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Suppose we start off with the traditional standard bivariate normal distribution:
$$\phi_2(x,y|\rho,\mu_x=0,\mu_y=0,\sigma_x=1,\sigma_y=1)=\frac{1}{2\pi\sqrt{1-\rho^2}}\exp \left(-\frac{x^2-2\rho x y + y^2}{2(1-\rho^2)}\right)$$
where the $\mu$s are the mean parameters, the $\sigma$s are the standard deviation paramete... |
Some background
I run a factor analysis of a time series $Y$ using a standard OLS model with n+1 independent variables $(F,X_1...X_n)$, where $F$ is the main factor (from an explanatory power perspective).
$X_i$ and $F$ are highly correlated ($\rho>0.8$) but on certain days $t$, $X_i(t)$ will diverge significantly from... |
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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... |
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Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
It is said that:
Abel summation and Euler summation are not comparable.
We were able to find examples of divergent series which are Euler summable but not Abel summable, for instance $$ 1-2+4-8+16-\dots$$
However, we couldn't find any example of a divergent series which is Abel summable but not Euler summable.
Do you k... |
I am stuck when it comes to finding the end value of a trig function. I have the following question:
$$ \tan^5x - 9\tan{x} = 0 $$
I worked the problem and got:
$$ \tan x = 0\\ \tan^4x-9 = 0\\ x = 0, \pi, \frac {\pi}{3}, \frac {2\pi}{3}, \frac {4\pi}{3}, \frac {5\pi}{3} $$
My book answer is $x = \frac {\pi k}{3}$ how do... |
Suppose we have a finite Egyptian fraction decomposition of a rational: $$\frac{n}{m} = \sum_{i=1}^k \frac{1}{x_i}$$ such that
(i) $x_i>0$,
(ii) $x_i \neq x_j$ for $i \neq j$, and
(iii) $\gcd(m, x_1,x_2,...x_k) = 1$.
Are their any known results concerning $\max_{i,j} |x_i-x_j|$ or maybe $\max_{i,j} |\frac{x_i}{x_j}|$?
... |
First, if $uv=0$ then $uTv=0$ a.e.: indeed, applying the hypothesis with the function $\epsilon u+\epsilon^{-1}v$ and evaluating on $\{u\neq 0\}$, we get$$0\le \epsilon^2uTu+\epsilon^{-2}vTv+uTv+vTu=\epsilon^2 uTu+uTv$$a.e. and deduce the claim (sending $\epsilon\to 0$). This gives the property $(*)$ that you showed.
I... |
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In this lab we will implement an OCR system. For simplicity we assume the texts contain only two letters: A and C, and that the letters are already well segmented into 10×10 pixel image chips. We will extract a simple feature from the image chips and use it in a bayesian decision framework to partition the image... |
One can scan the intensity $I$ of incoming linear polarized light by a linear polarizer, the outcome is the well known Malus' law.
$$I = I_0 \cos^2 \Theta$$
Deriving the dependence $I(\Theta)$ is rather easy, when going one step back to the electric field component and the relationship $I \sim |E|^2$.
Now, I was wonder... |
I'm running a Metropolis sampler (C++) and want to use the previous samples to estimate the convergence rate.
One easy to implement diagnostic I found is the Geweke diagnostic, which computes the difference between the two sample means divided by itsestimated standard error. The standard error is estimated from the spe... |
INFORMAL TREATMENT
We should remember that the notation where we condition on random variables is inaccurate, although economical, as notation. In reality we condition on the sigma-algebra that these random variables generate. In other words $E[Y\mid X]$ is meant to mean $E[Y\mid \sigma(X)]$. This remark may seem out o... |
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The K-means algorithm is the first unsupervised method we encounter in the course. The previous supervised methods worked with a set of observations and labels $\mathcal{T} = \{(\mathbf{x}_1, y_1), \ldots, (\mathbf{x}_n, y_n)\}$. The unsupervised methods use unlabeled observations $\mathcal{T} = \{\mathbf{x}_1, ... |
Damped wave equations with fast growing dissipative nonlinearities
1.
Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Caixa postal 668, 13560-970 São Carlos, São Paulo, Brazil
2.
Institute of Mathematics, Silesian University, 40-007 Katowice, Poland, Poland
u
tt$ + a u_t + A u = f(u), \ t... |
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Mon, 16 Apr 2018
I dreamed this one up in high school and I recommend it as an exercise for kids at an appropriate level.
Consider the set of all Roman numerals
$${ \text{I}, \text{II}, \text{III}, \text{IV}, \text{V}, \ldots, \text{XIII}, \text{XIV}, \text{XV}, \text{XVI}, \ldots,... |
Zzo38 is a user on Wikipedia (and other stuff as well). Also search on Google for "zzo38 OR zzo38computer"
Multi-licensed with Creative Communism I agree to multi-license my text contributions, unless otherwise stated, under Wikipedia's copyright terms and the terms of creative communism. Use it as you seem fit. Spread... |
I think the questions were about unconditional proofs or counter examples. I don't have an answer to any of those questions but I think it is still interesting to understand how the yoga of motives suggests natural answers to theses questions. Even though this may seem trivial to people familiar with the subject.
Let's... |
to solve and obtain the potential of a 1-D Hamiltonian we must solve an integral equation
$$ N(E)= A \int_{0}^{E}\frac{V^{-1}(x)}{\sqrt{E-x}}$$
fro a some constant 'A' , then my question is since the approximated espectral fucntion
$$ N(E)= <N(E)>+ \sum_{p.p.o}A_{p}e^{\frac{iS(E)}{\hbar}}+c.c $$
with $ <N(E)>$ meaning ... |
I need to find the norm of $x \in \mathbb{R}^2$ if the unit ball is defined by this inequality:
$B=(\begin{pmatrix} x_1\\ x_2 \end{pmatrix}: -a_1\leq x_1\leq a_1, -a_2\leq x_2\leq a_2 ) $.
What exactly I am asked to do? Clearly $|x_1| \leq a_1$ and $|x_2| \leq a_2$ so any norm is smaller or equal to $\sqrt{a_1^2+a_2^2}... |
I'm looking to solve the equation $$ x^2y'' + xy' - (x^2+p^2)y = 0 $$ in particular for $p = \frac12$. I've already determined the indicial equation to be $r^2 - p^2 = 0$, and so the roots are $r = \pm p$. I've also already determined a series solution (which seems to be a constant factor off, namely $a_0$, from the mo... |
So for this one I'm having trouble isolating for y. If its not possible then in the form with dy with the y variable and x with the x variable.
$$\frac{dy}{dx}-2xy=e^{x^{2}}.$$
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only tak... |
I am reading the chapter on electron-proton scattering from "Quantum Field Theory in a Nutshell". The author calculates the amplitude of the electron-proton scattering (up to the second order). The Feynman diagram used in this calculation is
We start by using the massive spin 1 boson as an exchange, and hope to get rid... |
A linear model has t-distributed noise $$ Y= bX + \epsilon $$ where $\epsilon \sim t(0, \sigma^2, df)$, with mean 0, variance $\sigma^2$ and dof $df$.
Given an independent sample $(x_i, y_i), i=1, \dots, n$, suppose we already have estimates of $b, \sigma^2, df$. How would you estimate a $1-\alpha$ prediction interval ... |
In some sense the empty set ($\emptyset$) and the global set of all sets ($G$) are the ends of the universe of mathematical objects. The world which $ZFC$ describes has an end from the bottom and is endless from the top. Even in a straight forward way one can find an equiconsistent theory (respect to $ZFC$) which its w... |
Yes, it is possible.
Consider the graph $\Gamma$ of$$z=\phi\left(\sqrt{x^2+y^2}\right),$$ where $\phi\colon\mathbb R\to \mathbb R$ is a convex even function with $\phi(0)=0$.With its intrinsic metric, $\Gamma$ forms an Alexandrov space.
Note that the curve $\gamma$ on the graph described by $y=0$ is formed by two geode... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
The problem is to find a line that passes through $p$ and has all the other points in $S$ on one side. This is a two-dimensional linear-programming problem, so it can be solved in $O(n)$ time using textbook geometric algorithms.But let me describe a self-contained solution.
To simplify notation, translate all the point... |
Determining the impedance of this circuit requires the implementation of the right tool. If you use brute-force analysis, simply considering series-parallel combination, you may quickly end-up with an algebraic paralysis to quote Dr. Middlebrook who forged the extra-element theorem or EET from which the fast analytical... |
So in a simple way we can define the electrostatic field considering the force exerted by a point charge on a unit charge. In other words we can define the electric field as the
force per unit charge.
To detect an electric field of a charge q, we can introduce a test charge q
0 and measure the force acting on it.
\(\ov... |
This is a confusing question because, while solubilities
can be reported in mL/L, there can be ambiguity when choosing a pressure during conversion to this unit, for instance using the following equation to convert from molarity $c$ to volume/volume units:
$$ \rho = \frac{cRT}{p}$$
In this online data page, for instanc... |
TL;DR: The $\ce{O-O}$ and $\ce{S-S}$ bonds, such as those in $\ce{O2^2-}$ and $\ce{S2^2-}$, are derived from $\sigma$-type overlap. However, because the $\pi$ and $\pi^*$ MOs are also filled, the $\pi$-type overlap also affects the strength of the bond, although the bond order is unaffected. Bond strengths normally dec... |
I've started learning some quantum physics and one often encounters special functions (like Legendre polynomials, Laguerre polynomials, Bessel functions, ...). Many calculations with these functions are immensely simplified (or maybe only made possible?) by making use of a generating function.
My physics book unfortuna... |
Other ways of writing Green's theorem
In the introductory page on Green's theorem, we wrote Green's theorem as \begin{align*} \dlint = \iint_\dlr (\curl \dlvf) \cdot \vc{k} \, dA \end{align*} or \begin{align*} \dlint = \iint_\dlr \left( \pdiff{\dlvfc_2}{x} - \pdiff{\dlvfc_1}{y}\right)dA, \end{align*} where $\dlvf(x,y) ... |
I am a bit disturbed lately since I don't know the answer this basic problem.
Say we have a standard isotropic antenna with some fixed parameters (load impedance, etc), and we feed this antenna with a sinusoidal current of the form: \begin{equation} I(t) = Acos(2\pi f_{c}t) \end{equation} where $f_{c}$ is the carrier f... |
The common understanding is that, setting air resistance aside, all objects dropped to Earth fall at the same rate. This is often demonstrated through the thought experiment of cutting a large object in half. The halves clearly can't then fall more slowly just by being sliced in two.
However, I believe the answer is th... |
Why is Power Analysis Important? Section
Consider a research experiment where the
p-value computed from the data was 0.12. As a result, one would fail to reject the null hypothesis because this p-value is larger than \(\alpha\) = 0.05. However, there still exist two possible cases for which we failed to reject the null... |
Just as in your previous question, there is no analytic solution to that problem. You're required to find some quick approximation that gives you a useful result. Rewrite the last equation as
$$p_c=\sqrt[9]{\frac{2.79\cdot 10^{-8}}{\binom{204}{9}}}\frac{1}{(1-p_c)^{195/9}}\tag{1}$$
If we boldly assume that $p_c\ll 1$ h... |
Rocky Mountain Journal of Mathematics Rocky Mountain J. Math. Volume 45, Number 2 (2015), 457-474. Nontrivial periodic solutions of second order singular damped dynamical systems Abstract
Assuming that the linear equation $x'' + h(t)x' + a(t)x = 0$ has a positive Green's function, we study the existence of nontrivial p... |
Assume I have a $m\times n$ Transition Matrix $A$ with $m$ different observations and $n$ represents a discrete state space. Each column counts the frequency that state $j\in [1...n]$ was visited from state $i\in [1,...,m]$. In reality the "states" are no integer numbers, but a discretized real valued variable. I need ... |
The goal of applying Valence Bond Theory to water is to describe the bonding in \(H_2O\) and account for its structure (i.e., appropriate bond angle and two lone pairs predicted from VSEPR theory).
The ground state electronic configuration of atomic oxygen atom is \(1s^2\,2s^2\,2p_x^2\,2p_y^1 \, 2p_z^1\) and of course ... |
I have a
markov chain with $Q(u,v)$ as transition probability matrix and $\pi(u)$ as stationary distribution defined on state space $\Omega$. The dimension of matrix $Q$ is $nxn$ and vector $\pi$ is $1xn$.
I need to construct a
vorticity matrix $\Gamma (u,v)$ of dimension $nxn$ which has below properties
$\Gamma$ is sk... |
2019-10-09 06:01
HiRadMat: A facility beyond the realms of materials testing / Harden, Fiona (CERN) ; Bouvard, Aymeric (CERN) ; Charitonidis, Nikolaos (CERN) ; Kadi, Yacine (CERN)/HiRadMat experiments and facility support teams The ever-expanding requirements of high-power targets and accelerator equipment has highligh... |
The Annals of Statistics Ann. Statist. Volume 11, Number 3 (1983), 793-803. Second Order Efficiency of Minimum Contrast Estimators in a Curved Exponential Family Abstract
This paper presents a sufficient condition for second order efficiency of an estimator. The condition is easily checked in the case of minimum contra... |
Frege did not see himself as regimenting existing practice. He explicitly says that he developed Begriffsschrift (concept-script) because he was dissatisfied with the vagueness of natural language for the
conceptual analysis of mathematics, the purpose of which was not to service practice but to remake it after exposin... |
If your system is of the form
$$\dot{x} = A\,x + B\,u + f \\y = C\,x + D\,u + g \tag{1}$$
with $f$ and $g$ constant vectors, then you can do a coordinate transformation $z=x+\alpha$ and $v=u+\beta$ with $\alpha$ and $\beta$ constant vectors which satisfies
$$\begin{bmatrix}A & B \\ C & D\end{bmatrix}\begin{bmatrix}\alp... |
I understand that I need at least 0.7V applied to the base to turn on
the base emitter junction,
Not exactly. A base-emitter junction can be considered forward-biased with larger or smaller magnitudes than \$700\:\text{mV}\$. It's just that the collector current (speaking now about common small-signal BJTs) will change... |
The momentum decomposition you wrote is valid only for a scalar (spinless), real field, satisfying the Klein-Gordon equation.
When considering a field with spin, like a spin-$1/2$ field satisfying the Dirac equation, you must include the
polarization vectors, obtaining something of the form$$ \psi_\alpha(x) = \sum_{\te... |
Definition:Prime Ideal of Ring Contents Definition
Let $R$ be a ring.
A prime ideal of $R$ is a proper ideal $P$ such that: $I \circ J \subseteq P \implies I \subseteq P \text { or } J \subseteq P$
for any ideals $I$ and $J$ of $R$.
A
prime ideal of $R$ is a proper ideal $P$ such that: $\forall a, b \in R : a \circ b \... |
In module one (1), we demonstrated the data preparation phase of time series analysis. In module two (2), we described few steps to calculate numerous summary statistics and verify the significance of their values.
In this module, we will walk you through time series smoothing in Excel using NumXL functions and tools. ... |
This post is the third in a series explaining Basic Time Series Analysis. Click the link to check out the first post which focused on stationarity versus non-stationarity, and to find a list of other topics covered. As a reminder, this post is intended to be a very applied example of how use certain tests and models in... |
: Brief introduction
Let $n \in \mathbb N$. The non-equality function, denoted $ NE : \{0,1\}^n \times \{0,1\}^n \to \{0,1\} $ is defined as follows:
\begin{align} \forall x,y\in \{0,1\}^n \;\;\; NE(x,y) = \begin{cases}1 & x\neq y \\ 0 & x = y\end{cases} \end{align}
In the setting of two party communication complexity,... |
The Physics of Scattering Experiments
The physics of scattering can be understood according to the Huygens-Fresnel principle of interference. Incoming radiation interacts with scatterers in the specimen (electrons in case of X-rays and atomic nuclei in case of neutrons), causing these to emit secondary, nearly spherica... |
Understanding the scattering results
The direct result of a small-angle scattering measurement is the scattering pattern, i.e. the two-dimensional image recorded by the position sensitive detector. This can be considered as a matrix of positive integer numbers, each matrix element corresponding to an image element of t... |
The local escape velocity (relative to a ZAMO) of an angular momentum free test particle in the vicinity of a naked singularity with spin a and charge ℧ can be derived with the Kerr Newman metric by setting the total conserved specific energy of the test particle (in natural units of G=M=c=k
c=1)
$${\rm E} = g_{\rm t t... |
Determinant The determinant of a square matrix $A = (a_{ij})$ of order $n$ over a commutative associative ring $R$ with unit 1 isthe element of $R$ equal to the sum of all terms of the form
$$(-1)^k a_{1i_1}\cdots a_{ni_n},$$ where $i_1,\dots,i_n$ is a permutation of the numbers $1,\dots,n$ and $k$ is the number of inv... |
Updated 07.11
We can chose the model to discuss the problem and so let us chose:
Model: Newtonian mechanics/Newtonian gravity, with the Universe filled with uniformly dense matter, interacting only gravitationally (in cosmology this called “dust matter”), and at the initial time of our spaceship journey all this matter... |
Consider two independent discrete random variables $y_1$ and $y_2$, both distributed with a Beta-Binomial distribution, with different number of successes $n_1$ and $n_2$ but the same parameters $a$ and $b$
$ p(y_1|n_1,a,b) = {n_1 \choose y_1} \dfrac{B(y_1 + a,n_1 -y_1 +b)}{B(a,b)} $
$ p(y_2|n_2,a,b) = {n_2 \choose y_2... |
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Flux quanta, magnetic field lines, merging – some sub-microscale relations of interest in space plasma physics
Tr... |
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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... |
A lot of what is written in the question is not correct.
The URCA process would be cycles of beta decay followed by inverse beta decay as follows.
$$n \rightarrow p + e + \bar{\nu_e}$$$$ p + e \rightarrow n + \nu_e$$
The neutrinos escape from the star, carrying away energy.
The URCA process is very important during the... |
Research Open Access Published: Neimark-Sacker bifurcation of a two-dimensional discrete-time predator-prey model SpringerPlus volume 5, Article number: 126 (2016) Article metrics
1241 Accesses
4 Citations
Abstract
In this paper, we study the dynamics and bifurcation of a two-dimensional discrete-time predator-prey mod... |
In real life, we come across many such incidents where a change in one quantity leads to the change in another quantity. For example, if the speed of a car is increased then the time taken to cover the same distance will decrease. Let’s take one more example if we want that the construction of a building to finish soon... |
Let $G$ be a Lie group and $V$ be a vector space. Let $\rho_{l} : G \times V \to V$ be a left representation and $\rho_r:V \times G \to V$ be a right representation which
commutes with $\rho_l$ in the sense that $\rho_l(g_1 , \rho_r(v , g_2) ) = \rho_r( \rho_l(g_1, v) , g_2)$. Then the group multiplication $(g_1,v_1) \... |
Uniqueness for Neumann problems for nonlinear elliptic equations
1.
Dipartimento di Ingegneria, Università degli Studi di Napoli Parthenope, Centro Direzionale, Isola C4 80143 Napoli, Italy
2.
Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS-Université de Rouen, Avenue de l'Université, BP.12 76801 Saint-Étienn... |
Find the value(s) of positive integer $n$ such that $n² + 19n + 48$ is a perfect square.
I factorised it to $(n+3)(n+16)$, but that gives negative integer answers $-3$ and $-16$. What do I do?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fie... |
I just had time to go over this more carefully. I know this is 1 year and a half old, but it's still an interesting (and unanswered) question.
Here is a toy example of my approach to solving this using a regularized regression estimator like Lasso. The only important parameters in this approach are:
min_lag ($L_{min} =... |
what is the interpretation of $|\langle AB \rangle|$ ? since $|\langle AB \rangle|^2 = \langle AB \rangle [\langle AB \rangle]^\dagger$ , could $|\langle AB \rangle| = \sqrt(|\langle AB \rangle|^2)$ ?
PS. : feel free to correct me
Physics Stack Exchange is a question and answer site for active researchers, academics an... |
I am aware that I am replying to an old question that has been satisfactorily answered, but I think it might be worth while pointing out, for the completeness of MathOverflow, that the question is discussed (in slightly greater generality, and with an example) as corollary 4.4.5 in the book
An Introduction to Gröbner B... |
Class-A amplifier design overview
After watching those two videos,
and Single transistor, 1W , I had to illustrate a slightly more sane design approach. To start out, here's the basic idea about how to drive a speaker (without having to find and use a flux-limiting, gapped, audio transformer -- which you will definitel... |
The Bessel Function $J_n(x)$ is defined, for a natural number $n$ and real number x, as
$J_n(x) = \frac{1}{2\pi}\int_0^{2\pi}\cos(n\theta-x\sin\theta)d\theta.$
By using contour integration with integrand $z^{n-1}\exp(\frac{-xz}{2})\exp(\frac{x}{2z})$, or otherwise, show that
$J_n(x)=\sum_{\substack{k=0}}^\infty\frac{(-... |
Fujimura's problem
Let [math]\overline{c}^\mu_n[/math] the largest subset of the triangular grid
[math]\Delta_n := \{ (a,b,c) \in {\Bbb Z}_+^3: a+b+c=n \}[/math]
which contains no equilateral triangles [math](a+r,b,c), (a,b+r,c), (a,b,c+r)[/math] with [math]r \gt 0[/math]; call such sets
triangle-free. (It is an intere... |
I am trying to understand the solution to the following question.
At which $c\in\mathbb{R}$ is the function $f:\mathbb{R}\rightarrow\mathbb{R}$ defined by $$f(x)=\begin{cases}x&\text{if $x$ is rational,}\\1-x&\text{if $x$ is irrational,}\end{cases}$$ continuous?
The solution states that the only answer is $c=1/2$, but ... |
Let $\ M'\ M''\ $ be simply-connected Hausdorff compact manifolds (possibly with boundary for another variant of the question). Let $\ f:M'\rightarrow M''\ $ be a continuous function which induces an isomorphism of the cohomological rings. Does there exist a continuous function $\ g:M''\rightarrow M'\ $ which induces t... |
The atmosphere of the Earth is mainly composed of nitrogen (N
2, 78%) and oxygen (O 2, 21%) molecules, which together make up about 99% of its total volume. The remaining 1% contains all sorts of other stuff like argon, water and carbon dioxide, but let's ignore those for now.
As you probably know, the oxygen we breath... |
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Thu, 29 Jan 2009
A simple trigonometric identity
Here I put
A at (0,0), B at (4,0), and 1 at(2,2). This is clear enough, but I wished that it were more nearlyequilateral.
So that night as I was waiting to fall asleep, I thought about the problem of finding lattice points that are a... |
Let's say that we have one area and in this area there are designated 5 points, $a, b, c, d, e.$ For these 5 points we count the number of a specific feature. We capture the values for two different days, for example:
$\begin{array}[t]{llllll|l} \text{date} & a & b & c & d & e & \text{sum}\\\hline \text{first day}& 10 ... |
Let $G$ be a semisimple algebraic group over an algebraically closed field of arbitrary characteristic. (I'm most interested in the positive characteristic case). Let $B \subseteq G$ be a Borel subgroup. Let $\cal T$ denote the tangent bundle of the flag variety $G/B$ and let $\pi : {\cal T} \to G/B$ be the projection.... |
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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... |
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In this chapter we learned about left and right adjoints, and about joins and meets. At first they seemed like two rather different pairs of concepts. But then we learned some deep relationships between them. Briefly:
Left adjoints ... |
Tsukuba Journal of Mathematics Tsukuba J. Math. Volume 20, Number 2 (1996), 471-478. Proper n-homotopy equivalences of locally compact polyhedra Abstract
We prove the following theorem which is a locally compact analogue of results of $S$. Ferry and the author. Theorem. Let $f:X\rightarrow Y$ be a proper map between fi... |
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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 ... |
Let $R$ be a finite ring with unity. Prove that every nonzero element of $R$ is either a unit or a zero-divisor.
In a finite commutative ring with unity, every element is either a unit or a zero-divisor. Indeed, let $a\in R$ and consider the map on $R$ given by $x \mapsto ax$. If this map is injective then it has to be... |
Function examples
A function is a mapping from a set of inputs (the domain) to a set of possible outputs (the codomain). The definition of a function is based on a set of ordered pairs, where the first element in each pair is from the domain and the second is from the codomain. But, a metaphor that makes the idea of a ... |
Consider a heteroskedastic model of the form, $y_i|x_i \sim \mathcal{N}\left(x_i, \text{exp}\{\boldsymbol\beta^\top\boldsymbol{x}\}\right)$ where $\boldsymbol{\beta}=\left[\beta_0,\beta_1\right]$ and $\boldsymbol{x}=\left[1,x_i\right]$. $x_i$ and $\boldsymbol{\beta}$ must be estimated from the data.
We set a multivaria... |
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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... |
What is the importance of eigenvalues/eigenvectors?
Short Answer Eigenvectors make understanding linear transformations easy. They are the "axes" (directions) along which a linear transformation acts simply by "stretching/compressing" and/or "flipping"; eigenvalues give you the factors by which this compression occurs.... |
User:Nikita2 Pages of which I am contributing and watching
Analytic function | Cauchy criterion | Cauchy integral | Condition number | Continuous function | D'Alembert criterion (convergence of series) | Dedekind criterion (convergence of series) | Derivative | Dini theorem | Dirichlet-function | Ermakov convergence cr... |
The Guinier approximation
The study of the shape and size distribution of nanoparticles is a traditional field of application of SAXS. The scattering intensity of a spherical particle of radius $R$ and homogeneous scattering length density $\Delta\rho$ inside it, for example, can be calculated as
$$I_\mathrm{sphere}(q)... |
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In this chapter we learned about left and right adjoints, and about joins and meets. At first they seemed like two rather different pairs of concepts. But then we learned some deep relationships between them. Briefly:
Left adjoints ... |
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''derived numbers''
''derived numbers''
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A concept in the theory of functions of a real variable. The upper right-hand Dini derivative
<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d032/d032530/d0325301.png" /> is defined to be the limes superior of the quot... |
Bragg peaks
If some sort of periodicity on the resolvable size range is present in the sample under investigation, usually many orders of relatively sharp peaks manifest themselves in the scattering pattern. This can be understood as a special case of the scattering, the so-called Bragg-reflection principle.
According ... |
Answer
To feed 200 people we need: 35.7 lb of meat, 50 lb of potatoes, and 21.4 lb of carrots.
Work Step by Step
We know that 25 lb of meat fed 140 people. To find out how much meat is needed to feed 200 people, we set up a proportion: $\displaystyle \frac{25~lb}{140~people}=\frac{x}{200~people}$ Cross-multiply: $25*20... |
Here is a much simpler proof from
Special Functions and Their Applications by N. N. Lebedev.
We begin with Legendre's differential equation\begin{equation}[(1-x^{2})P^{\prime}_{n}(x)]^{\prime} +n(n+1)P_{n}(x) = 0,\quad n \in \mathbb{Z}_{0}^{+}\label{eq:lp1}\tag{1}\end{equation}
The first step is to multiple equation \e... |
Suppose $X_1$ and $X_2$ are independent $N(0,1)$ variables.
Define $$Y_1=X_1\,\text{sign}(X_2)\quad,\quad Y_2=X_2\,\text{sign}(X_1)$$
I have to show that $(Y_1,Y_2)$ is not bivariate normal and find the correlation between $Y_1$ and $Y_2$.
It is easy to see that both $Y_1$ and $Y_2$ are themselves univariate normal.
An... |
I understand that in general the wave function can take complex numbers, however when talking about combining atomic orbitals to form molecular orbitals we talk about the phase of the orbital being positive or negative to create constructive or destructive interference. It seems as if we have lost the aspect of the wav... |
For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
gmc_nxtman Posts: 1147 Joined: May 26th, 2015, 7:20 pm Kazyan wrote:
Component found in a CatForce result:
Code: Select all
x = 42, y = 67, rule = LifeHistory
A$.2A$2A5$7.A$8.2A$7.2A19$24.2A$24.2A2$39.A$37.A3.A$3... |
Jacob, Thomas K and Mishra, Saurabh and Waseda, Yoshio (2000)
Refinement of thermodynamic properties of $ReO_2$. In: Thermochimica Acta, 348 (1-2). pp. 61-68.
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Jacob_[publication_year]_Thermochimica-Acta.pdf
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Abstract
The standard Gibbs energy of f... |
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Abstract: We study the force generation by a set of parallel actin fil... |
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Sun, 22 Mar 2015
Shortly after I posted A public service announcement about contracts Steve Bogart asked me on on Twitter for examples of dealbreaker clauses. Some general types I thought of immediately were:
A couple of recent specific examples:
Sat, 21 Mar 2015
E... |
In this article I’m about to present the process of decoding previously recorded FSK transmission with the use of Python, NumPy and SciPy.
The data was gathered using SDR# software and it is stored as a wave file that contains all the IQ baseband data @ 2.4Msps
The complete source code for this project is available her... |
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