text stringlengths 256 16.4k |
|---|
I have just read the nice survey by Granville and Martin about prime races.I wonder what happens if one changes the rules for the prime races as follows.Fix $q$ a modulus (an integer $>1$). For $a$ an integer relatively prime to $q$, one has a Mertens-like formula $$\sum_{p<x, \atop p \equiv a \pmod{q}} \frac{1}{p} = \... |
Suppose I have survival data coming from a cohort study. The outcome of interest is death and a subject can die either because of cancer or because of other causes. The two outcomes under study are therefore mutually exclusive.
Now, suppose that I'm interested in assessing whether the magnitude of the associations betw... |
2018-08-25 06:58
Recent developments of the CERN RD50 collaboration / Menichelli, David (U. Florence (main) ; INFN, Florence)/CERN RD50 The objective of the RD50 collaboration is to develop radiation hard semiconductor detectors for very high luminosity colliders, particularly to face the requirements of the possible u... |
The wiki page and links seem good except maybe on history. For that see e.g. Coolidge (1940, pp. 278-282):
§2. Circular transformations.
The point transformations of the plane which carry points on a line
or circle into points on a line or circle, are surely the simplest and most
interesting plane transformations, afte... |
Stokes' theorem examples
Stokes' theorem relates a surface integral of a the curl of the vector field to a line integral of the vector field around the boundary of the surface. After reviewing the basic idea of Stokes' theorem and how to make sure you have the orientations of the surface and its boundary matched, try y... |
Rocky Mountain Journal of Mathematics Rocky Mountain J. Math. Volume 48, Number 6 (2018), 1829-1840. Cuntz-Pimsner algebras of group representations Abstract
Given a locally compact group $G$ and a unitary representation $\rho :G\to U({\mathcal H})$ on a Hilbert space $\mathcal {H}$, we construct a $C^*$-correspondence... |
Both questions are related. Use the following expresion:
${\displaystyle E_{2}-E_{1}={\frac {m_{e}e^{4}}{2(4\pi \epsilon _{0})^{2}\hbar ^{2}}}({\frac {1}{n^{2}_1}-\frac {1}{n^{2}_2})}}$.
For the energy of an 1s hydrogen electron then,calculate the difference between states 2 and 1 (where 2 will represent the ion and 1 ... |
Difference between revisions of "Timeline of prime gap bounds"
Line 865: Line 865:
| 53?# ([http://terrytao.wordpress.com/2014/02/09/polymath8b-viii-time-to-start-writing-up-the-results/#comment-271862 Nielsen])
| 53?# ([http://terrytao.wordpress.com/2014/02/09/polymath8b-viii-time-to-start-writing-up-the-results/#comm... |
305 results for "table".
One question on determining whether statements are propositions.
Four questions about truth tables for various logical expressions.
Exam (6 questions) Draft
CC BY Published
Last modified 23/08/2019 17:30
No subjects selected No topics selected
No ability levels selected
A random heating questio... |
Aesthetics are by far and away the last thing aircraft designers are optimising for. A better question might be, why do aerodynamically-efficient designs look pleasing, but that would likely be an art or psychology question and off-topic here.Since aircraft could travel at appreciable speeds, designs have focused prima... |
The Extension of Combinatorial Solutions for Cooperative Games Abstract
In this paper, a new model to solve the social selfish coefficient \( \alpha \in \left[ {0,1} \right] \) for the \( \alpha \)-egalitarian Shapley values and a new convex combinations of single-value in terms of a coalition forming weight coefficien... |
Description Material: IBS CTPU admin office Email: mijin1024@ibs.re.kr Telephone: +82-42-878-8402
Speaker: Kiwoon Choi (IBS-CTPU) Material: Slides This talk analyzes the present status of sub-GeV thermal dark matter annihilating through Standard Model mixing. In these scenarios, the requirement that dark matter be a th... |
Let $f,g$ be entire functions such that $f(g(z))=0, \forall z.$ Could anyone advise me on how to prove/disprove: either $g(z)$ is constant or $f(z) =0, \forall z \ ?$
Hints will suffice, thank you.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in relate... |
Suppose I have 100 objects. I have some "detection criteria" such that I can tell you that 25/100 objects have been "detected." Therefore, my detection fraction is 25%. Now, I want to derive an error bar for my detection experiment. I can do this easily if I assume a binomial distribution: $df = \sqrt{f(1-f)/N} = \sqrt... |
I'm trying to calculate the spin and color averaged gg->gg cross section, and I am stumbling upon gauge invariance:
Must the amplitude not be invariant under replacements $\epsilon_i \to \epsilon_i + \kappa_i p_i$ where $p_i\cdot\epsilon_i=0$ and $\kappa_i$ is arbitrary? For me it is not :/
I have summed the 4-gluon di... |
After a whirlwind tour of the English department, the tour entered the Mathematics department.
Upon entering, I immediately heard some interesting conversations:
"It's like a puzzle, that game..."
"I think the key is to rationalise it, by making a recurrence..."
"You have to use Cantor's diagonal argument, and take it ... |
Marco
The equation looked something like this…(1)
\begin{align} \definecolor{blue}{rgb}{.525,.631,.922}\pagecolor{blue} xy + (x^2 - ye^y)y' = 0 \end{align}(2)
\begin{align} \definecolor{blue}{rgb}{.525,.631,.922}\pagecolor{blue} M + Ny'=0 \end{align}
The book only mentioned this equation:(3)
\begin{align} \definecolor{... |
Archive:
Subtopics:
Comments disabled
Tue, 07 Feb 2017
[ Note: The tables in this article are important, and look unusually crappy if you read this blog through an aggregator. The properly-formatted version on my blog may be easier to follow. ]
A few months ago I wrote about puzzles of the following type: take four dig... |
For $\Sigma = \{a,b\}$, let $S_n = \{w\mid w \in \Sigma^{*} \land |w| = n\}$.
Let $C_n \subset \Sigma^{*}$ be the language of circular strings that contain as substrings all elements of $S_n$. For instance, $bbaaaababaabbbba \in C_4$
I have formulated the problem of finding the subset of $C_n$, formed by the circular s... |
The ROOT team has adopted Doxygen for generating the reference manual. Here you will find a number of conventions and tips for converting the existing source code to generate proper documentation.
How to generate the doxygen documentation
Developers may generate the documentation by hand to see the results of the curre... |
The worst-case time complexity of an algorithm is the time complexity for the worst-case input. Insertion sort takes $\Theta(n^2)$ in the worst-case, not $O(n)$. However, mergesort and heapsort each take $\Theta(n \log n)$ in the worst-case, and so achieve the $\Omega(n \log n)$ lower bound.
Suppose $n!$ is roughly $10... |
We consider a thin disk whose center is $O$ and radius is $R$, which has an electric surface charge density of $\sigma$. We want to find the expression of the electric field $\vec{E}$ at a point $M$ of the $(O_z)$ axis using the definition of an electric field at a point, where $(O_z)$ is perpendicular to the disk. The... |
Mini-Workshop on Symplectic Geometry
10/07/2015
VU Amsterdam
Mini-Workshop on Symplectic Geometry on 7 October 2015 at VU Amsterdam
Faculty of Science
Sciences
Conference / Symposium / Seminar
On October 7, 2015 the Vrije Universiteit Amsterdam will host a Mini-Workshop on Symplectic Geometry, click here for the poster... |
I'm wondering what is the formula for induced drag
in a stalled regime, i.e. in a regime where the $C_L$ (coef. of. lift) has started to decrease but is still nonzero.
I've a feeling that the conventional formula for induced drag$$D_i = \frac{L^2}{\frac{1}{2}\rho V^2 \pi b^2 \epsilon}$$ (taken e.g. from this answer) wh... |
It looks like you're new here. If you want to get involved, click one of these buttons!
Last time we studied meets and joins of partitions. We observed an interesting difference between the two.
Suppose we have partitions \(P\) and \(Q\) of a set \(X\). To figure out if two elements \(x , x' \in X\) are in the same par... |
Most densely-defined unbounded linear operators on Hilbert spaces have a very large domain. In fact, for a lot of natural operators the intersection of their domains are still dense.
Let us consider some counterexamples:
Let $T : \mathbb Q^n \subset \mathbb R^n \rightarrow \mathbb R^m$ be a densely-defined unbounded op... |
I have been introduced to $E =mc^2$ and binding energy recently while studying nuclear physics and I have a hard time understanding the following:
Mass-Energy what does $E=mc^2$ really mean, as I have read some posts and from what I understand it is not the fact that "energy is transformed to mass" so what does this eq... |
I would have expected the correlation coefficient to be the same as a regression slope (beta), however having just compared the two, they are different. How do they differ - what different information do they give?
Assuming you're talking about a simple regression model $$Y_i = \alpha + \beta X_i + \varepsilon_i$$ esti... |
Current browse context:
math.AC
Change to browse by: References & Citations Bookmark(what is this?) Mathematics > Commutative Algebra Title: Ulrich elements in normal simplicial affine semigroups
(Submitted on 15 Sep 2019)
Abstract: Let $H\subset {\mathbb N}^d$ be a normal simplicial affine semigroup, $R=K[H]$ its semi... |
A natural place to start, depending upon your mathematical background might be the modern cardinal generalizations of the voting literature. Consider the following toy model, and feel free to adapt any parts which don't seem appropriate to the problem at hand.
Data: Say we have a fixed, finite population of players $N$... |
Difference between revisions of "Talk:Gamma-function"
(Mid-TeX)
(Mid TeX)
Line 1: Line 1:
''$\Gamma$-function''
''$\Gamma$-function''
+
$
$
Line 103: Line 104:
$$
$$
−
5) In the real domain, $ $ for $ $ and it assumes the sign $ $ on the segments $ $, $ $ (Fig. b).
+
5) In the real domain, $$ for $$ and it assumes the ... |
Square Root of 2 is Irrational/Classic Proof Theorem $\sqrt 2$ is irrational. Proof
Thus it follows that:
$(1): \quad 2 \divides p^2 \implies 2 \divides p$
where $2 \divides p$ indicates that $2$ is a divisor of $p$.
So:
$\sqrt 2 = \dfrac p q$
for some $p, q \in \Z$, and:
$\gcd \set {p, q} = 1$
where $\gcd$ denotes the... |
Try the following:
The weight $w_i$ of an element $i$ in the heap $H$ is its depth in the corresponding binary tree. So the element in the root has weight zero, its two children have weight 1 and so on. The you define as potential function
$$\Phi(H)=\sum_{i\in H}2 w_i.$$
Let us now analyze the heap operations. For
inse... |
Nagoya Mathematical Journal Nagoya Math. J. Volume 157 (2000), 103-127. Integers free of small prime factors in arithmetic progressions Abstract
For real $x \ge y \ge 2$ and positive integers $a$, $q$, let $\Phi(x, y; a, q)$ denote the number of positive integers${} \le x$, free of prime factors${} \le y$ and satisfyin... |
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 ... |
I am trying to understand Theorem 2.9 from Ch. VII of Serge Lang's Algebra. The statement is the following:
Let $A$ be an integral domain which is integrally closed in its field of fractions $K$. Let $f(x)\in A[x]$ be monic and irreducible. Let $\mathfrak{p}$ be a maximal ideal of $A$ and let $\overline{f}(x)\in (A/\ma... |
let $(X, \leq_*)$ be a partially ordered set.
Assume there is an isomorphism $f: (X,\leq_*) \to (\mathbb Z, \leq)$
let $A \subseteq X$ be a well ordered subset of $X$ with an upper bound. Meaning there is an element $b \in X$ such that $\forall a \in A, a\leq_* b$.
Show that $A$ is a finite set.
I'm not sure how to app... |
Derivatives of transcendental functions
The new material here is just a list of formulas for taking derivatives of exponential, logarithm, trigonometric, and inverse trigonometric functions. Then any function made by composing these with polynomials or with each other can be differentiated by using the chain rule, prod... |
I have read How can antibonding orbitals be more antibonding than bonding orbitals are bonding?. But I am intersted in a specific derivation. During lecture my professor stated that the overlap $S_{ij}$ integral can be between -1 and 1. In other words, $$-1<\int\psi^*_i\psi_j\,dx<1$$ He further mentioned that a negativ... |
One should start at the definition of an infinite series to see what is going wrong. We have
$$\sum_{n=0}^\infty a_n=\lim_{N\to\infty}\sum_{n=0}^Na_n$$
In this case, we have
$$\sum_{n=0}^\infty x^n=\lim_{N\to\infty}\sum_{n=0}^Nx^n$$
Now, I will draw attention to the partial sums: As your students say, there is some can... |
There are different kinds of equality. Equality is said to be
extensional when things are equal when their parts are equal, so to speak:
Equality the elements of $A \times B$ is extensional if, for all $u, v : A \times B$, $u = v$ if and only if $\pi_1(u) = \pi_1(v)$ and $\pi_2(u) = \pi_2(v)$. Here $\pi_1$ and $\pi_2$ ... |
I did a little work on this problem in Bielefeld in 1991, based on a suggestion by Waldhausen.
Let $G$ be a finite group. The algebraic $K$-theory $A^G(X)$ of the category of finite retractive $G$-spaces and $G$-maps over and under $X$, with $G$-homotopy equivalences as the weak equivalences, does indeed have a Segal-t... |
ADDED (29 May, 2013)
As has been pointed out in the comments, there has been great progress since this answer was first written, and the conjectures below have now been proved, thanks to ground-breaking work of Agol, Kahn--Markovic and Wise. Here's a brief summary of some of the highlights. (Shameless self-promotion: s... |
TL;DR: Use lookup tables, because we're not in Kansas any more. We're off to see the Wizard...
Just looking at the wizard, there seems to be a fairly regular progression. You get the first spell of spell level \$S\$ when your class level \$C\$ satisfies
\begin{align}\frac{C+1}{2} & \geq S &\Leftrightarrow&& C-2S+1 & \g... |
Pandey, SB and Sahu, DK and Resmi, L and Sagar, R and Anupama, GC and Bhattacharya, D and Mohan, V and Prabhu, TP and Bhatt, BC and Pandey, JC and Parihar, Padmaker and Castro-Tirado, AJ (2003)
Optical observations of the bright long duration peculiar GRB 021004 afterglow. [Preprint]
PDF
0211108.pdf
Download (334kB)
Ab... |
Difference between revisions of "Fujimura's problem"
(→n=4)
(→General n)
Line 56: Line 56:
== General n ==
== General n ==
− + − + + + + +
lower bound for <math>\overline{c}^\mu_n</math> is 3(n-1), made of all points in <math>\Delta_n</math> with exactly one coordinate equal to zero.
A trivial upper bound is
A trivial ... |
That was an excellent post and qualifies as a treasure to be found on this site!
wtf wrote:
When infinities arise in physics equations, it doesn't mean there's a physical infinity. It means that our physics has broken down. Our equations don't apply. I totally get that
. In fact even our friend Max gets that.http://blo... |
In response to Peter Kämpf's answer to this question, why did moving the CG back on the Wright Flyer improve its stability?
It did not improve stability, but flyability.
The Wright Flyer had the CG located aft of the neutral point and was unstable in pitch. A longitudinally unstable aircraft will deviate from its trim ... |
Definition:Lower Closure Contents Definition
Let $\left({S, \preccurlyeq}\right)$ be an ordered set.
Let $a \in S$.
The lower closure of $a$ (in $S$) is defined as: $a^\preccurlyeq := \left\{{b \in S: b \preccurlyeq a}\right\}$
Let $T \subseteq S$.
The lower closure of $T$ (in $S$) is defined as: $T^\preccurlyeq := \bi... |
2.3.2 - Binomial Sampling
When data are collected on a pre-determined number of units and are then classified according to two levels of a categorical variable, a binomial sampling emerges. Consider the High-risk Drinking Example where we have high-risk drinkers versus non-high-risk drinkers. In this study there was a ... |
A model of chemical pollution in a lake
A pristine lake of area 2 km
2 and average depth of 10 meters
has a river flowing through it at a rate of 10,000 m 3 per day. A factory
is built beside the river and releases 100 kg of chemical waste
into the lake each day. What will be the amounts of chemical
waste in the lake o... |
This question already has an answer here:
I came across this problem while solving another one. I will show how far I could get on my own:
Suppose that $\sqrt 3 \in Q(\sqrt[4]2)$. Since $Q(\sqrt3)$ is the smallest field containing both $Q$ and $\sqrt3$, thus $Q(\sqrt3)\subset Q(\sqrt[4]2)$.
Now $[Q(\sqrt[4]2):Q] =4 $ a... |
Search
Now showing items 1-10 of 155
J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed i... |
Archive:
Subtopics:
Comments disabled
Fri, 17 May 2019
Last year a new Math Stack Exchange user asked What's the difference between !!\frac00!! and !!\frac10!!?.
I wrote an answer I thought was pretty good, but the question was downvoted and deleted as “not about mathematics”. This is bullshit, but what can I do?
I can... |
If you're given that the limit exists (as the OP stipulates), then you can have all kinds of fun computing what the limit is. To begin with, you can get rid of the square root symbol by multiplying top and bottom by $(\cos x)^{\sin x}+\sqrt{1-x^3}$, which has limit $2$ as $x\to0$, yielding
$$L=\lim_{x\to0}{(\cos x)^{2\... |
Consider a capacitor connected to a battery of voltage $V $. Let the capacitor have an area $A$, and a distance $L$ between the plates. Assume that the capacitor has a layer of linear dielectric (of dielectric constant $κ$, so that $ε = κε_0$) of thickness $L/2$ on the lower plate.
The capacitance is $C=\frac{2\kappa \... |
This is the first tutorial in our ongoing series on time series spectral analysis. In this entry, we will closely examine the discrete Fourier transform (aka DFT) and its inverse, as well as data filtering using DFT outputs. The DFT is basically a mathematical transformation and may be a bit dry, but we hope that this ... |
It looks like you're new here. If you want to get involved, click one of these buttons!
Last time we studied meets and joins of partitions. We observed an interesting difference between the two.
Suppose we have partitions \(P\) and \(Q\) of a set \(X\). To figure out if two elements \(x , x' \in X\) are in the same par... |
A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.
A for awesome Posts: 1901 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: vi... |
I'm stuck with an Exercise in Hatcher's Algebraic Topology. (Exercise 1.2.6)
This problem asks me to show that the complement of a discrete subspace of $\mathbb{R}^n$ is simply-connected if $n\ge 3$, using the fact that if $Y$ is obtained by attaching $3$-cells to a path-connected space $X$, then the inclusion $X \hook... |
reference: http://www.stat.wisc.edu/~bates/UseR2008/WorkshopD.pdf from page 120.
Now I want to fit a generalized logistic mixed model, where $\beta$ is fixed effect, $\theta$ is variance covariance parameter of random effects, $u$ is the random effects, $\tilde{u}$ is the empirical random effects. The likelihood functi... |
A class of languages $\mathcal{L}$ is closed against concatenation if for every pair of languages $L_1, L_2 \in \mathcal{L}$ we also have $L_1 \cdot L_2 \in \mathcal{L}$.
Here, $A \cdot B = \{ v \cdot w \mid v \in A, w \in B \}$.
A class of languages $\mathcal{L}$ is closed against homomorphism if for every language $L... |
This package allows users to run adaptive mixture network regularized generalized linear models (Gaussian, logistic, and Cox regression). The model looks like \[argmax_{\beta}\left\{ \frac{1}{2n}l\left(\beta\right)-\lambda_{1}\sum_{i=1}^{p}w_{i}\left|\beta_{i}\right|-\frac{\lambda_{2}}{2}\left|\beta\right|^{T}L\left|\b... |
Which substances have the most extreme enthalpies of formation per gram at standard temperature and pressure?
Beryllium oxide −23.96 kJ/g Lithium fluoride −23.75 kJ/g Beryllium fluoride −21.84 kJ/g Beryllium hydroxide −21.01 kJ/g Lithium hydroxide −20.24 kJ/g Lithium oxide −19.93 kJ/g Boron trioxide −18.29 kJ/g Magnesi... |
A support vector machine (SVM) is a supervised learning algorithm that can be used for binary classification or regression. Support vector machines are popular in applications such as natural language processing, speech and image recognition, and computer vision.
A support vector machine constructs an optimal hyperplan... |
This is a slightly more advanced version of another question here.
Let $\textbf{CRing}$ be the category of commutative rings with unit. Let $\textbf{Dom}$ be the category of integral domains – by which I mean a non-trivial commutative ring with unit such that the zero ideal is prime. Let $\textbf{Fld}$ be the category ... |
Review Questions Review Questions Array Creation
Q05.01 Create an array of the numbers
1,
5,
19,
30
Q05.02 Create an array of the numbers
-3,
15,
0.001,
6.02e23
Q05.03 Create an array of integers between -10 and 10
Q05.04 Create an array of 10 equally spaced angles between 0 and 2\pi
Q05.05 Create an array of logarithm... |
Show that for $l(n) = \log \log n$, it holds that $\text{DSPACE}(o(l)) = \text{DSPACE}(O(1))$.
It's well known fact in Space Complexity, but how to show it explicitly?
Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. It only takes a minute to... |
I have to calculate the sum:
$$\sum_{j=0}^{\infty}(j+1)\cdot\left(\frac{1}{1.05}\right)^{j+1}$$
I know it is convergent from the ratio test.
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 jo... |
The Annals of Probability Ann. Probab. Volume 19, Number 1 (1991), 423-451. A Borel Measurable Version of Konig's Lemma for Random Paths Abstract
Starting at $x$ in a Polish space $X$, a player selects the distribution $\sigma_0$ of the next state $x_1$ from the collection $\Gamma (x)$ of those distributions available ... |
2018-09-11 04:29
Proprieties of FBK UFSDs after neutron and proton irradiation up to $6*10^{15}$ neq/cm$^2$ / Mazza, S.M. (UC, Santa Cruz, Inst. Part. Phys.) ; Estrada, E. (UC, Santa Cruz, Inst. Part. Phys.) ; Galloway, Z. (UC, Santa Cruz, Inst. Part. Phys.) ; Gee, C. (UC, Santa Cruz, Inst. Part. Phys.) ; Goto, A. (UC,... |
The core of continuous wavelet transform
$$ C_s(\tau,a) = \int s(t) \psi^*_{\tau,a}(t) dt$$
discretization is that (this is only one of the numerous possibilities) one can find constants $a_0$ and $b_0$, whose product $a_0 b_0 <C_\psi$ ($C_\psi$ depending on the wavelet), such that the following sampling pattern
$$c_{j... |
About the simplest thing you can do is interpolate normalized counts over time and (almost) the simplest form of interpolation is linear.
Specifically, suppose $y_i$ is the state population at time $i$ and $x_i$ is some other count (by age, tract, or whatever). Define $\xi_i = x_i/y_i$. Suppose $i$ is a year for which ... |
Technical devices for reducing the number of axioms
In a recent article, I wrote:
I guessed it was a mere technical device, similar to the one that
we can use to reduce five axioms of group theory to three. …
The fact that you can discard two of the axioms is mildly
interesting, but of very little practical value in gr... |
This is related to Lang Real and Functional Analysis Chpt XVI, Sec 1.
Let $A$ be a banach algebra. Let $v\in A$. Spectrum of $v$ is defined as $\{z\in C\vert$ $v-ze$ is not invertible$\}$.
Thm 1.2 Let $A$ be an unital commutative normed algebra over real. Assume there is $j\in A$ s.t. $j^2=-e$. Let complex number $C=R+... |
Category:Definitions/Subtraction
As the set of integers is the Inverse Completion of Natural Numbers, it follows that elements of $\Z$ are the isomorphic images of the elements of equivalence classes of $\N \times \N$ where two tuples are equivalent if the difference between the two elements of each tuples is the same.... |
My near-future hope is to set up my own weblog where each new blog item is my write-up of notes from my math lectures. The purpose of this is twofold:
I then need to be able to write mathematical expressions in my HTML using TeX syntax and have the expressions converted to images. TeX (father of LaTeX (father of Itex))... |
Search
Now showing items 1-10 of 18
J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
Search
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 ... |
I want to know the difference between these three languages and it would be great if you would give some examples as well.
closed as unclear what you're asking by David Richerby, Tom van der Zanden, Luke Mathieson, hengxin, vonbrand Mar 30 '16 at 15:47
Please clarify your specific problem or add additional details to h... |
Nets emerges from the work of Moore and Smith to understand integrals, i.e., integrals are the great example of nets. For localizing it, imagine you want to calculate
$$\int_a^bf(x)\,dx$$
for a sufficient good function $f$. Now, we consider all pairs of $(\{X_i\}_{i<n},\{\xi_i\}_{i<n})$, where $\{X_i\}_{i<n}$ is a part... |
The Annals of Mathematical Statistics Ann. Math. Statist. Volume 23, Number 4 (1952), 493-507. A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations Abstract
In many cases an optimum or computationally convenient test of a simple hypothesis $H_0$ against a simple alternative $H_1... |
I could have made this question very brief but instead I've maximally gone the other way and explained a huge amount of background. I don't know whether I put off readers or attract them this way. The question is waay down there.
Let $f$ be a cuspidal modular eigenform of level $\Gamma_0(N)\subseteq SL_2(\mathbf{Z})$ (... |
Answer
$\vec{L} = mr^2 \vec{\omega}$
Work Step by Step
We know that $\omega r =v$ and that $\vec{\omega}$ is in the k direction. Thus: $\vec{L} = mvr\hat{k} = mr^2 \omega \hat{k} = mr^2 \vec{\omega}$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll ... |
I need to bulid a context-free grammar for
$\qquad \mathscr{L_4}=\{w\in\{a,b,c\}^* \mid w\text{ is not palindrome at all}\}$
Not palindrom at all:We will say that a word $w$ is not palindrome at all if for all $i$ such that $1\leq i\leq |w|$ the $i$ letter from the beginning of $w$ is not the same like the $i$ letter o... |
This is not "enough proof". The main problem of your proof is that it just lacks words. A proof should explain what you have in your head. So the first thing is to clearly states what you want to prove.
We want to prove that $n^2$ is not $O(\log n)$.
Then you have to explain how you will do it:
Assume toward a contradi... |
It looks like you're new here. If you want to get involved, click one of these buttons!
Isomorphisms are very important in mathematics, and we can no longer put off talking about them. Intuitively, two objects are 'isomorphic' if they look the same. Category theory makes this precise and shifts the emphasis to the 'iso... |
Feynman diagrams provide a very compact and intuitive way of representing interactions between particles. These diagrams can be included into LaTeX documents thanks to a few packages. One of the older packages is
feynmf which uses MetaPost in order to generate the diagrams. More recently, a new package called Ti
kZ-Fey... |
We want to solve the eigenproblem $\hat{H}|\psi\rangle=\lambda |\psi\rangle$. Since $|\psi\rangle$ lives in an infinite dimensional Hilbert space, this isn't fit to put on to a computer. Instead, we discretize space into $N$ points. $\vec{\psi}$ is now an $N$ dimensional column vector, and $\bf H$ is now an $N\times N$... |
It looks like you're new here. If you want to get involved, click one of these buttons!
Isomorphisms are very important in mathematics, and we can no longer put off talking about them. Intuitively, two objects are 'isomorphic' if they look the same. Category theory makes this precise and shifts the emphasis to the 'iso... |
Can anybody suggest how I can compute the second moment (or the whole moment generating function) of the cosine of two gaussian random vectors $x,y$, each distributed as $\mathcal N (0,\Sigma)$, independent of each other? IE, moment for the following random variable
$$\frac{\langle x, y\rangle}{\|x\|\|y\|}$$
The closes... |
Question:
Is $\mathbb{Z}= \{\dots, -3, -2, -1, 0 ,1 ,2 , 3, \dots \}$ countable?
My attemp so far:
Let us create the following one-to-one correspondence between $\mathbb{Z}$ and $\mathbb{N}$. $$\begin{matrix}1 & 2 & 3 & 4 & 5 & 6 & 7 & \dots \\ \updownarrow & \updownarrow & \updownarrow & \updownarrow & \updownarrow & ... |
I was given the following task which I struggle with.
Prove the following statement, or disprove it by giving a counter example: if $\sum_{n=1}^\infty a_n$ is convergent then $\sum_{n=1}^\infty (a_n)^3$ is also convergent. I think the statement is true. My intuition is that $|a_n|$<1 starting some index $N$ (since the ... |
As you’ve observed, the projected line segment is not symmetric about the view line to the circle’s center—the center shifts. Another reason that you might be having some trouble working this out is that the apparent width of the ellipse also depends on the visual angle subtended by the circle, which varies with both t... |
Q1:
The benefits of doing a geometry optimization is finding a mimimum energy state, which tends to be the most probable state a molecule exists in. This is in contrast to a molecular dynamics simulation which gives information about distributions of states. Geometry optimizations have the disadvantage of less informat... |
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 ... |
I'm studying Intro to Topology by Mendelson.
The problem statement is,
Let $A,B\subset X$, $X$ a topological space. If $A$ is connected, $B$ open and closed, and $A\cap B\neq\emptyset$ then $A\subset B$.
My proof is,
By way of contradiction, suppose that $A$ is not a subset of $B$. Then there exists an $a\in A$ such th... |
A complex symmetric matrix can be 'diagonalized' using a unitary matrix: If $A$ is a rank-$n$ complex symmetric matrix, there is a unitary matrix $W \in U(n)$ such that $W A W^T$ is a real non-negative diagonal matrix.
I wonder whether there are similar statements for $$W \in \frac{SU(n) \times \mathbb{Z}_{n k}}{\mathb... |
Let $(\Omega,\mathcal A,\mu)$ be a measure space and $(f_n)$ a sequence of $\mu$-integrable functions, which converges uniformly to $f:\Omega\to\mathbb R$.
1) If $\mu$ is finite, $f$ is also integrable.
2) If $\mu$ is $\sigma$-finite, $f$ needn't be integrable. In case $f$ is integrable, $\lim_{n\to\infty}\int f_n d\mu... |
A complete review on derivatives would be lengthy. We try to touch on some topics that are used often in STAT 414 but not everything can be covered in the review. There are many good calculus books and websites to help you review. Students like the book
Forgotten Calculus: A Refresher Course with Applications to Econom... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.