogeneous Media
June 2015 , Volume 10 , Issue 2
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Export/Reference:
Abstract:
We study the approximation of Wasserstein gradient structures by their finite-dimensional analog. We show that simple finite-volume discretizations of the linear Fok... |
Do we have complexity classes with respect to, say, average-case complexity? For instance, is there a (named) complexity class for problems which take expected polynomial time to decide?
Another question considers the
best case complexity, exemplified below:
Is there a class of (natural) problems whose decision require... |
Let $$f(x,y)=\sum_{n\in\mathbb{Z}\backslash\{0\}}\frac{1}{n}e^{2\pi i(xn+yn^2)} $$ Is it true that $\|f\|_{L^{\infty}(\mathbb{R}^2)}<\infty$? i.e. is $f$ essentially bounded?
The answer is yes. Fix $x,y$, and write $e(\alpha) := e^{2\pi i \alpha}$.
Using a Littlewood-Paley partition of unity and the triangle inequality... |
Let $X$ be a smooth projective complex analytic space. We can cook up a complex analytic version of Bloch's cycle complex by declaring
$z^n(X^{\rm an}, m)$
is the free abelian group on all codimension $m$ analytic cycles on $X\times\Delta^n$ ($\Delta^n$ being the usual standard $n$ simplex in complex analytic spaces, i... |
Let $\chi : (\mathbb Z/f\mathbb Z)^\times \to K = \mathbb Q(\mu_{\phi(f)})$ be a primitive Dirichlet character. Assume moreover that it is
not quadratic, that is, $\chi^2$ is not the trivial character. Let $\pi_1,\dots,\pi_g$ be the primes lying over $2$ and $v_1,\dots,v_g$ be the corresponding valuations. Recall that:... |
Some excellent ideas and approaches to this problem. The first partof the problem (when the triangle is larger than the square) isfairly accessible; as is the part where the two equal sides of thetriangle shrink to less than half the length of the side of thesquare but the bit in between is tricky!!
The first solution ... |
Passive vibration suppression of plate using multiple optimal dynamic vibration absorbers Abstract
In the present paper, the optimization problem of the dynamic vibration absorbers (DVAs) for suppressing vibrations in thin plates within the wide frequency band is investigated. It is considered that the plate has simply... |
The Beta distribution has the PDF:
$$f\left(x\right)=\frac{x^{\alpha-1}\left(1-x\right)^{\beta-1}}{\mathrm{B}\left(\alpha,\beta\right)}$$
for $0<x<1$, and $f(x)=0$ otherwise. The parameters $\alpha,\beta$ are positive real numbers.
The mean and variance are given by:
$$\mu=\frac{\alpha}{\alpha+\beta},\quad\sigma^{2}=\f... |
The feature that makes LaTeX the right editing tool for scientific documents is the ability to render complex mathematical expressions. This article explains the basic commands to display equations.
Contents
Basic equations in LaTeX can be easily "programmed", for example:
The well known Pythagorean theorem \(x^2 + y^2... |
Steven from City of Sunderland College sent us in a wonderful, complete solution to this problem, which we recommend reading in full to any budding problem solver. The main points are as follows:
The gravitational potential energy of a cannon ball of mass $m$ at a distance $r$ from the centre of a planet of mass $M$ is... |
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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 ... |
Equilibrium Acids and Bases and their Ionisations Strong acid : 100% dissociation HClO 4, H 2SO 4, HNO 3, HI, HBr HCl + H_{2}O \rightarrow H^{+} + Cl^{-} Strong base : NaOH, KOH, RbOH, CsOH, Ba(OH) 2 Weak acid : Which undergoes partial dissociation
Hydrogen ion concentration :
K_{a} = \frac{C{\alpha} \ C{\alpha}}{C - C... |
The simple regression linear model looks like $y = X\beta + \epsilon$ and among constraints we have independent white noise $\epsilon_i \sim N(0, \sigma^2)$. Fitting with least mean squares gives the know normal equations in the form:
$\hat{\beta} = (X^TX)^{-1}X^Ty$
To optimize with least mean square one does not use a... |
Working paper Open Access
Maurice H.P.M. van Putten
Surveys of the Local Universe show a Hubble expansion significantly greater than $\Lambda$CDM estimates from the Cosmic
Microwave Background by Planck. This may present a challenge to our application of general relativity to cosmology. Such tensions are expected in qu... |
As Sasho suggested, I am putting my comment as an answer.
The separations between
monotone versions of $\mathsf{NC}^1/\mathsf{poly}$ and $\mathsf{P/poly}$ versions of complexity are long known (Karchmer-Wigderson, Grigni-Sipser, etc), but in the non-monotone world almost nothing was known. Fortunately, Ben Rossman has ... |
We prove the equivalences $(1) \Leftrightarrow (2)$ and $(2) \Leftrightarrow (3)$.
$(1) \implies (2)$
Suppose that $R$ is a field. Let $I$ be an ideal of $R$.If $I=(0)$, then there is nothing to prove.So assume that $I\neq (0)$.
Then there is a nonzero element $x$ in $I$.Since $R$ is a field, we have $x^{-1}\in R$.
Sin... |
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Now showing items 1-10 of 26
Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
Because complex exponentials $e^{\jmath \omega t}$, which are results of Fourier transform, are the eigenfunctions for linear, time invariant (LTI) systems. See eigenfunction of LTI. Also see this answer on SP.SE.Thus, Fourier transform is useful for analyzing linear (not suitable for non-linear one) time invariant (ca... |
The dependence of a response variable on two factors, A and B, say, is of interest.
Factor A has a levels and Factor B has b levels. In total there are a x b treatments. Sample sizes for all treatment groups are equal (balanced design). Goal: to study the simultaneous effects of the two factors on the response variable... |
This question already has an answer here:
Find $$\lim_{n\to\infty} \sum_{k=1}^{n}\left( \frac{k}{n}\right)^{n}$$
I can't compare it with similar series and I can't change it to Riemann's sum.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fiel... |
I'm stuck on the following question and would greatly appreciate any help:
A lossless transmission line is formed by a wire of radius a placed in vacuum a distance d above an infinite conducting plane with $d>>a$. Calculate the capacitance and Inductance per unit length.
I'm able to calculate the capacitance per unit l... |
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Tuesday, 13 May 2014 :: day 1
Heavy Flavor I
Conveners: Daniel Kikola, Zhenyu Ye, Yifei Zhang
(Cytosin : 09:00 - 12:30)
Time Talk Presenter 09:00 QM rehearsal: Open charmed hadron production in p+p, Au+Au and U+U collisions at STAR ( 01:00 ) 1 file Zheny... |
From my last three posts, I think we are ready to model the motion of a mass on a spring:
So, just like I did with the tennis ball, I will show you equations that describe this motion.
Now again, to develop these equations requires calculus, so I will just provide the final result. But before I do, just how does one be... |
An element $a \in \mathbb{Z}_n$ is a quadratic residue in $\mathbb{Z}_n$ if it's congruent to some perfect square modulo $n$.
Is there an efficient algorithm to find all quadratic residues in $\mathbb{Z}_n$?
$n$ is composite and we know all it's factors if that helps. Update:
We have one more restriction: $n$ = $p_1 p_... |
65 4 Homework Statement Two identical audio speakers, connected to the same amplifier, produce monochromatic sound waves with a frequency that can be varied between 300 and 600 Hz. The speed of the sound is 340 m/s. You find that, where you are standing, you hear minimum intensity sound a) Explain why you hear minimum-... |
Recall the third isomorphism theorem of groups:Let $G$ be a group and let $H, K$ be normal subgroups of $G$ with $H < K$.Then we have $G/K$ is a normal subgroup of $G/H$ and we have an isomorphism\[G/K \cong (G/H)/(G/K).\]
Proof 1 (Using third isomorphism theorem)
Since $H, K$ are normal subgroups of $G$ and $H < K$, t... |
If $A$ is a noetherian domain and not a field then the infinite product $M=A\times A\times \dots$ is not free. Suppose there is a basis. For $x\in M$ define its support to be the finite set of basis elements for which the coefficient is not zero. Note that if the supports of $x$ and $y$ are disjoint then their union is... |
Rank Abundance Graphs
Species abundance distribution can also be expressed through rank abundance graphs. A common approach is to plot some measure of species abundance against their rank order of abundance. Such a plot allows the user to compare not only relative richness but also evenness. Species abundance models (a... |
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Long-range angular correlations of π, K and p in p–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV
(Elsevier, 2013-10)
Angular correlations between unidentified charged trigger particles and various species of charged associated particles (unidentified particles, pions, kaons, protons ... |
Let $I \subset \mathbb{R}$ and for $\forall n \in \mathbb{N}: f_n \in C(I, \mathbb{R})$. Prove that if for any $\sigma:\mathbb{N} \rightarrow \mathbb{N}$ bijection, the series $$\sum_n f_{\sigma(n)}$$ converges uniformly on $I$, then $$\sum_n |f_n|$$ also converges uniformly on $I$. I'm thinking of a proof by contradic... |
I've seen a number of 2D Poisson disc sampling algorithms online that use a grid to accelerate checking for existing points within the minimum radius [![r][r image]][r link] of a candidate point. For example:
They use a grid of squares of side $\frac{r}{\sqrt2}$, which is the same side length that I intuitively came up... |
Evidence for the production of three massive vectorbosons in $pp$ collisions with the ATLAS detector
Pre-published on: 2019 June 27
Published on: 2019 October 04
Abstract
A search for the production of three massive vector bosons in proton--proton collisions is performed using data at $\sqrt{s}=13\,TeV$ recorded with t... |
Let $w$ denote the weight on $A$ so that $1-w$ is the weight on $B$. Recall from the properties of variance that
$\sigma_p^2 = w^2\sigma_A^2 + 2w(1-w)\sigma_A\sigma_B \rho_{AB}+ (1-w)^2\sigma_B^2$
Without loss of generality, assume $\sigma_A \geq \sigma_B$. We wish to show that
$w^2\sigma_A^2 + 2w(1-w)\sigma_A\sigma_B ... |
This question already has an answer here:
I have a long equation that must fit in a two-column journal. I know how to break up the right-hand terms nicely, but even so it won't fit and I need the equal signs to start on a new line, but I can't figure out how to do it nicely.
Here is what I've tried:
\begin{align*}p(\{K... |
Estimating a firm’s true market value presents a challenge for financial professionals and technical analysts. Researchers at Bank of England have investigated this problem to understand how a firm’s true value is affected by periods of high market volatility.
A firm’s assets are subject to uncertainties such as profit... |
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