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Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
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Now showing items 1-10 of 26
Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
Statement of the problem
Given a continuous map $f:G \rightarrow D^2$ where $G$ is a compact simply connected Lie group and $D^2$ is the unit disk in the plane, I have shown that:
There exists a simple (non-self-intersecting, except at a single point) loop $\gamma \subset G$ that maps injectively to a simple loop $f(\g... |
[2.13.6] An expression representing, in a functional form, the spectral radiance of a blackbody as a function of the wavelength and the temperature. L_{\lambda }=dI_{\lambda}/dA' = c_{1L}\left (\lambda \right )^{-5} \cdot f\left ( \lambda T \right )
or L_{\lambda } T^{-5}=c_{1L}(\lambda T)^{-5} \cdot f(\lambda T) f\lef... |
I was following the coleman lectures on "Aspects of symmetry" particularly the chapter about the 't Hooft's model. Then I have wandered into older papers like the 't Hooft's papers and many others. And concerning the reason why there are no free quarks in this model it seems to me that their reasoning is the following:... |
Table of Contents
The Interior of Sets in Finite Topological Products
In the following theorem we will show that if $\{ X_1, X_2, ..., X_n \}$ is a finite collection of topological spaces and $A_i \subseteq X_i$ for all $i \in \{ 1, 2, ..., n \}$ then the interior of the product of these sets is equal to the product of... |
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Supported Layouts container Examples amp-mathml.amp.html
This extension creates an iframe and renders a MathML formula.
<amp-mathml layout="container" data-form... |
Precision Measurement of the Boron to Carbon Flux Ratio
Carbon nuclei in cosmic rays are thought to be mainly produced and accelerated in astrophysical sources, while boron nuclei are entirely produced by the collision of heavier nuclei, such as carbon and oxygen, with the interstellar matter. Therefore, the boron to c... |
Focus Questions
The following questions are meant to guide our study of the material in this section. After studying this section, we should understand the concepts motivated by these questions and be able to write precise, coherent answers to these questions. What is the polar (trigonometric) form of a complex number?... |
I am not an expert at all in the subject of Lie groups, lattices, arithmetic groups and rigidity. But, lately I am interested in Margulis superrigidity theorem, which in most versions can be stated as follows:
Theorem.
Let $G$ and $G'$ be semisimple connected real center-free Lie groups without compact factors with $\m... |
In David J. Griffiths's
Introduction to Electrodynamics, the author gave the following problem in an exercise.
Sketch the vector function$$ \vec{v} ~=~ \frac{\hat{r}}{r^2}, $$ and compute its divergence, where$$\hat{r}~:=~ \frac{\vec{r}}{r} , \qquad r~:=~|\vec{r}|.$$ The answer may surprise you. Can you explain it?
I f... |
Table of Contents
Clopen Set Criterion for Disconnected Topological Spaces
Recall from the Connected and Disconnected Topological Spaces page that a topological space $X$ is said to be disconnected if there exists open sets $A, B \subset X$, $A, B \neq \emptyset$, $A \cap B = \emptyset$, and such that:(1)
Furthermore w... |
Power of a Lens is one of the most interesting concepts in ray optics. The detailed concept of this topic is given in the below article so that learners can understand this chapter more effectively.
Simply put, the power of a lens in Ray Optics is its ability to bend light. The greater the power of a lens, the greater ... |
Well, it becomes a bit clearer when we see the final formulas of Ref. 1:
$$\delta \langle a_f , t_f |a_i , t_i \rangle ~=~ \frac{i}{\hbar} \int_{t_i}^{t_f} \! dt \langle a_f , t_f | \delta L(t) |a_i , t_i \rangle \tag{7.126}$$
$$ \delta^{\prime} \delta \langle a_f , t_f |a_i , t_i \rangle ~=~\frac{1}{2}\left(\frac{i}{\... |
The Interior Points of Sets in a Topological Space Examples 2
Recall from The Interior Points of Sets in a Topological Space page that if $(X, \tau)$ is a topological space and $A \subseteq X$ then a point $a \in A$ is called an interior point of $A$ if there exists an open set $U \in \tau$ such that:(1)
We also proved... |
The following problem has appeared in 2013 January qualifying exam in Purdue University, which is publicly available here.
Problem 3. Let $\{a_k\}$ be sequence of positive numbers such that $a_n\to\infty$ as $n\to\infty$. Prove that the following limit exists $$ \lim_{k\to\infty}\int_{0}^{\infty} \frac{e^{-x}\cos(x)}{a... |
Dirr, Nicolas and Luckhaus, Stephen 2001. Mesoscopic limit for non-isothermal phase transition. Markov processes and related fields 7 (3) , pp. 355-381. Abstract
Motivated by the problem of modeling nucleation in non-isothermal systems, we consider the stochastic evolution of a coupled system of a lattice spin variable... |
H(w) =1/ (square root of 2) That sounds a bit confusing, we usually refer to the cutoff point as the -3 dB point.
That is the same though, -3 dB is
half the power.
Let me explain: take your \$H(\omega) = \frac{1}{\sqrt2}\$
That means that at that \$\omega\$ the
voltage is divided by \$\sqrt2\$, if this voltage is appli... |
This example will use an elementary dipole and loop antenna and analyze the wave impedance behavior of each radiator in space at a single frequency. The region of space around an antenna has been defined in a variety of ways. The most succinct description is using a 2-or 3-region model. One variation of the 2-region mo... |
In the previous chapter we found that we could differentiate functions of several variables with respect to one variable, while treating all the other variables as constants or coefficients. We can integrate functions of several variables in a similar way. For instance, if we are told that \(f_x(x,y) = 2xy\), we can tr... |
Source Significance
In the first release of the CSC, detect and flux significance were related, since sources were accepted for inclusion in the catalog if their flux significance exceeded a given threshold.
In CSC 2.0, three separate metrics are used to describe the significance of detection and flux determination.
De... |
Table of Contents
The Dimension of The Null Space and Range Examples 1
Recall from The Dimension of The Null Space and Range page that if $T$ is a linear map from $V \to W$ and $V$ is finite-dimensional then we have the following formula relating the dimension of $V$ to the dimension of the the null space of $T$ and th... |
Can any polynomial $P\in \mathbb C[X]$ be written as $P=Q+R$ where $Q,R\in \mathbb C[X]$ have all their roots on the unit circle (that is to say with magnitude exactly $1$) ?
I don't think it's even trivial with degree-1 polynomials... In this supposedly simple case, with $P(X)=\alpha X + \beta$, this boils down to fin... |
The Dimension of The Null Space and Range Examples 2
Recall from The Dimension of The Null Space and Range page that if $T$ is a linear map from $V \to W$ and $V$ is finite-dimensional then we have the following formula relating the dimension of $V$ to the dimension of the the null space of $T$ and the dimension of the... |
Action functionals that attain regular minima in presence of energy gaps
1.
EPFL, Chaire d’Analyse Mathématiques et Applications, CH-1015 Lausanne, Switzerland
inf$\{\int_a^b L(t,x,\dot x): x\in W_0^{1,1}(a,b)\} $< inf$\{\int_a^bL(t,x,\dot x): x\in W_0^{1,\infty}(a,b)\}$
(where $ W_0^{1,p}(a,b)$ denote the usual Sobole... |
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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 ... |
The Dimension of The Null Space and Range Examples 3
Recall from The Dimension of The Null Space and Range page that if $T$ is a linear map from $V \to W$ and $V$ is finite-dimensional then we have the following formula relating the dimension of $V$ to the dimension of the the null space of $T$ and the dimension of the... |
We have been learning how we can understand the behavior of a function based on its first and second derivatives. While we have been treating the properties of a function separately (increasing and decreasing, concave up and concave down, etc.), we combine them here to produce an accurate graph of the function without ... |
This answer partially disagrees with Motl's. The crucial point is to consider the difference between the abelian and non-abelian case. I totally agree with Motl's answer in the non-abelian event — where these identities are usually denominated Slavnov-Taylor's rather than Ward's, so that I will refer to the abelian cas... |
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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 ... |
I am reading some lecture notes that unfortunately don't seem to be available online, but that are quite close in spirit in their treatment of the Dirac equation to Sakurai's "Advanced Quantum Mechanics". At some point the $4\times4$ matrices $\Sigma_k$ are introduced as infinitesimal generators of the action of rotati... |
@user193319 I believe the natural extension to multigraphs is just ensuring that $\#(u,v) = \#(\sigma(u),\sigma(v))$ where $\# : V \times V \rightarrow \mathbb{N}$ counts the number of edges between $u$ and $v$ (which would be zero).
I have this exercise: Consider the ring $R$ of polynomials in $n$ variables with integ... |
Possible Duplicate: Density of a Set on $\mathbb{R}$?
I have to show that show that $A=\{ \frac{m}{2^n}:m\in \mathbb {Z},n\in \mathbb {N}\} $ is dense in $\mathbb {R}$.
A set A is dense in $\mathbb {R}$ if $\overline A=\mathbb {R}$.
But also $Y$ is a subset of $X$, we say that $Y$ is dense in $X$, if for every $x\in X$... |
I'm trying to understand BRST complex in its Lagrangian incarnation i.e. in the form mostly closed to original Faddeev-Popov formulation. It looks like the most important part of that construction (proof of vanishing of higher cohomology groups) is very hard to find in the literature, at least I was not able to do so. ... |
In my post Trigonometry Yoga, I discussed how defining sine and cosine as lengths of segments in a unit circle helps develop intuition for these functions.
I learned the circle definitions of sine and cosine in my junior year of high school, in the class that would now be called pre-calculus (it was called “Trig Senior... |
The action shown in the question is a functional of $\phi$, not of $x$. A change of the integration variable $x$ is just a relabeling of the index set. It does not transform the dynamic variables $\phi$ at all, so no: a change of variable does not correspond to a conserved quantity.
More explicitly, if $y(x)$ is a mono... |
And I think people said that reading first chapter of Do Carmo mostly fixed the problems in that regard. The only person I asked about the second pset said that his main difficulty was in solving the ODEs
Yeah here there's the double whammy in grad school that every grad student has to take the full year of algebra/ana... |
I'm going to find an example of
uniform algebra and show that satisfying the definition. Example: Show that The Gelfand transform $\widehat{f}$ is uniform algebra.
We know that:
A uniform algebra is a
closed subalgebra$\mathcal A$ of the complex algebra $C(X)$ that contains the constantsand separates points. Here $X$ i... |
From the famous Double-slit experiment, it is clear that electrons do behave as wave as well as particle. When it is detected by geiger counter, "click" sound appears & no matter how greatly the voltage is decreased along the cathode tube, "click" & never "
half click" appears. So, electrons always arrive at lumps like... |
There's a mapping $f:X\rightarrow Y$.
1.for all $A,B\subset X$, $f(A\cap B)=f(A)\cap f(B)$, prove $f$ is injective.
2.for all $A\subset X$, $f(A^{c})=[f(A)]^{c}$, prove $f$ is bijective.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. I... |
For some non-negative numbers $m_1$, $m_2$, $E$ I define a function $$ f\left(\boldsymbol{q},E\right)=\frac{1}{2\omega_{1}\omega_{2}}\frac{1}{\omega_{1}+\omega_{2}+E}+\frac{1}{4\omega_{1}\omega_{2}}\frac{1}{\omega_{1}-\omega_{2}-E}+\frac{1}{4\omega_{1}\omega_{2}}\frac{1}{\omega_{2}-\omega_{1}-E} $$ where $$ \omega_{1,2... |
Effects of the noise level on nonlinear stochastic fractional heat equations
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China
We consider the stochastic fractional heat equation $\partial_{t}u=\triangle^{\alpha/2}u+\lambda\sigma(u)\dot{w}$ on $[0,L]$ with Dirichlet boundary condition... |
Misconceptions on Galileo's experiment at Pisa Tower
I think a lot of people have misconceptions on the implication of Galileo's experiment at Pisa Tower. Wikipedia says that Galileo “is said to have dropped two spheres of different masses from the Leaning Tower of Pisa to demonstrate that their time of descent was ind... |
If $Y_n$ is a Poisson random variable with mean $n^{1/2}$
$S_n = \left(\frac{\sqrt{2} Y_n - \sqrt{2n}}{n^{1/4}}\right)$
If we consider a sequence $S_1, S_2, . . . S_n$, provide the the limiting distribution.
Attempt
Mgf of $Y_n$ is as follows:
$M_{Y_n}(t) = exp\sqrt{n}(e^{t} -1)$
So for all $t \in \mathbb{R}$, we have
... |
I have an optimization problem where all the constraints are linear but some of the type: $$ y_i = \frac{x_i}{\sum_k x_k} $$
It seems that the equality can be relaxed to an inequality adding the linear constraint: $$ \sum_k y_k =1. $$
I further have the constraints: $$x_i\geq0$$ $$0\leq y_i \leq 1$$
The question is if ... |
Analysis of a nonlinear system for community intervention in mosquito control
1.
Department of Mathematics, Bentley College, 175 Forest Street, Waltham, MA 02452, United States
2.
Department of Population and International Health, Harvard School of Public Health, 665 Huntington Avenue, Boston, MA 02115, United States, ... |
Some explanations first
The substitution in the question introduces the reduced wave function $u(r)$ by solving the original radial equation in polar coordinates,
$$-\frac{1}{2}\left(R''(r)+\frac {1}{r}R'(r)\right) - \frac{1}{r}R(r) + \frac {m^2}{2r^2}R(r) = E R(r)$$
using the
ansatz
$$R(r)\equiv \frac{1}{\sqrt{r}}u(r)... |
@Secret et al hows this for a video game? OE Cake! fluid dynamics simulator! have been looking for something like this for yrs! just discovered it wanna try it out! anyone heard of it? anyone else wanna do some serious research on it? think it could be used to experiment with solitons=D
OE-Cake, OE-CAKE! or OE Cake is ... |
Let $X$ be a topological space and $X=X_1 \cup X_2$ with $X_1, X_2$ nonempty open irreducible subsets. Then $X$ is irreducible iff $X_1 \cap X_2 \ne \emptyset$.
The easy part: if it were $X_1 \cap X_2 = \emptyset$ then we would have $$ X = (X \setminus X_1) \cup (X \setminus X_2) $$ and this is impossible since $X$ is ... |
@DavidReed the notion of a "general polynomial" is a bit strange. The general polynomial over a field always has Galois group $S_n$ even if there is not polynomial over the field with Galois group $S_n$
Hey guys. Quick question. What would you call it when the period/amplitude of a cosine/sine function is given by anot... |
I am working on a linear analysis problem where we have boiled down the problem to finding a continuous function $f:\mathbb{R} \to \mathbb{R}$ that is bounded, but has infinite derivative at zero. So far, we have conjured up the example $$f_n(x) = \frac{2}{\pi}\arctan(nx)$$ This sequence of functions will have infinite... |
Well there should be a distinction between types and terms somehow. If we had a "plus 10" function it wouldn't make any sense to apply it to a type. What is a type plus 10? So we need some kind of type system that differentiates between types and terms. This much is unavoidable. I suspect that this is the brunt of your... |
Well, I'll answer anyway, since Wikipedia isn't MSE, but to be clear, while the math doesn't come from Wikipedia, I'm more or less going to directly copy the story of the conjecture from Wikipedia.
Next, I'd like to point out that the statement is now known as the Quillen-Suslin theorem after both gave independent proo... |
There are many ways to study approaches to equilibrium, which is obvious as there are many ways to drive a system out of equilibrium. So there is really no unique answer to your question. However, various universal results are known. These include various fluctuation theorems. The most famous of which is usually called... |
I'm reading the following set of notes on Taylor series and big O-notation, written by a professor at Columbia: http://www.math.columbia.edu/~nironi/taylor2.pdf. He repeatedly refers to what he calls "limit comparison", by which he means the theorem that for $a_n, b_n$ sequences of positive real numbers such that $b_n ... |
Algebra is one of the major parts of Mathematics in which general symbols and letters are used to represent quantities and numbers in equations and formulae. The more basic parts of algebra are called elementary algebra and more abstract parts are called modern algebra or abstract algebra. Algebra is very important as ... |
Learning Objectives
Evaluate square roots. Use the product rule to simplify square roots. Use the quotient rule to simplify square roots. Add and subtract square roots. Rationalize denominators. Use rational roots.
A hardware store sells \(16\)-ft ladders and \(24\)-ft ladders. A window is located \(12\) feet above the... |
Let $R$ be a finite ring with identity $1$, and assume $\exists x,y\in R$ such that $ xy=1$. How can I show it implies $yx=1$?
Hint: $xy=1$ implies that left multiplication by $y$ is one-to-one. Can you draw a conclusion whether or not there is a $z$ such that $yz=1$?
If so, you can complete the argument by showing tha... |
When using SVM, we need to select a kernel.
I wonder how to select a kernel. Any criteria on kernel selection?
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up.Sign up to join this c... |
I'm reading "The variational principles of mechanics- Lanczos",
The author mentions a relation between Work-Function $U(q_1,q_2,\cdots,q_n,\dot q_1,\dot q_2,\cdots,\dot q_n)$ and the potential energy $V(q_1,q_2,\cdots,q_n)$
$$V=\sum_{i=0}^n \frac{\partial U}{\partial \dot q_i}\dot q_i-U \tag{1}$$
$q_i$'s are the genera... |
I am getting stuck in two integrals involving Bessel functions and hoping someone to help me out.
We know that the Bessel function, $$J_v(x)=x^v\sum_{r=0}^{\infty}\frac{(-1)^rx^{2r}}{2^{2r+v}r!\Gamma(r+v+1)},$$ and the modified Bessel function, $$I_v(x)=\sum_{r=0}^{\infty}\frac{1}{r!\Gamma(r+v+1)}\left(\frac{x}{2}\righ... |
Lindelöf, Countably Compact, and BW Spaces Review
Lindelöf, Countably Compact, and BW Spaces Review
We will now review some of the recent material regarding Lindelöf spaces, countably compact spaces, and BW spaces.
Recall from the Lindelöf and Countably Compact Topological Spacespage that a topological space $X$ is sai... |
In this section we describe a systematic method that determines the greatest common divisor of two integers. This method is called the Euclidean algorithm.
[lem1] If \(a\) and \(b\) are two integers and \(a=bq+r\) where also \(q\) and \(r\) are integers, then \((a,b)=(r,b)\).
Note that by theorem 8, we have \((bq+r,b)=... |
This is a model that is used to model soccer scores, so $i$ and $j$ are, respectively, home and away teams. Random variables $(x,y)$ are the goals scored by the home and away teams, respectively. Parameter $\lambda$ is a known mean goals scored by the home team and $\mu$ is the mean goals scored by the away team. I hav... |
Functional a posteriori error estimates and adaptivity for IgA schemes Dr. Svetlana Matculevich March 28, 2017, 3:30 p.m. S2 059
We are concern with guaranteed error control of Isogeometric Analysis (IgA) numerical approximations of elliptic boundary value problems (BVPs). The approach is discussed within the paradigm ... |
A few questions about the equivalence between 2-types and crossed modules. For simplicity, assume everything is connected.
What is the precise statement? Is there an equivalence of categories (or at least a bijection of isomorphism classes) of the form
$$\{\text{2-truncated spaces}\}[\text{weak homotopy equivalence}^{-... |
I am trying to find the volume inside the sphere $x^2 + y^2 + z^2 = 9$, but outside the hyperboloid $x^2 + y^2 - z^2 = 1$. by using a triple integral. for some reason i just cant seem to come up the bounds of integration for this problem. To be more precise, its the region lying to the side of the hyperboloid, that wra... |
Wind direction (here measured in degrees, presumably as a compass direction clockwise from North) is a circular variable. The test is that the conventional beginning of the scale is the same as the end, i.e. $0^\circ = 360^\circ$. When treated as a predictor it is probably best mapped to sine and cosine. Whatever your ... |
I have found a new proof of the Barwise extension theorem, that wonderful yet quirky result of classical admissible set theory, which says that every countable model of set theory can be extended to a model of $\text{ZFC}+V=L$.
Barwise Extension Theorem. (Barwise 1971) $\newcommand\ZF{\text{ZF}}\newcommand\ZFC{\text{ZF... |
Focus Questions
The following questions are meant to guide our study of the material in this section. After studying this section, we should understand the concepts motivated by these questions and be able to write precise, coherent answers to these questions. How do we use the Law of Sines and the Law of Cosines to he... |
I've been playing with the Von Mises distribution for a project I'm doing in python and I'm confused about it.
I'm drawing the pdf, which is defined by wikipedia here as $p(x|\mu, k) = \frac{\exp{(k \cos(x-\mu))}}{\tau I_0(k)}$ for the angle $x$, centre $\mu$ and dispersion or concentration $k$ or $kappa$ (and $\tau = ... |
There is a top-down approach to induction that works in a very general setting. Let $\Omega$ be a set and $f:\Omega^I\to\Omega$ be a function (what I say generalizes to having many such functions) where $I$ is a nonempty set and $\Omega^I$ the set of all functions from $I$ to $\Omega$. If $I=\{1,2\}$, $f$ is essentiall... |
On the last question, I am not sure how good you are at the representation theory, but the following fact is true: take so(d,2) (we need so(3,2) for this work), use the conformal base, i.e. Lorentz generators $L_{ab}$, translations $P_a$, conformal boosts $K_a$ and dilatation $D$, $a,b=1..d$. $P$ and $K$ behave as rais... |
The Dimension of The Null Space and Range
The Dimension of The Null Space and Range
We have looked at the Null Space of a Linear Map and the Range of a Linear Map. Let $T \in \mathcal L (V, W)$. We have already proven that $\mathrm{null} (T)$ is a subspace of the domain $V$ and that $\mathrm{range} (T)$ is a subspace o... |
An interesting application of the spectral gap/algebraic connectivity is to determine the synchronizability of linearly coupled dynamical nodes, which can be formulated as follows:
\[\frac{dx_{i}}{dt} =R(x_{i}) +\alpha{\sum_{j\epsilon{N_{i}}}(H(x_j) -H(x_i)}) \label{(18.6)}\]
Here \(x_i\) is the state of node \(i\), \(... |
A power series is a type of series with terms involving a variable. More specifically, if the variable is \(x\), then all the terms of the series involve powers of \(x\). As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define new f... |
Vopěnka's principle and Vopěnka cardinals Vopěnka's principle is a large cardinal axiom at the upper end of the large cardinal hierarchy that is particularly notable for its applications to category theory. In a set theoretic setting, the most common definition is the following:
For any language $\mathcal{L}$ and any p... |
Graph Isomorphisms
We first look at the definition of what an isomorphism between two graphs $G$ and $H$:
Definition: For two graphs $G = (V(G), E(G))$, and $H = (V(H), E(H))$ the graph $G$ is an isomorphism of $H$ if there exists a bijection such that $f: V(G) \rightarrow V(H)$ so that $\left\{ {x, y}\right\} \in E(G)... |
Sequences of Complex Numbers
A sequence of real numbers is an infinite ordered list $(a_n)_{n=1}^{\infty}$ of real numbers. We can similarly define a sequence of complex numbers.
Definition: A Sequence of Complex Numbers is an infinite ordered list of complex numbers $(z_n)_{n=1}^{\infty} = (z_1, z_2, ..., z_n, ...)$ w... |
$\frac{d}{dt}|_{t=0} \alpha(t) = [X,Y](p)$, where $\alpha(t):= \phi_{-\sqrt{t}}^Y \circ \phi_{-\sqrt{t}}^X \circ \phi_{\sqrt{t}}^Y \circ \phi_{\sqrt {t}}^X$.
I think Fredrik's proof is nice everywhere except for here(the last formula)
Now we use that $(\phi_h^X)^{-1}=\phi_{-h}^X$ to get from $ \lim_{h \to 0} \frac {1}{... |
Difference between revisions of "Lower attic"
From Cantor's Attic
(the Takeuti-Feferman-Buchholz ordinal)
(37 intermediate revisions by 6 users not shown) Line 1: Line 1: −
[[File:SagradaSpiralByDavidNikonvscanon.jpg |
+ +
[[File:SagradaSpiralByDavidNikonvscanon.jpg | | Sagrada Spiral photo by David Nikonvscanon
+
]]
−... |
Outline: Derivatives of the Laplace equations, the wave equations and diffusion equation; Methods to solve equations: separation of variables, Fourier series and integrals and characteristics; maximum principles, Green’s functions.
Here you can find homework problems and solutions. The problems are selected fromthe tex... |
Introduction to Differential Equations
Consider the equation $f(x) = x^2 -3x + 1$. To solve this equation is to find the roots of $f$, which we can obtain with the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. For the example above, the roots are $x = \frac{3 + \sqrt{5}}{2}$ and $x = \frac{3 - \sqrt{5}}{2... |
Research talks;Partial Differential Equations;Mathematical Physics
In this talk we present recent results on the Hall-MHD system. We consider the incompressible MHD-Hall equations in $\mathbb{R}^3$.
$\partial_tu +u \cdot u + \nabla u+\nabla p = \left ( \nabla \times B \right )\times B +\nu \nabla u,$ $\nabla \cdot u =0... |
We'll now consider the nonhomogeneous linear second order equation
\begin{equation}\label{eq:2.3.1}
y''+p(x)y'+q(x)y=f(x), \end{equation}
where the forcing function \(f\) isn't identically zero. The next theorem, an extension of Theorem \((2.1.1)\), gives sufficient conditions for existence and uniqueness of solutions ... |
If $(X,\tau)$ has more than $1$ point and is $T_2$ and connected, do we necessarily have $|X| =|\tau|$?
Consider the topology on $\mathbb{R}^2$ generated by subsets that are open in some line from the origin. This topological space is connected, has the cardinality of continuum, and has $2^c$ open subsets.
The $\frak{c... |
This is a heuristic explanation of Witten's statement, without going into the subtleties of axiomatic quantum field theory issues, such as vacuum polarization or renormalization.
A particle is characterized by a definite momentum plus possible other quantum numbers. Thus, one particle states are by definition states wi... |
Higher Order Homogenous Differential Equations - Complex Roots of The Characteristic Equation
Recall from the Higher Order Homogenous Differential Equations - Constant Coefficients page that if we have an $n^{\mathrm{th}}$ order linear homogenous differential equation with constant coefficients $a_0, a_1, ..., a_n \in ... |
Definition
Let \(S\) be a set with a binary operation \(\star\), and with identity \(e\). Let \(a \in S\), then \(b\in S \) is called an inverse of \(a\) if \(a \star b= b \star a=e.\)
Example \(\PageIndex{1}\):
For every \(a \in \mathbb{Z}\), \(-a\) is the inverse of \(a\) with the operation \(+\). For every \(a \in \... |
In this talk we present a proof of the Kodaira's theorem that gives a sufficient condition on the existence of an embedding of a Kahler manifold into CPn. This proof is based on the Kodaira Vanishing theorem, using a sheaf-cohomological translation of the embedding conditions.לאירוע הזה יש שיחת וידאו.הצטרף: https://mee... |
My Answer
You should set your limit order to: $s (v+1)^{-0.0314192 \sqrt{t}}$where $s$ is the current price, $t$ is the time in years you'rewilling to wait, and $v$ is the annual volatility as a percentage.
If you want to be $p$ percent sure (instead of 0.98), set your limitorder to:
$s (v+1)^{-\sqrt{\pi } \sqrt{t} \te... |
This is my first exercise for space state models and I've a few questions I'd need to resolve before I actually start doing the exercise. Unfortunately, I'm self teaching (I have no professor to ask) and I'm afraid there's no solution companion for Durbin and Koopman (2012)!
Consider the local level model (2.3).
(a) Gi... |
On the uniqueness of ground state solutions of a semilinear equation containing a weighted Laplacian
1.
Facultad de Matemáticas, Universidad Católica de Chile, Casilla 306, Correo 22 - Santiago
2.
Department of Mathematics, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile
$(P)\qquad\qqu... |
I'm aware that there's a simple proof by contradiction for this, mainly:
Assume $x_1 \neq x_2$. If $f(x_1)=f(x_2)$, then $g(f(x_1))=g(f(x_2))$ which, since $g \circ f$ is injective, implies $x_1=x_2$. By contradiction, $f$ is injective.
I wanted to see if the method of direct proof I used is valid. Could someone just s... |
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Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
Unique Factorization Domains (UFDs)
Unique Factorization Domains (UFDs)
Definition: Let $(R, +, \cdot)$ be an integral domain. Then $R$ is a Unique Factorization Domain if the following properties are satisfied: 1) Every element $a \in R$ that is nonzero and that is not a unit can be expressed as a product of irreducib... |
In the previous section, we explored the short run behavior of quadratics, a special case of polynomials. In this section, we will explore the short run behavior of polynomials in general.
Short run Behavior: Intercepts
As with any function, the vertical intercept can be found by evaluating the function at an input of ... |
Recall that $\mathbb{Z}[i]=\{a+bi:a,b \in \mathbb{Z}\}$, i.e., the Gaussian integers, and $\mathbb{Z}[\sqrt{2}]=\{a+b\sqrt{2}:a,b \in \mathbb{Z}\}$.
I want to show that $\mathbb{Z}[i] \not\cong \mathbb{Z}[\sqrt{2}]$.
Suppose, to the contrary, that they are isomorphic. Then there exists a bijective ring homomorphism $\p... |
Let $f:[a,b] \to \mathbb{R}^2$ be a continuous curve on the plane.
Question:Are there numbers $a \leq x \leq c \leq y \le b$ such that $$(c-a)f(x)+(b-c)f(y) = \int_a^b f(t) \, dt \ ?$$
In other words, is there a Riemann sum with two terms that hits the bull's-eye?
EDIT: Prompted by a down-vote, maybe I should give some... |
Properties of Polynomials
We are about to look at an important concept known as an
eigenvalue shortly, but before then, we must secure a foundation of knowledge on polynomials. We have looked at polynomials throughout the Linear Algebra section on the site, for example, when we looked at $\wp (\mathbb{R})$ as the set o... |
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