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Difference between revisions of "Group cohomology of dihedral group:D8"
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==Homology groups for trivial group action==
==Homol... |
The best way to see the differences is to use the Thevenin equivalent for a resistor divider set up between two ideal (no source resistance of their own) voltage sources. Often, this is just some supply voltage and ground.
Let's look at the obvious case:
simulate this circuit – Schematic created using CircuitLab
The le... |
Intuition:A way to see what is going on is to see the affine approximation of $e^x$ around $0$: $$e^u \simeq e^0 + (e^\prime)(0) x = 1 + x$$ (this can be made formal by Taylor approximations to order $1$, for instance). This implies that your quantity is roughly $\left(x+ 1+ \frac{x}{3}\right)^{3/x} = \left(1+ \frac{4x... |
For any finite cyclic group $H$ with generator $t$, an automorphism of $H$ is completely determined by its effect on $t$ (which it must take to $t^k$ for some $k$ prime to the order of $t$). Hence Aut($H$) is abelian.
Next we show that if $H$ is any subgroup of $G$, then $N_G(H)/C_G(H)$ is isomorphic to a subgroup of A... |
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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 ... |
If there are 4 people involved, and every two of them should be able to know the secret (the polynomial is just a line) and you are given $f(x)$ and $x$ for each of those people, and you know one of them is a cheater, how do you find the cheater?
Shamir's secret-sharing scheme has $n$ shares of a secret. The shares are... |
There are two ways that lookaheads 'come into being'. The first is that the start production $S' \rightarrow S$ has lookahead $\$$ in the initial state of the $LR(1)$ automaton. Hence, $S' \rightarrow \bullet S, \$$ is an item in the initial state.
Pendantry note: we therefore accept in the state containing the item $S... |
The parameter $\frac{1}{12}$ is kind of weird, it has the factor of 3, when the problem is about integration or derivation，we can assume it's about quadratic function.
what's more, as $f(0) = f(1) = 0$, we assume the equality stands when the function is symmetrical.
after trying, we can see function $f(x) = x(1-x)$ can... |
I'm studying Hopf-Rinow theorem and I don't see a step in the proof. Could someone help me, please?
(Definition) Let's $(M, \langle,\rangle)$ an ANII(axiom numerability 2) and Hausdorff Riemannian manifold. If $M$ is connected and $p,q \in M$. We define: $$d_L:M\times M \longrightarrow [0,\infty)$$ $$(p,q)\longmapsto i... |
SIR model: swine flu
From JSXGraph Wiki
Revision as of 14:46, 8 June 2011 by Michael
The SIR model (see also Epidemiology: The SIR model) tries to predict influenza epidemics. Here, we try to model the spreading of the H1N1 virus, aka swine flu.
According to the CDC Centers of Disease Control and Prevention: "Adults sh... |
Classic examples of Taylor polynomials
Some of the most famous (andimportant) examples are the expansions of ${1\over 1-x}$, $e^x$,$\cos x$, $\sin x$, and $\log(1+x)$ at $0$: right from the formula,although simplifying a little, we get\begin{align*}{1\over 1-x}&=1+x+x^2+x^3+x^4+x^5+x^6+\ldots\\e^x&=1+{x\over 1!}+{x^2\o... |
Definition:Balanced Incomplete Block Design Definition
A
Balanced Incomplete Block Design or BIBD with parameters $v, b, r, k, \lambda$ is a block design where: $v$ is the number of points in the design $b$ is the number of blocks $k$ is the size of each block $r$ is the number of blocks any point can be in $\lambda$ i... |
I now introduce the problem:
Let assume $\mathbf{z} = (z_1, z_2,z_3)$ be a trivariate normal variable. I want to find the covariance matrix of $\mathbf{z}$. I now that the density of $(z_1, z_2)$ is a bivariate normal with mean vector $(\mu_1, \mu_2)$ and covariance matrix $$ \left( \begin{array}{cc} \sigma_1^2 & \sigm... |
I'm having trouble proving the following inequality:
$$\forall p>1 \quad \forall m\geq 0 \quad \dfrac{m^2\Gamma(\dfrac{2m}{p})\Gamma(\dfrac{2m}{q})}{\Gamma(\dfrac{2m+2}{p})\Gamma(\dfrac{2m+2}{q})}\geq\dfrac{1}{4}p^2(p-1)^{\frac{2}{p}-2},$$ where as usual $q=\dfrac{p}{p-1}$. In fact, it seems clear from Mathematica that... |
There is exist tradition to formulate axiom schemes such as induction, comprehension or replacment in a way like "for each formula $\phi(y,\overline{x})$ with free variables $y$ and $\overline{x}=x_1,...,x_n$ we have $\forall \overline{x} ( \text{text of axiom scheme which include } \phi(y,\overline x))$". To not be va... |
The expected value of
colMeans will allways be unbiased, no matter whether you inrease
NObs or
Niter, but the difficult part of your question is, whether the variances will change.
We know that
estimates $\sim N_2(\mu = \beta, ~ \Sigma = \sigma_\varepsilon^2 \cdot (X_{NObs}^T X_{NObs})^{-1})$ with $\beta$ being
beta, $... |
Journal of Differential Geometry J. Differential Geom. Volume 99, Number 1 (2015), 77-123. On the algebra of parallel endomorphisms of a pseudo-Riemannian metric Abstract
On a (pseudo-)Riemannian manifold $(\mathcal{M}, g)$, some fields of endomorphisms, i.e. sections of $\mathrm{End}(T \mathcal{M})$, may be parallel f... |
I want to find a non-deterministic $2$-tape Turing Machine, that accepts the language $L$ over $\Sigma=\{0,1,\#\}$ in linear time, $$L=\{x\#y \mid x,y \in \{0,1\}^\star, x \text{ is contained in } y\}$$
$$$$
Does the Turing Machine look as follows?
The tape $1$ contains the input $w$ and the tape $2$ contains blanks.
T... |
Let $(V, \| \cdot \|)$ be a normed vector space and $W$ be a linear subspace.
Prove that $T: V^*/W^{\perp} \to W^*, \ T(x^* + W^{\perp}) = y^*$ where $y^*(x) = x^*(x)$ for all $x \in W$, is an isometric isomorphism.
$\perp$ denotes the annihilator, and $*$ the dual. There was a hint included that said
"First show that ... |
Probabilists often work with Polish spaces, though it is not always very clear where this assumption is needed.
Question: What can go wrong when doing probability on non-Polish spaces?
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.Sign up to join this comm... |
Let $X$ be a smooth compact 4-manifold. Then every element of $H_2(X;\mathbb{Z})$ can be represented by a smooth embedded orientable surface and we have the so called genus function $G: H_2(X; \mathbb{Z}) \to \mathbb{Z}_{\geq 0}$ which assigns to a homology class the smallest genus of such a smooth surface needed to re... |
Answer
$$\cos t=\sqrt{1-\sin^2t}$$ The equation is not an identity, which can be proved by trying $t=\pi$.
Work Step by Step
$$\cos t=\sqrt{1-\sin^2t}$$ To disprove this equation is an identity, we can take $t=\pi$. At $t=\pi$, $$\cos t=\cos\pi=-1$$ and $$\sqrt{1-\sin^2t}=\sqrt{1-\sin^2\pi}=\sqrt{1-0^2}=\sqrt1=1$$ As $... |
Answer
a) The car can navigate the curve. b) $18.4\ m/s$
Work Step by Step
a) We know that 27.78 meters per second equals 100 kilometers per hour. Using the equation on page 209, we find: $=(27.7778^2)/(85\times 9.81)=.92$ This is less than the SSF, so the car can navigate the curve. b) We use the equation on page 209 ... |
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Now showing items 1-1 of 1
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
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Now showing items 1-5 of 5
Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
"Abstract: We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, insta... |
There are indeed several approximations, depending on the shape of the wing. Generally, the lift curve slope is $2\pi$ only for a flat plate in inviscid 2D flow (with Kutta condition fulfilled). With thicker airfoils, the lift curve slope in 2D increases slightly. It also increases with Mach number proportional to the ... |
In my last post, I multiplied a 2 × 2 matrix by another 2 × 2 matrix. Now let’s multiply a 2 × 2 matrix by a 2 × 1 matrix. If you were paying attention last time, this is possible because the inside dimensions are the same (2= 2) and the resulting matrix will be a 2 × 1 matrix, that is, the outside dimensions.
This is ... |
I think Ced is correct here; parabolas are going to get you the most bang for your buck where minimizing the second derivative is concerned.
This answer gives a slightly more generalized solution for achieving that parabolic shape, and other shapes (in case your requirements change a bit, maybe). I'm going to make a fe... |
In many studies, we measure more than one variable for each individual. For example, we measure precipitation and plant growth, or number of young with nesting habitat, or soil erosion and volume of water. We collect pairs of data and instead of examining each variable separately (univariate data), we want to find ways... |
Reindeer are a feature of Christmas season. They were added with the introduction of the Christmas season in version 1.04. Reindeer will occasionally jump across the screen (from left to right) and give cookies when clicked. As of v.2.002, they are of occasionally variable size and now wobble while bouncing across the ... |
Search
Now showing items 1-1 of 1
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Search
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... |
This elliptic curve has smallest conductor amongst elliptic curves over $\Q$ of rank 3.
magma: E := EllipticCurve("5077a1");
sage: E = EllipticCurve("5077a1")
gp: E = ellinit("5077a1")
\( y^2 + y = x^{3} - 7 x + 6 \)
Mordell-Weil group structure Infinite order Mordell-Weil generators and heights
\(P\) = \( \left(-2, 3\... |
Let $$z(x,y)=\int_{1}^{x^{2}-y^{2}}[\int_{0}^{u}\sin(t^{2})dt]du.$$ Calculate $$\frac{\partial^{2}z}{\partial x\partial y}$$
I tried to solve this using the Fundamental Theorem of Calculus.
I also found an solution like this: using Fundamental Theorem of Calculus, we get: $$\frac{\partial z}{\partial y}=\left[\int_{0}^... |
$\mathbf{Question:}$ $(H,+)$ is a subgroup of $(\mathbb{R},+)$ such that $H \cap [-1,1]$ is finite and contains elements other than $0$. Show that $(H,+)$ must be cyclic.
$\mathbf{Attempt:}$ Since $\{0\}\cup T= H \cap [-1,1]$ is finite [$0 \not\in T$, $\emptyset \subsetneq T$], so we can completely enumerate $T$. Let $... |
Hypothesis Test about the Population Mean ( μ) when the Population Standard Deviation ( σ) is Known
We are going to examine two equivalent ways to perform a hypothesis test: the classical approach and the p-value approach. The
classical approach is based on standard deviations. This method compares the test statistic (... |
Aldehydes, Ketones and Carboxylic Acids Properties and Uses of Carboxylic Acids Chemical properties:
(ii) Reducing with Tollen's reagent:
only formic acid will give this test (iii) Fehling test (iv) Formic acid does not react with NH 2OH PHYSICAL PROPERTIES Up to nine carbons of carboxylic acid are liquid in state with... |
skills to develop
To understand what \(F\)-distributions are. To understand how to use an \(F\)-test to judge whether two population variances are equal. \(F\)-Distributions
Another important and useful family of distributions in statistics is the family of \(F\)-distributions. Each member of the \(F\)-distribution fam... |
I've been thinking about, implementing and using the Extreme Learning Machine (ELM) paradigm for more than a year now, and the longer I do, the more I doubt that it is really a good thing. My opinion, however, seems to be in contrast with scientific community where -- when using citations and new publications as a meas... |
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Now showing items 11-20 of 27
Pseudorapidity dependence of the anisotropic flow of charged particles in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV
(Elsevier, 2016-11)
We present measurements of the elliptic ($\mathrm{v}_2$), triangular ($\mathrm{v}_3$) and quadrangular ($\mathrm{v}_4$) anisotropic azimutha... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
Hypothesis Test for a Population Proportion ( p)
Frequently, the parameter we are testing is the population proportion.
We are studying the proportion of trees with cavities for wildlife habitat. We need to know if the proportion of people who support green building materials has changed. Has the proportion of wolves t... |
In standard $f(R)$ gravity we consider the Lagrangian of the form $L=\frac{1}{16\pi G}f(R)\epsilon$, where $\epsilon$ is the spacetime volume form and similarly, we consider the boundary term to be of the form $l=\frac{1}{8\pi G}f'(R)\epsilon_{\partial \mathcal{M}}$, where $\epsilon_{\partial \mathcal{M}}$ is the space... |
Hypothesis Test about a Variance
When people think of statistical inference, they usually think of inferences involving population means or proportions. However, the particular population parameter needed to answer an experimenter’s practical questions varies from one situation to another, and sometimes a population’s ... |
If a variable, say X, is
normally distributed with mean ##\mu## and variance ##\sigma^2## then mathematicians write ##X \sim \mathcal{N}(\mu, \sigma^2)##.
If a variable, say Y, is
log-normally distributed and the underlying normal distribution has mean ##\mu## and variance ##\sigma^2## then mathematicians write ## Y \s... |
Waves can be in the group and such groups are called as wave packets, so the velocity with a wave packet travels is called group velocity. Velocity with which the phase of a wave travels is called phase velocity. The relation between group velocity and phase velocity are proportionate.
Group Velocity And Phase Velocity... |
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 \... |
skills to develop
To understand how to use an \(F\)-test to judge whether several population means are all equal
In Chapter 9, we saw how to compare two population means \(\mu _1\) and \(\mu _2\).
In this section we will learn to compare three or more population means at the same time, which is often of interest in pra... |
Can you tell me if my answer is correct:
Show that the set $P^{\omega_\omega}(\omega)$ exists.
My answer:
Let $P^0 (\omega) = \omega$, $P^{\alpha + 1}(\omega) = P(P^\alpha (\omega))$ and for a limit ordinal $\lambda$ let $P^\lambda (\omega) =\bigcup_{\beta < \lambda} P^\beta (\omega)$.
The transfinite recursion theorem... |
How to Select the Right Light Pipe Homogenizing Rod
Much like optical fibers, light pipe homogenizing rods utilize total internal reflection (TIR) to transmit light from the entrance to the exit of the light pipe. The substrate’s refractive index is the only factor that influences the light pipe’s critical angle, which... |
I have a question regarding formula in SURF article by Bay et al.
Theory
Given a point $p=(x,y)$ in an image $I$, the Hessian matrix $\mathcal{H}$ in $x$ at scale $\sigma$ is defined as follows
$$ \mathcal{H}(p, \sigma) = \begin{bmatrix}L_{xx}(p, \sigma) & L_{xy}(p, \sigma)\\L_{xy}(p, \sigma)& L_{yy}(p, \sigma)\end{bma... |
The Annals of Applied Probability Ann. Appl. Probab. Volume 27, Number 3 (2017), 1452-1477. Model-free superhedging duality Abstract
In a model-free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semistatic strategies. We also show that the initial c... |
Someone asked on another site about ways to evaluate $\int \ln x \ dx $ without using integration by parts.
My response was the following:
$$ \begin{align} \int\ln x \, dx & =\int\lim_{t\to 0}\frac{x^{t}-1}{t} \, dx \\ &= \lim_{t\to 0}\frac{1}{t}\int (x^{t}-1) \, dx \\ &=\lim_{t\to 0}\frac{1}{t}\left(\frac{x^{t+1}}{t+1... |
So now that you know about matrices, we can use them to add a third way to solve a system of equations. You will need to read my previous 3 posts on matrices if you are unfamiliar with how to multiply matrices.
In the last post on System of Equations, I looked at the system:
2
x + 3 y = 51 3 x + 2 y = 49
And in my last... |
I have 8 country stock indexes and 1 world stock index. I do not actually have time series data but I'm given the following data:
$\mu$, the vector of expected future returns for all 8 country indexes and world index (9 indexes). $\Omega$, the variance covariance matrix of all 9 indexes.
I'm forming a MV efficient and ... |
Event detail
Seminar | March 4 | 12:10-1 p.m. | 939 Evans Hall
Nicolai Reshetikhin, UC Berkeley
For finite dimensional representations $V_1, \dots , V_m$ of a simple finite dimensional Lie algebra $\mathfrak g$ consider the tensor product $W=\otimes _{I=1}^m V_i^{\otimes N_i}$. The first result, which will be presented... |
I want to know if there is a way to find for example $\ln(2)$, without using the calculator ?
Thanks
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
And let's not forget t... |
Let me describe the standard way to do this kind of computation. The key claim is that to obtain this kind of formulas, one can pretend that the vector bundle is a sum of line bundles (even if it is not true in general). This claim is called the splitting principle and can be justified but I will not do it here (unless... |
$$ \frac{3}{1-\sin^6x-\cos^6x}=(\tan x + \cot x)^2$$ Need help with an identity I got for my high school homework. Can't seem to find a way to prove it. Please help with easiest way to do it. Thanks!
The RHS reads
$$\left(\frac sc+\frac cs\right)^2=\frac{1^2}{c^2s^2}$$ hints you to rework the denominator of the LHS.
Te... |
Why are so many algebraists nowadays interested in cluster algebras?
(This is a rewording of one half of the closed question Cluster algebras and teichmuller theory.)
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.Sign up to join this community
One reason i... |
In the MWE below, created following other threads from the website, I would like to know how to change the following two things:
1) How to add the buttons which link back to the question (E.g. the button "Back to problem 1.1" in the MWE below) at the end of the solution, as I have done with the button "Solution" which ... |
As pointed out by Peter K., it is important to distinguish between Laplace and Fourier transforms. The first few transform pairs in your question are Fourier transform pairs, whereas the last pair is a correspondence of the
unilateral Laplace transform:
$$F(s)=\int_{0}^{\infty}f(t)e^{-st}dt$$
In the last transform pair... |
On thing to keep in mind is that IR and UV divergences appear in different kinematical regimes: UV divergences are basically due to the fact that in loop integrals there are not sufficient propagators to make the integral fall off at infinity. E.g for a bubble integral
$\int d^4l \frac{1}{l^2(l-p)^2}$ will be logarithm... |
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... |
In
electrodynamics, the retarded potentials are the electromagnetic potentials for the electromagnetic field generated by time-varying electric current or charge distributions in the past. The fields propagate at the speed of light c, so the delay of the fields connecting cause and effect at earlier and later times is ... |
I was thinking of this today as I was looking over my complex analysis notes.
If you have some complex number $z$, then we can define it using Euler's formula as $z=a+ib=\cos\theta+i \sin\theta$. Say we have the case that $z=3+4i=25(\cos\theta+i\sin\theta)$. Then $25\cos \theta=3$, and $25\sin\theta=4$. But this would ... |
Let $K$ be an ideal of the direct product $R\times S$.Define\[I=\{a\in R \mid (a,b)\in K \text{ for some } b\in S\}\]and\[J=\{b\in S \mid (a, b)\in K \text{ for some } a\in R\}.\]
We claim that $I$ and $J$ are ideals of $R$ and $S$, respectively.
Let $a, a’\in I$. Then there exist $b, b’\in S$ such that $(a, b), (a’, b... |
Understanding Neutral Density Filters
Neutral Density (ND) filters are designed to reduce transmission evenly across a portion of a specific spectrum. ND filters are typically defined by their Optical Density (OD) which describes the amount of energy blocked by the filter. A high optical density value indicates very lo... |
This is an old revision of the document!
Abbreviation:
SchrCat
A
is a category $\mathbf{C}=\langle C,\circ,\text{dom},\text{cod}\rangle$ such that Schroeder category
every morphism is an isomorphism: $\forall x\exists y\ x\circ y=\text{dom}(x)\text{ and }y\circ x=\text{cod}(x)$
Let $\mathbf{C}$ and $\mathbf{D}$ be Schr... |
I would like to obtain analytic solutions to the following PDE system: \begin{equation} \rho_t + D(\lambda)\,\rho_\lambda = A(\lambda) \rho, \tag{1} \end{equation} with $\rho = (\rho_0,\rho_1)^T$, $D$ is the diagonal matrix \begin{equation} D(\lambda) = \begin{pmatrix} -(1+a)\lambda & 0 \\ 0 & p_b-\lambda\end{pmatrix},... |
Skills to Develop
To learn how to construct a confidence interval for the difference in the proportions of two distinct populations that have a particular characteristic of interest. To learn how to perform a test of hypotheses concerning the difference in the proportions of two distinct populations that have a particu... |
ISSN:
1556-1801
eISSN:
1556-181X
All Issues
Networks & Heterogeneous Media
December 2014 , Volume 9 , Issue 4
Special issue on the mathematics of concrete
Select all articles
Export/Reference:
Abstract:
Although the concrete is a simple man-made material with initially-controlled composition (for instance, all ingredie... |
KKT conditions from Wikipedia:
We consider the following nonlinear optimization problem: $$ \text{Minimize }\; f(x) $$ $$ \text{subject to: }\ g_i(x) \le 0 , h_j(x) = 0 $$ The number of inequality and equality constraints are denoted $m$ and $l$, respectively.
Suppose that the objective function $f : \mathbb{R}^n \righ... |
In the general equation of the compressibility factor $Z$, we define $Z$ as $$Z=\frac{pV}{nRT}$$ Here, what is $p$? Is it $p_\text{real}$ or $p_\text{ideal}$? Also, what is $V$? $V_\text{real}$ or $V_\text{container}$?
Both quantities are of the real gas.
Note that for the ideal gas behaviour, the compressibility facto... |
The news has been so unrelentingly bad these past few weeks that I’m taking momentary refuge in good old numerology. I happened to re-read this blog post by John Baez about the
free modular lattice on 3 generators. This is a nice bit of pure math that features rather prominently the numbers 3, 8, 24 and 28. The numerol... |
My question concerns Section 6.1 of Hori's 'Linear Models of Supersymmetric D-branes' (http://arxiv.org/abs/hep-th/0012179).
Firstly, some background. The quantum field theory in question is a 2d ${\cal N}=(2,2)$ Landau-Ginzburg (LG) model on a worldsheet with boundaries (e.g. the infinite strip, or a disk). Boundary c... |
ASU Electronic Theses and Dissertations
This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree inform... |
ISSN:
1937-5093
eISSN:
1937-5077 Kinetic & Related Models
September 2012 , Volume 5 , Issue 3
Issue dedicated to Michel Chipot
on the occasion of his 60th birthday
Select all articles
Export/Reference:
Abstract:
We present a Fourier transform formula of quadratic-form type for the collision operator with a Maxwellian k... |
So far I have avoided division of fractions. This is not hard, in fact, it’s almost as easy as multiplying but I would like to show why the method works.
First consider 6 ÷ 2. This problem is asking the question, “How many 2’s fit into 6?”. The answer is 3 sets of 2’s make up 6. If the problem was 6 ÷ 3, the question w... |
Home > First look at time-dependent CP violation using early Belle II data
BELLE2-CONF-PROC-2019-007
Stefano Lacaprara
24 June 2019 Abstract: Time dependent CP-violation phenomena are a powerful tool to precisely measure fundamental parameters of the Standard Model and search for New Physics. The Belle II experiment at... |
I want to get a better grasp of what a rigorous formal proof is. So I was hoping to find proofs of interesting results using natural deduction or Hilbert system or similar. The "interesting result" could be anything from infinitude of primes to Lagrange's theorem. "Interesting result" is not $x \wedge y \implies y \wed... |
Sobolev spaces of order 2 are known to form a Hilbert space. Consider such a Sobolev space of (order 2) functions on the domain $f:\mathbb{R}\rightarrow \mathbb{R}$. What is an example for the basis of such a Sobolev space.
As mentioned above, the question is not well-posed in this form since the answer depends not onl... |
A slight infinite extension of this Show that two bounded sequences have convergent subsequences with the same index sequence
Let $S$ be a compact metric space. Suppose, for each $m\in\mathbb{N}$, $\{x(m,n)\}_{n\geq 1}$, is a sequence in $S$. The question is can we always get a strictly increasing sequence of natural n... |
I was having trouble proving by induction with this problem. $$\sum_{i=1}^n \frac{3}{4^i} < 1$$ for all $n \geq 2$ I went to see my professor and he said try proving this equality $$\sum_{i=1}^n \frac{3}{4^i} < 1 - 1/4^n $$ Where did he get the $$1-(1/4^n)$$ from? How would I prove this? And is it still proving the sam... |
200 1
Hi there!
I'd like to calculate the work done by the gravitational force. I know the work is defined by the integration of a 1-form: [tex]L=\int_\gamma \omega[/tex] where [tex]\omega=F_xdx+F_ydy+F_zdz[/tex] This works fine in cartesian coordinates and I know how to integrate it, but what if I want to use spherica... |
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Now showing items 1-2 of 2
Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
Your realisation is correct and something chemistry teachers try to hammer into their students’ heads time and time again (and yet, the point is still often lost):
Catalysts will never change the thermodynamics of a reaction. They only ease the path of the reaction. Forward and backward reactions will be accelerated eq... |
$\lim_{x \rightarrow 27} \frac{x^{1/3} - 3}{x - 27}$.
Hello,
I am stuck on this one. I am sure there is a simple step but I am not seeing it. Thanks in advance for the help.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes ... |
In my last post, you saw another maths shortcut – exponents. But I used examples where the exponents were positive integers. It turns out that mathematically, any number, be it negative, fractional, or irrational, can be used as an exponent. Let’s expand our knowledge here by looking at exponents that are not positive ... |
Note that we always have $H \subset N_G(H)$.Hence our goal is to find an element in $N_G(H)$ that does not belong to $H$.
Since $G$ is a nilpotent group, it has a lower central series\[ G=G^{0} \triangleright G^{1} \triangleright \cdots \triangleright G^{n}=\{e\},\]where $G=G^{0}$ and $G^{i}$ is defined by\[G^i=[G^{i-1... |
I have some trouble understanding the benefits of Bayesian networks.
Am I correct that the key benefit of the network is that one does not need to use chain rule of probability in order to calculate joint distributions?
So, using the chain rule:
$$ P(A_1, \dots, A_n) = \prod_{i=1}^n (A_i \mid \cap_{j=1}^{i-1} A_j) $$
l... |
Here's some piece of the bigger picture. Maass forms and holomorphic modular forms are both automorphic representations for $GL(2)$ over the rationals. An automorphic representation is a typically huge representation $\pi$ of an adele group (in this case $GL(2,\mathbf{A})$, with $\mathbf{A}$ the adeles of $\mathbf{Q}$)... |
Electromagnetic Waves Displacement Current The magnetic field due to current carrying conductor, i cis determined by using the Ampere’s circuit law.
\tt \int \overrightarrow{B} \cdot \overrightarrow{dl} = \mu_{0} i_{c}
Conduction current, i cis produced by the time varying magnetic field \tt i_{c} \propto \frac{dB}{dt}... |
Let $\Gamma$ be a finite abelian group, and let $P$ be the polytope in $\mathbb{R}^\Gamma$ defined to be the points $x$ satisfying the following inequalities:
$$\begin{array}{cl} \sum_{g\in G} x_g \le |G| & \forall G \le \Gamma \\ x_g \ge 0 & \forall g \in \Gamma \end{array}$$
where $G \le \Gamma$ means $G$ is a subgro... |
Design and Performance of the ICON EUV Spectrograph 219 Downloads Citations Part of the following topical collections: Abstract
We present the design, implementation, and on-ground performance measurements of the Ionospheric Connection Explorer EUV spectrometer,
ICON EUV, a wide field (\(17^{\circ}\times 12^{\circ}\)) ... |
I've been trying to read Gross' paper on Heegner points on $X_0(N)$ and I am stuck on a few details. The definition he is working with is that a heegner points is a pair $y=(E,E')$, where $E$ and $E'$ are elliptic curves admitting an isogeny that has cyclic kernel of order $N$ and where $E$ and $E'$ both have complex m... |
Multiple solutions for a class of $(p_1, \ldots, p_n)$-biharmonic systems
1.
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States
2.
Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah 67149, Iran
Keywords:p_{n})$-biharmonic systems, critical po... |
We define a $2\times 2$ Givens rotation matrix as:
$${\bf G}(\theta) = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) &\cos(\theta) \end{bmatrix}.$$
On the other hand, we define a $2\times 2$ hyperbolic rotation matrix as:
$${\bf H}(y)=\begin{bmatrix} \cosh( y) & \sinh( y) \\ \sinh( y) &\cosh( y) \end{bma... |
"Abstract: We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, insta... |
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