text stringlengths 256 16.4k |
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texlive 2012 debian package:
\documentclass[]{article}%\usepackage{amsmath} \begin{document} \begin{align} & \uparrow\sum F\end{align}\end{document}
compile with
htlatex report.tex "htm,mathml" " -cunihtf"
gives
/usr/share/texmf/tex/generic/tex4ht/html-mml.4ht) (/usr/share/texmf/tex/generic/tex4ht/html4-uni.4ht)) (./re... |
Gödel's System T in TypeScript
Recently, I’ve been reading Bove and Dybjer’s paper on
“Dependent Types at Work” where Kurt Gödel’s System T is briefly described. It is a type system based on the Simply Typed Lambda Calculus and includes booleans and natural numbers. The unusual thing about it is that it allows us to pe... |
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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... |
Since the fppf cohomology group ${\rm{H}}^1(F, \alpha_p) = F/F^p$ is visibly uncountable (where $p = {\rm{char}}(F) > 0$), perhaps you meant to assume $G$ is smooth (and then fppf cohomology coincides with etale cohomology, which in turn coincides with Galois cohomology as in the title of the question). The cohomology ... |
Journal of Symbolic Logic J. Symbolic Logic Volume 48, Issue 3 (1983), 529-538. Classifying Positive Equivalence Relations Abstract
Given two (positive) equivalence relations $\sim_1, \sim_2$ on the set $\omega$ of natural numbers, we say that $\sim_1$ is $m$-reducible to $\sim_2$ if there exists a total recursive func... |
Definition:Right Angle
Jump to navigation Jump to search
In the above diagram, the line $CD$ has been constructed so as to be a
Definition
The measurement of a right angle is $\dfrac{180^\circ} 2 = 90^\circ$ or $\dfrac \pi 2$.
In the words of Euclid:
When a straight line set up on a straight line makes the adjacent ang... |
Given a convex hexagon $ABCDEF$. All its sides are equal (it can be irregular). Furthermore, $AD = BE = CF$. How can I prove that a circle can be inscribed in this hexagon?
Let $O$ be the intersection point of diagonals $AD$ and $BE$ (see diagram below) and set $a=OB$, $b=OD$, $d=AD=AE$, $\theta=\angle AOB=\angle DOE$.... |
In a question, I have to find the acceleration of a fluid parcel in a steady line vortex. I am given that $u_\theta=\frac{A_0}{r}$. So for a steady line vortex, the parcels are following circular paths therefore in cylindrical coordinates, $u_r=u_z=0$ and the acceleration comes from the Lagrangian derivative
$\frac{D\v... |
Normal modes are used to describe the different vibrational motions in molecules. Each mode can be characterized by a different type of motion and each mode has a certain symmetry associated with it. Group theory is a useful tool in order to determine what symmetries the normal modes contain and predict if these modes ... |
A little bit of background: As stated in your notes, this equation is obtained using the Fraunhofer diffraction formula (which is an approximation to the more general Rayleigh-Sommerfeld formula). According to the Fraunhofer diffraction integral, given the transmittance function of the diffractive screen:$$U(x',y')=\ca... |
I was trying to understand the final section of the paper "Revisiting Baselines for Visual Question Answering". Authors state that their model performs better with a
binary loss in comparison to a softmax loss. I wonder what actually a binary loss mean in this case? I think the softmax loss is the same term for binary ... |
Given normally distributed integers with a mean of 0 and a standard deviation $\sigma$ around 1000, how do I compress those numbers (almost) perfectly? Given the entropy of the Gaussian distribution, ...
A few days ago this appeared on HN http://www.patrickcraig.co.uk/other/compression.htm. This refers to a challenge f... |
I will assume $X_i$ independent in this post. To get a feel for the problem, recall the special case of uniform distribution, corresponding to $\alpha=1$, i.e. $\mathrm{Beta}(1,1) \stackrel{d}{=} U(0,1)$.
The sum of $n$ iid uniform distribution was studied by J.O. Irwin and P. Hall, and the result is known as Irwin-Hal... |
Differential and Integral Equations Differential Integral Equations Volume 20, Number 12 (2007), 1423-1433. Positive solutions for a class of infinite semipositone problems Abstract
We analyze the positive solutions to the singular boundary value problem \[-\Delta u = \lambda[ f(u)-1/u^{\alpha}]; x \in \Omega\] \[u = 0... |
Prediction and Forecasting
Yes you are correct, when you view this as a problem of prediction, a Y-on-X regression will give you a model such that given a instrument measurement you can make an unbiased estimate of the accurate lab measurement, without doing the lab procedure.
Put another way, if you are just intereste... |
Because a problem is in
NP if, and only if, "yes" instances have succinct certificates. Informally, this means that the solution to any instance is at most polynomially large in the size of the instance, and if you're given an instance and something that is claimed to be a solution to it, you can check in polynomial ti... |
I found out that the
symbol for union, ∪, was created in 1895 by Giuseppe Peano in his Formulario Mathematico but of course the use of the word "union" in mathematics was older. Do you have a source for the earliest occurrence?
I found out that the
Intersection and union. The symbols $\cap$ and $\cup$ were used by Gius... |
Based on this question: What is the homology groups of the torus with a sphere inside?
I'm trying to find the fundamental group of this space using the Seifert–van Kampen theorem. If $U$ is the torus and $V$ is the sphere, then $U\cap V$ is the circle, thus we have the following fundamental groups:
$\pi_1(U)=\mathbb Z\... |
Answer
The two points of intersection are: $(3, \frac{\pi}{3})$ and $(3, \frac{5\pi}{3})$
Work Step by Step
$r = 3$ $r = 2+2~cos~\theta$ To find the points of intersection, we can equate the expressions for $r$: $3 = 2+2~cos~\theta$ $2~cos~\theta = 1$ $cos~\theta = \frac{1}{2}$ $\theta = \frac{\pi}{3}, \frac{5\pi}{3}$ ... |
Dini criterion for the convergence of Fourier series
A criterion first proved by Dini for the convergence of Fourier series in [Di].
TheoremConsider a summable $2\pi$ periodic function $f$ and a point $x\in \mathbb R$. If thereis a number $S$ and a $\delta>0$ such that\begin{equation}\label{e:Dini}\int_0^\delta |f(x+u)... |
In the review Foundations of Black Hole Accretion Disk Theory, the authors defines an effective potential for Kerr geometry as (Chap. 2, eqn. 23) $$\mathcal{U}_{eff}=-\frac{1}{2}\ln\left|g^{tt}-2lg^{t\phi}+l^2g^{\phi\phi}\right|$$ where $l=\dfrac{\mathcal{L}}{\mathcal{E}}=-\dfrac{u_\phi}{u_t}$ is the specific angular m... |
Definition:Jacobian/Determinant Definition
Let $U$ be an open subset of $\R^n$.
$\displaystyle \map \det {\mathbf J_{\mathbf f} } := \begin{vmatrix} \map {\dfrac {\partial f_1} {\partial x_1} } {\mathbf x} & \cdots & \map {\dfrac {\partial f_1} {\partial x_n} } {\mathbf x} \\ \vdots & \ddots & \vdots \\ \map {\dfrac {\... |
Definition:Normal Subgroup/Definition 1 Definition
Let $G$ be a group.
Let $N$ be a subgroup of $G$.
$N$ is a normal subgroup of $G$ if and only if: $\forall g \in G: g \circ N = N \circ g$
where $g \circ N$ denotes the subset product of $g$ with $N$.
The statement that $N$ is a normal subgroup of $G$ is represented sy... |
I was given this answer:
So I was told that
$$\tan(x) = 2$$ Then, they said from this statement they could know that: $$\cos(x) = \frac{1}{\sqrt{5}}$$ $$\sin(x) = \frac{2}{\sqrt{5}}$$
Now, I understand that if I do
$$\tan^{-1}(2) = 63.4$$
And then after that I can get the ratio of cosine and sine. However, I don't know... |
Problem
Is there an irrational $\alpha\in\mathbb{R}\backslash\mathbb{Q}$ such that the set $S= \{\,\{2^N\alpha\} :N\,\in\mathbb{N}\}$ is
not dense in $[0,1]$.
Here $\{x\}=x-\lfloor x\rfloor$ is the
fractional part of $x$.
Questions very similar to this have been asked in the past. For example
However right now I can't ... |
I'm having trouble understanding some of the subtleties of working with bras and kets when considering the standard 1-D quantum oscillator.
Say I am given a state vector at $t=0$, $$|\Psi(t=0)\rangle = A \sum_{q=0}^{Q_o} \frac{1}{q+i}|\phi_q\rangle$$
Where $Q_o$ is a positive finite integer.
I am given the number opera... |
For $1\leq p<\infty$ an approach to define fractional Sobolev spaces is by Sobolev-Slobodeckij spaces a generalisation of Hölder continuity. For example letting $U\subset\mathbb{R}^n$ then,
$ \left\|u\right\|^p_{W^\mu_p(U)} = \left\|u\right\|^p_{W^{\lfloor\mu\rfloor}_p(U)} + \sum \int_U \int_U \frac{|D^\alpha u(x)-D^\a... |
The geometric analogue to darij grinberg's answer is that you are effectively asking whether the product of two particular irreducible algebraic varieties is also irreducible. Here is how the translation works.
The two polynomial rings $K[x_1, \dots, x_m]$ and $K[y_1, \dots, y_n]$ are the coordinate rings of the affine... |
I have a doubt about how the time step is calculated in kinetic montecarlo simulations.
One state with index $i$ is connected to other $N$ states, indexed by $j=1...N$, by transitions that happen with rates $r_{ij}$ (form $i$ to $j$). At each iteration of the algorithm, one of the $N$ transitions is randomly chosen (wi... |
I don't think it's correct to talk about probabilities in context of random forests, as random forest classifiers do not attempt to produce accurate probabilities (see Olson et al. ). It's better to view the output as some score in the interval [0,1].
In random forest classification, each class $c_i, i \in {1, ..., k}$... |
I think your question implicates another question (which is also mentioned in some comments here), namely: Why are all energy eigenvalues of states with a different
angular momentum quantum number $\ell$ but with the same principal quantum number $n$ (e.g. $3s$, $3p$, $3d$) degenerate in the hydrogen atom but non-degen... |
One way to solve this without using the laplace transform is by taking this back to the differential equation which produced this transfer function.
The transfer function:
$$\dfrac{Y(s)}{r(s)}=\dfrac{6s+100}{s^2+12s+100} $$
This could be re-written as:
$$(s^2+12s+100)Y(s)=(6s+100)r(s) $$
Back to the time domain:
$$y''+... |
Answer
The hill makes an angle of $3.8^{\circ}$ with the horizontal.
Work Step by Step
Let $\theta$ be the angle the hill makes with the horizontal. The car's weight of $2800~lb$ is directed straight down. The force of $186~lb$ is directed up the hill at an angle of $\theta$ above the horizontal. We can draw a triangle... |
I'm studying chapter 5 of Discrete-Time Signal Processing 3rd edition by Alan Oppenheim and I'm having serious difficulties understanding how he obtained equation 5.57. For those who don't have this book I tell you that in this part it is analyzing the frequency, phase and group delay of
$$ 1- re^{j \theta} e^{-j \omeg... |
In Griffiths'
Intro to QM [1] he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being
$$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right)$$
(cf. last formula on p. 101). He then says that these eigenfunctions are not square integrable because
$$\int_{-\infty}^{\infty}g_{\lambda}\lef... |
An important remark: since the function $f(x) = \begin{cases} 1 & x \in \mathbb{Q} \\ 0 & x \in \mathbb{R} \setminus \mathbb{Q} \end{cases}$ is clearly Lebesgue-integrable (being equal to $0$ almost everywhere), you are probably asking about Riemann integrability. In this case, though, you have a problem: the concept o... |
ADDED (29 May, 2013)
As has been pointed out in the comments, there has been great progress since this answer was first written, and the conjectures below have now been proved, thanks to ground-breaking work of Agol, Kahn--Markovic and Wise. Here's a brief summary of some of the highlights. (Shameless self-promotion: s... |
Let us define the following matrix:
$C=AB$
where $B$ is a block diagonal matrix with $N$ blocks, $B_1$, $B_2$ … $B_N$, each of dimensions $M \times M$. I know that $B_k = I_M - \mu R_k$ with $R_k$ equals to a hermitian matrix and $\mu$ some positive constant. Moreover, I know that the the entries of the matrix $A$ are ... |
Here's a quote from Andrew Gilpin (1993) advocating Maurice Kendall's $τ$ over Spearman's $ρ$ for theoretical reasons:
[Kendall's $τ$] approaches a normal distribution more rapidly than $ρ$, as $N$, the sample size, increases; and $τ$ is also more tractable mathematically, particularly when ties are present.
I can't ad... |
How to show that the series convergent
$$\frac{1}{2^2\log{2}}-\frac{1}{3^2\log{3}}+\frac{1}{4^2\log{4}}-\dots$$
The series can be written as $$\sum_{n=1}^\infty (-1)^{n+1}\frac{1}{(n+1)^{2}\log{(n+1)}}$$ I want to use Leibnitz's test. Here $u_n=\frac{1}{(n+1)^{2}\log{(n+1)}}\to 0$ as $n\to \infty$
How to show $u_n$ is ... |
How can Hawking radiation with a finite (greather than zero) temperature come from the event horizon of a black hole? A redshifted thermal radiation still has Planck spectrum but with the lower temperature (remember CMB with temperature redshifted by expansion of the universe). Now, redshift at the event horizon is inf... |
I am sure it's just your eyelashes creating a filtering effects, but if you look a a bright(ish) light source such as a lightbulb while squinting, if looks like you are seeing straight light rays emitting from the lightbulb, I assume you can't see an individual ray of light like this?
As Qmechanic noted, a question pre... |
Vor's answer gives the standard definition. Let me try to explain the difference a bit more intuitively.
Let $M$ be a bounded error probabilistic polynomial-time algorithm for a language $L$ that answers correctly with probability at least $p\geq\frac{1}{2}+\delta$. Let $x$ be the input and $n$ the size of the input.
W... |
Primitive Pythagorean triplets $a^2 = b^2 + c^2, \gcd(b,c) = 1$ are given by $a = r^2 + s^2$, $b = r^2 - s^2$ and $c = 2rs$ where $r > s$ are natural numbers. Let the $n$-th primitive triplet be the one formed by the $n$-th smallest pair in increasing order of $(r,s)$.
Claim 1: Let $\mu_n$ be the arithmetic mean of the... |
Volume 56 Issue 2 / Pages.117-120 / 2016 / 2466-1384(pISSN) / 2466-1392(eISSN)
DOI QR Code
Appearance of osteoporosis in rat experimental autoimmune encephalomyelitis Ahn, Meejung ; Kang, Sohi ; Park, Channam ; Kim, Jeongtae ; Jung, Kyungsook ; Yang, Miyoung ; Kim, Sung-Ho ; Moon, Changjong ; Shin, Taekyun Received : 2... |
while I was reading about charge conjugation I found some (apparently) contradictory facts. For example Itzykson & Zuber says (page 153) "Up to a phase, $\cal C$ interchanges particles and antiparticlas with the same momentum, energy and helicity" while Zee (pag. 101) "You can easily convince yourself that the charged ... |
Moser-lower.tex
\section{Lower bounds for the Moser problem}\label{moser-lower-sec}
In this section we discuss lower bounds for $c'_{n,3}$. Clearly we have $c'_{0,3}=1$ and $c'_{1,3}=2$, so we focus on the case $n \ge 2$.
Observe that if $\{w(1),w(2),w(3)\}$ is a geometric line in $[3]^n$, then $w(1), w(3)$ both lie in... |
He explains this by citing the fact that the square of the wave function which gives the probability density is maximum at the origin.
Not exactly.
The answer by @dsva explains why this is wrong and I'll just expand that in a minute, but first note that it's easy to see why this is wrong.
If the electron was most likel... |
Bulletin of the Belgian Mathematical Society - Simon Stevin Bull. Belg. Math. Soc. Simon Stevin Volume 14, Number 4 (2007), 641-652. Achievement of continuity of $(\varphi,\psi)$-derivations without linearity Abstract
Suppose that $\frak A$ is a $C^*$-algebra acting on a Hilbert space $\frak K$, and $\varphi, \psi$ are... |
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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... |
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... |
Review Questions Review Questions For Loops
Q09.01 Create a for loops to print out the numbers 1 to 10.
Q09.02 Create a for loop to print out the number -1 to -10 starting at -1 and ending at -10.
Q09.03 Create a for loop to print out all the letters in the word
'love'
Q09.04 Use a for loop to sum the elements in the l... |
Quasirandomness
Quasirandomness is a central concept in extremal combinatorics, and is likely to play an important role in any combinatorial proof of the density Hales-Jewett theorem. This will be particularly true if that proof is based on the density increment method or on some kind of generalization of Szemerédi's r... |
2019-09-04 12:06
Soft QCD and Central Exclusive Production at LHCb / Kucharczyk, Marcin (Polish Academy of Sciences (PL)) The LHCb detector, owing to its unique acceptance coverage $(2 < \eta < 5)$ and a precise track and vertex reconstruction, is a universal tool allowing the study of various aspects of electroweak an... |
I am looking into the method to calculate the sample size if we would want the specific coefficient significantly different from zero. I have 4 independent variables and 1 dependent variable. And I have 50 observations so far. I would like to know how many more observations do I need to get one of the coefficients sign... |
Consider the simplest possible case in which the time reversal operator $\hat{\mathrm{T}}$ is given by the operation of complex conjugation $\hat{\mathrm{K}}$.
We can view $\mathrm{T}$ is an anti-untary operator on the Hilbert space of our quantum system. In particular, we can determine its action on the momentum opera... |
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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... |
So to recap, you are starting with a covector $T_a$, and then you take was is called the "exterior derivative" to get a rank (0,2) tensor $A_{ab}$ defined by $A_{\mu \nu} = T_{\mu,\nu} - T_{\nu,\mu}$. Here the comma in the subscript denotes partial derivative so that $T_{\mu,\nu}=\dfrac{\partial}{\partial y^\nu} T_\mu$... |
I am studying an article of Berestychi-Caffarelli-Niremberg - Monotonicity for elliptic equations in unbounded Lipschitz domains, and I don't understand a convergence in the demonstration of the lemma 3.4.
Suppose that $u\in C^2(\Omega)\cap C(\overline\Omega)$, such that $$ \left\{ \begin{array}{rl} \Delta u+f(u)=0, & ... |
Voronin´s Universality Theorem (for the Riemann zeta-Function) according to Wikipedia: Let $U$ be a compact subset of the "critical half-strip" $\{s\in\mathbb{C}:\frac{1}{2}<Re(s)<1\}$ with connected complement. Let $f:U \rightarrow\mathbb{C}$ be continuous and non-vanishing on $U$ and holomorphic on $U^{int}$. Then $\... |
Here is a closely related pair of examples from operator theory, von Neumann's inequality and the theory of unitary dilations of contractions on Hilbert space, where things work for 1 or 2 variables but not for 3 or more.
In one variable, von Neumann's inequality says that if $T$ is an operator on a (complex) Hilbert s... |
Earlier we showed how unity factors can be used to express quantities in different units of the same parameter. For example, a density can be expressed in g/cm
3 or lb/ft 3. Now we will see how conversion factors representing mathematical functions, like D = m/v, can be used to transform quantities into different param... |
Difference between revisions of "Upper and lower bounds"
(→Asymptotics)
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== n=5 ==
== ... |
As dkaeae indicated in his comment, a right-moving or staying Turing machine (TM) is essentially a finite deterministic automaton (FDA). Here's a proof.
Let $M$ be such a machine, whose transition rules is in the form of $\delta(q, \gamma)=(t, \beta, d)$ where $q$ is the current state, $\gamma$ is the contents of the c... |
In mathematics, we often write relations between $a$ and $b$ in the form $aRb$. I mean this both in the sense that we write that string to represent an abstract relation, as well as using that form to write expressions with particular relations. In almost every case, these are read as "$a$ [relation] $b$." For a few ex... |
Triple integral examples Example 1
A cube has sides of length 4. Let one corner be at the origin and the adjacent corners be on the positive $x$, $y$, and $z$ axes.
If the cube's density is proportional to the distance from the xy-plane, find its mass.
Solution:The density of the cube is $f(x,y,z) = kz$ for some consta... |
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... |
Parametrized curve arc length examples Example 1
Write a parameterization for the straight-line path from the point (1,2,3) to the point (3,1,2). Find the arc length.
Solution:
The vector from (1,2,3) to (3,1,2) is
$\vc{d} = (3,1,2)-(1,2,3) = (2,-1,-1)$. We can parametrize the
line segment by
\begin{align*}
\dllp(t) = ... |
Line integrals as circulation
The vector line integral introduction explains how the line integral $\dlint$ of a vector field $\dlvf$ over an oriented curve $\dlc$ “adds up” the component of the vector field that is tangent to the curve. In this sense, the line integral measures how much the vector field is aligned wit... |
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Now showing items 1-10 of 24
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 ... |
Let $p>1.$ Define the set
$$C=\left\{\mu=\{\mu_n\}_{n=0}^\infty: \{\mu_n\}\subseteq (0,1), \;\{\mu_n\} \textrm{ decreasing, } \sum_{n=0}^\infty\mu_n(n+1)^p =1\right\}.$$
Determine $$\inf_{\mu\in C}\; \sum_{n=0}^\infty\mu_n(n+1).$$
This problem arises when we try to find a sharp upper bound on the dual norm of the deriv... |
This question is very similar to this one, but the difference is that I'm asking for a
strong deformation retraction. Notation/Definitions: (all maps are by definition continuous) A homotopy between maps $f,g\!:X\rightarrow Y$ is a map $H(x,t)\equiv H_t(x):X\!\times\!I\rightarrow Y$, $H_0\!=\!f$, $H_1\!=\!g$; denoted $... |
Search
Now showing items 1-7 of 7
The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron i... |
Learning Objectives
To convert a value reported in one unit to a corresponding value in a different unit using conversion factors.
During your studies of chemistry (and physics also), you will note that mathematical equations are used in many different applications. Many of these equations have a number of different va... |
I used Hückel's method along with a Linear Combination of Atomic Orbitals (LCAO) to calculate an estimate for the orbital energies of cyclobutadiene ($\ce{C4H4}$) and butadiene ($\ce{C4H6}$). For butadiene, I ended up with the result
$E = \alpha \pm 1.62 \beta$ and $E = \alpha \pm 0.62 \beta$,
where $\alpha$ and $\beta... |
How much weight can you put on a bike tire? What does it depend on?
closed as unclear what you're asking by Kyle Kanos, ACuriousMind♦, JamalS, John Rennie, Qmechanic♦ Apr 12 '15 at 14:50
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s ha... |
Currently I am trying to improve my knowledge of thermodynamics and I have stumbled upon the following description of a thermodynamic system in which I don't fully understand the calculation:
A container with an ideal gas is given in which a piston with a certain weight resides and the movement of the piston is frictio... |
Answer
$$\frac{\sec x}{\csc x}=\tan x$$ $\text{E}$ is the answer.
Work Step by Step
$$A=\frac{\sec x}{\csc x}$$ 2 Reciprocal Identities related to $\sec\theta$ and $\csc\theta$ state that $$\sec\theta=\frac{1}{\cos\theta}$$ $$\csc\theta=\frac{1}{\sin\theta}$$ That means we can rewrite $A$ as follows: $$A=\frac{\frac{1}... |
Basically, the problem is: For a set $S$ of positive numbers, find a minimal number $d$ that is not a divisor of any element of $S$, i.e. $\forall x \in S,\ d \nmid x$.
Denote $n = |S|$ and $C = \max(S) $. Consider the function $F(x) = $ the least prime number not dividing $x$. It is easy to see that $F(x) \leq \log x$... |
Current browse context:
astro-ph.CO
Change to browse by: Bookmark(what is this?) Astrophysics > Cosmology and Nongalactic Astrophysics Title: First results from the HAYSTAC axion search
(Submitted on 2 Jan 2018)
Abstract: The axion is a well-motivated cold dark matter (CDM) candidate first postulated to explain the abs... |
I am trying to construct a LRT to test the hypothesis $H_0: p \ge p_0$ and $H_1: p < p_0$ where $\alpha = .1$ and $p_0 = .6$ and give a critical region.
Attempt:
$\lambda(x) = \frac{"restricted" MLE}{"unrestricted" MLE} = \frac{L(\hat{\theta_0}|X)}{L(\hat{\theta}|X)}$
I am looking for $P(X \in \Re) \le \alpha$ and $P(\... |
Upper bound of $e$
$$\frac{1}{7!}\approx0.000198\ldots<0.000457\ldots\frac{1}{3^7}$$
Therefore, for $n\geq7$, $\frac{1}{n!}<\frac{1}{3^n}$
$$\begin{aligned}e&=\sum_{0\leq n\leq7}\frac{1}{n!}+\sum_{8\leq n}\frac{1}{n!}\\e&<\sum_{0\leq n\leq 7}\frac{1}{n!}+\sum_{n=8}^\infty\frac{1}{3^n}\\e&<\sum_{0\leq n\leq 7}\frac{1}{n... |
Main Page The Problem
Let [math][3]^n[/math] be the set of all length [math]n[/math] strings over the alphabet [math]1, 2, 3[/math]. A
combinatorial line is a set of three points in [math][3]^n[/math], formed by taking a string with one or more wildcards [math]x[/math] in it, e.g., [math]112x1xx3\ldots[/math], and repl... |
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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... |
Inline equations #
Inline equations are wrapped between
\(and
\).
$wrapping also works, but it is not preferred as it comes with restrictions like “there should be no whitespace between the equation and the
$delimiters”.
So
$ a=b $will not work (it will look like: $ a=b $), but
$a=b$will work (it will look like: \(a=b\... |
Dice permutations are calculated as "Permutations with repetition/replacement," which means, intuitively speaking, that if you roll 2d6, getting a 6 on the first die does not prevent you from getting a 6 on the second die. (As opposed to "Permutations without repetition/replacement." An example of that is putting putti... |
Hi i'm trying to carry out the following indefinite integral:
$$\int \frac{1}{e^{-q} - q} \, dq$$
mathematica is not helping me, and i think it is not solvable by substitution method.
any idea on how to solve it?
thanks in advance
Mathematics Stack Exchange is a question and answer site for people studying math at any ... |
For the standard Kalman filter we must assume $\boldsymbol{\theta}_t$ and $y_t$ are jointly Gaussian. So in short, we know they are joint Gaussian because we assumed it in the first place. This assumption is made for convenience in estimation and I do not see any obvious reason why you would want to relax this assumpti... |
Difference between revisions of "Main Page"
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A spreadsheet containing the latest upper and lower bounds for <math>c_n</math> can be found [http://spreadsheets.google.com/ccc?key=p5T0SktZY9DsU-uZ1tK7VEg here]. Here are the proofs of our [[upper and lower bounds]] for these con... |
Observation of electromagnetic Dalitz decays J/\psi \to P e^+e^- 2014 (English)In: PHYSICAL REVIEW D, ISSN 2470-0010, Vol. 89, no 9, article id 092008Article in journal (Refereed) Published Resource typeText Abstract [en]
Based on a sample of (225.3\pm2.8)\times 10^{6} J/\psi events collected with the BESIII detector, ... |
I have a question on page 655 of Peskin and Schroeder.
The second equation of (19.23) is discussed here. But the first equation of (19.23) is still a mystery. $$ \underset{\epsilon \to 0}{\text{symm lim}}=\left\{\frac{\epsilon^{\mu}}{\epsilon^2}\right\} =0 $$ How can we understand this? Thanks.
I have a question on pag... |
It is obvious the flux of the whole sphere is $\iiint_V 3r^2 dV = \frac{12}5\pi R^5 = 7500\pi$. I guess there's no problem you getting this.
Then we subtract the flux in the region with $|x|,|y|,|z|\ge 4$ from $7500\pi$. We notice that this will create 6 circular holes from the sphere. By symmetry the flux of all 6 hol... |
Let $(X,d)$ be metric space with $d(f,g)=\sup |f(x)-g(x)|$ where $X$ is the set of continuous function on $[0,1/2]$. Show $\Phi:X\rightarrow X$ $$\Phi(f)(x)=\int_0^x \frac{1}{1+f(t)^2}dt$$ has a unique fixed point $f(0)=0$.
b) Show that it satisfies $\frac{df}{dx}=\frac{1}{1+f(x)^2}$
My attempt:
I assumed $[0,1/2]$ is ... |
An object $C$ in an additive category admitting all filtered direct limits $\mathcal{C}$ is called "of finite type" if the canonical map $$\underrightarrow{\lim} Hom_{\mathcal{C}}(C,F(i))\to Hom_{\mathcal{C}}(C,\underrightarrow{\lim}F)$$ is injective for every $I$ directed poset for every functor $F:I\to \mathcal{C}$
I... |
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In the previous lab we have switched from the generative approach of classifier design to the discriminative one. Particularly, we have implemented the Perceptron algorithm. In this lab, we will continue examining the discriminative domain by implementing popular Support Vector Machines (SVM) classifier.
The per... |
I am confused about, what I believe, refers to passive and active transformations in QM. What I have understood so far is that the matrix elements $\langle \psi| \hat{H}|\phi\rangle$ should remain unchanged under transformations; this implies that $\hat{H} = \hat{U}^\dagger \hat{H} \hat{U}$.
On the other hand, under ce... |
Research Open Access Published: A numerical solution of a singular boundary value problem arising in boundary layer theory SpringerPlus volume 5, Article number: 198 (2016) Article metrics
650 Accesses
Abstract
In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to ... |
Difference between revisions of "Quasirandomness"
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of
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quasirandom <math>\{}</math>
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to , '' , <math>\{}</math> is .
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<math>\</math> '''' we .
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in in the density the density ]]this of , of the density .
− + − + − + −... |
This question already has an answer here:
I came across this in proving that the $\sqrt{3}$ is irrational
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This question alr... |
Spreading speeds and traveling waves of a parabolic-elliptic chemotaxis system with logistic source on $\mathbb{R}^N$
Department of Mathematics and Statistics, Auburn University, Auburn University, AL 36849, USA
$\label{IntroEq0-2}\begin{cases}u_{t}=Δ{u}-χ\nabla·(u\nabla{v})+u(1-u),{x}∈\mathbb{R}^N,\\{0}=Δ{v}-v+u,{x}∈\... |
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