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Women’s Health Survey: One-Sample Hotelling's T-Square Section
In 1985, the USDA commissioned a study of women’s nutrition. Nutrient intake was measured for a random sample of 737 women aged 25-50 years. Five nutritional components were measured: calcium, iron, protein, vitamin A and vitamin C. In previous analyses of ... |
I came across John Duffield Quantum Computing SE via this hot question. I was curious to see an account with 1 reputation and a question with hundreds of upvotes.It turned out that the reason why he has so little reputation despite a massively popular question is that he was suspended.May I ...
@Nelimee Do we need to m... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
This is a hard problem for me to word in the title, so I'll try to do better now. Consider the following "game":
You are sitting in a room beside a table. In the middle of the table there exists a box containing a very large sum of money. The box will only open if you've waited long enough (the time to wait is a random... |
Let $p_k$ be the $k^{th}$ prime number.
Find the least $n$ for which $(p_1^2+1)(p_2^2+1) \cdots (p_n^2+1)$ is divisible by $10^6$.
I have no idea where to start on this problem. Any help would be appreciated.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professional... |
I am interested in the following constrained optimization problem:
$$\text{Minimize }J_p(F, G) = \int_0^1 \left(\frac{F}{f} + \frac{1-G}{g}\right)^{-1} dx.$$
over a pair of cumulative distributions functions $F$ and $G$, with $f := F'$ and $g := G'$, subject to the following constraints:
Their Jensen Shannon divergence... |
In the univariate case, the data can often be arranged in a table as shown in the table below:
1 2 \(\dots\) g 1 \(Y_{11}\) \(Y_{21}\) \(\dots\) \(Y_{g_1}\) Subjects 2 \(Y_{12}\) \(Y_{22}\) \(\dots\) \(Y_{g_2}\) \(\vdots\) \(\vdots\) \(\vdots\) \(\vdots\) \(n_i\) \(Y_{1n_1}\) \(Y_{2n_2}\) \(\dots\) \(Y_{gn_g}\)
The col... |
Multi-output Matrix T Process
Summary
The multi-output matrix T regression model was first described by Conti and O' Hagan in their paper on Bayesian emulation of multi-output computer codes. It has been available in the
dynaml.models.stp package of the
dynaml-core module since v1.4.2.
Formulation¶
The model starts fro... |
Learning Objectives
By the end of this section, you will be able to:
Describe how quasars were discovered Explain how astronomers determined that quasars are at the distances implied by their redshifts Justify the statement that the enormous amount of energy produced by quasars is generated in a very small volume of sp... |
Limit on num_vars?
Post Reply
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1of 1
I have a strange issue, I have added four new parameters to cosmomc putting them in parameter positions 14, 15 ,16 and 17. This has moved \Omega_\Lambda, Age/Gyr, \Omega_m, \sigma_8, z_{re} and H_0 to parameter positions 18, 19, 20, 21, 22, and 24.
The problem is when ... |
Example 7-7: Spouse Data (Question 1) Section Question 1: Do the husbands respond to the questions in the same way as their wives?
Before considering the multivariate case let's review the univariate approach to answering this question. In this case we will compare the responses to a single question.
Univariate Paired ... |
Example 8-1 Pottery Data (MANOVA) Section
Before carrying out a MANOVA, first check the model assumptions:
The data from group ihas common mean vector \(\boldsymbol{\mu}_{i}\) The data from all groups have common variance-covariance matrix \(\Sigma\). Independence:The subjects are independently sampled. Normality:The d... |
Example 8-3: Pottery Data (MANOVA) Section
After we have assessed the assumptions, our next step is to proceed with the MANOVA.
Using SAS
This may be carried out using the Pottery SAS Program below.
Download the SAS Program here: pottery.sasView the video explanation of the SAS code.
Using Minitab
View the video below ... |
While attempting to evaluate the integral $\int_{0}^{\frac{\pi}{2}}\sinh^{-1}{\left(\sqrt{\sin{x}}\right)}\,\mathrm{d}x$, I stumbled upon the following representation for a related integral in terms of hypergeometric functions:
$$\small{\int_{0}^{1}\frac{x\sinh^{-1}{x}}{\sqrt{1-x^4}}\,\mathrm{d}x\stackrel{?}{=}\frac{\G... |
I was trying to prove this trigonometric identity, it looks like using the elementary relations should be enough, but I still can't find how:
$$\frac{1}{2}\sin^2 a \ \sin^2 b + \cos^2a \ \cos^2 b = \frac{1}{3} + \frac{2}{3} \biggl( \frac{3}{2}\cos^2 a - \frac{1}{2} \biggr)\biggl( \frac{3}{2}\cos^2 b - \frac{1}{2}\biggr... |
I have a dream. I want my maths writing to magically be made into a
.tex file so that I can edit it. I want to write my papers, my exams, my lecture notes,
everything, by hand, then wave a magic wand to convert them to something pretty (and editable!).
For example, could I scan in my writing and run some program which ... |
Statistics Theory New submissions 1-13]
[ showing up to 2000 entries per page: fewer | more ]
New submissions for Mon, 23 Sep 19 [1] arXiv:1909.09302 [pdf, ps, other] Title: Robust Estimation and Shrinkage in Ultrahigh Dimensional Expectile Regression with Heavy Tails and Variance HeterogeneitySubjects: Statistics Theo... |
To prove that some decision problem $P$ is NP-complete, my understanding is that it suffices to show that the problem is in NP [...] and to demonstrate that some known NP-complete problem $Q$ can be reduced to $P$ [...] by
some kind of appropriate reduction in polynomial time. We can then say that we can solve $Q$ in p... |
The following shows two examples to construct orthogonal contrasts. In each example, we consider balanced data; that is, there are equal numbers of observations in each group.
Example 8-6: Section
In some cases, it is possible to draw a tree diagram illustrating the hypothesized relationships among the treatments. In t... |
I'm trying to understand how people actually measure decay constants that are discussed in meson decays. As a concrete example lets consider the pion decay constant. The amplitude for $\pi ^-$ decay is given by,
\begin{equation}
\big\langle 0 | T \exp \left[ i \int \,d^4x {\cal H} \right] | \pi ^- ( p _\pi ) \big\rangl... |
ok, suppose we have the set $U_1=[a,\frac{a+b}{2}) \cup (\frac{a+2}{2},b]$ where $a,b$ are rational. It is easy to see that there exists a countable cover which consists of intervals that converges towards, a,b and $\frac{a+b}{2}$. Therefore $U_1$ is not compact. Now we can construct $U_2$ by taking the midpoint of eac... |
Lesson 4: Confidence Intervals Objectives Construct and interpret sampling distributions using StatKey Explain the general form of a confidence interval Interpret a confidence interval Explain the process of bootstrapping Construct bootstrap confidence intervals using the standard error method Construct bootstrap confi... |
Generalized Least Squares
Summary
The
Generalized Least Squares model is a regression formulation which does not assume that the model errors/residuals are independent of each other. Rather it borrows from the Gaussian Process paradigm and assigns a covariance structure to the model residuals.
Warning
The nomenclature
... |
Recently I asked a question regarding how to mix a glossy and diffuse shader in my path tracer: Mix shader looks wrong on my path tracer. I thought it was incorrect, but a comparison between mine and Blender's seems correct. However, now I am lost in how I would approach making the surface of a mirror look rough as thi... |
I have a question from the paper "More Abelian Dualities in 2+1 Dimensions".
https://arxiv.org/pdf/1609.04012.pdf
On page 3, it says that we flow towards IR by sending $\alpha\rightarrow\infty$ and tuning the mass to zero.
$$S[\phi ;A]=\int d^{3}x |(\partial_{\mu}-iA_{\mu})\phi|^{2}-\alpha|\phi|^{4}.$$ My question is t... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
A cloud has relative humidity of 100% or more. Is it correct to say that the mixing ratio of a cloud is undefined? My reasoning is that dry air in a cloud is negligible therefore $w = \frac{x g}{ 0 kg}$
No, it is not undefined.
A relative humidity of 100% refers to cases in which the atmosphere holds as much water, as ... |
Q1 What are the values of x for which \[\frac {x^3 + 3x^2 + 2x} { x^2 + 5x +6} = 0 \]
Q2 Let x be the required Arithmetic Mean, then 8, x, 16 form three successive terms in the Aritmetic Progression. Find x.
Q3 The sum of the first and third terms of a Geometric progression is \[6\frac{1}{2}\] and the sum of the second... |
One reason I call this site a “blag” and not a “blog” is that I’m always late.
For example, I’m finally typing up the group-theory homework assignment which Ben gave last Monday (and which will be due next Monday). During our seminar over in BU territory, we discussed the relations among the Lie groups
SU(2) and SO(3) ... |
PCTeX Talk Discussions on TeX, LaTeX, fonts, and typesetting
Author Message zedler Joined: 03 Mar 2006 Posts: 15
Posted: Mon Mar 27, 2006 11:53 am Post subject: spacing of mathrm Hello,
\documentclass{book}
\usepackage{times,mtpro2}
\begin{document}
$(\mathrm j$
\end{document}
gives touching glyphs.
Michael Michael Spi... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
By default, the eye an the projection reference point PRP are in (0,0,0). I can change the eye position with gluLookAt(), but how can I change the PRP (i.e., the convergence position for a set of parallel lines) for a perspective projection in OpenGL?
Eye position, projection reference point PRP, camera center, or proj... |
Decomposing the language $L$ into union or intersection of two simplerlanguages is useful to prove that L is regular, but it will not helpyou (in general) to prove that $L$ is not regular. The union orintersection of two non regular languages can be regular.
However, you can use these closure properties differently, to... |
The underlying philosophy of constructivism in mathematics is that in order to prove that something exists, we need to "find" or "construct" it.
In NBG (von Neumann–Bernays–Gödel axiomatic set theory) one can only quantify over sets, as in ZFC (where classes can also be informally treated specifying formulas, for examp... |
"Abstract: We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, insta... |
This question is in reference to an answer I posted here yesterday.
In it I derived the partition function for a harmonic oscillator as follows
$$q = \sum_{j}e^{-\frac{\epsilon_j}{kT}}$$
For the harmonic, oscillator $\epsilon_j = (\frac{1}{2}+j)\hbar \omega$ for $j \in \{ 0,1,2.. \}$
Note that $\epsilon_0 \neq 0$ there... |
I want to find the increasing and decreasing intervals of a quadratic equation
algebraically without calculus.
The truth is I'm teaching a middle school student and I don't want to use the drawing of the graph to solve this question.
Mathematics Stack Exchange is a question and answer site for people studying math at a... |
The discovery of decimal arithmetic
The discovery of decimal arithmetic in ancient India, together with the well-known schemes for long multiplication and long division, surely must rank as one of the most important discoveries in the history of science. The date of this discovery, by an unknown Indian mathematician or... |
I am really confused if $\alpha_1=(e^{\pi/2},1)$ and $\alpha_2=(\sqrt[3]{110},1)$ are linearly independent or linearly dependent in $\mathbb{R}^2$. (Hoffman and Kunze, page no. $48$.)
Consider $c_1\alpha_1+c_2\alpha_2=0$. Then $c_1(e^{\pi/2},1)+c_2(\sqrt[3]{110},1)=(0,0)$. This gives two equations: \begin{align*} c_1e^... |
The answer is
No.
The keyword is that the
Coulomb force (which hasn't been spelled out), the main forces binding the atoms together in the lattice of solid-state or condensed matter for the long pole, supposed to have retarded time to transmit the force/information between the atoms.
Again,
Coulomb force, is part of El... |
L^2 Curvature Bounds on Manifolds with Bounded Ricci Curvature Speaker(s):Aaron Naber (Northwestern University) Location:MSRI: Simons Auditorium Tags/Keywords
algebraic geometry and GAGA
complex differential geometry
mathematical physics
Kahler metric
mirror symmetry
curvature estimates
Ricci curvature lower bounds
geo... |
Quadratic Equations Practise solving quadratic equations algebraically with this self-marking exercise.
This is level 4; Three terms where the squared term has a coefficient other than one and the expression factorises. You can earn a trophy if you get at least 7 correct.
Instructions
Try your best to answer the questi... |
"Abstract: We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, insta... |
Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes this energy is obvious, such as in the warmth of the summer Sun. Other times, it is subtle, such as the unfelt energy of gamma rays, which can destroy living cells.
Electromagnetic waves bring energy into a system by virtue o... |
Young's Modules is defined as,
$Y = \frac{\sigma}{\epsilon}$
where $\sigma$ is the strain defined as $\sigma = F/A$ and $\epsilon$ is the stress defined as $\epsilon = \frac{\Delta L}{L_0}$.
In this case we require the stress, thus re-arranging the first equation gives,
$\sigma = \epsilon Y$
After plugging in the defin... |
Quadratic Equations Practise solving quadratic equations algebraically with this self-marking exercise.
This is level 5; The difference between two squares. You can earn a trophy if you get at least 7 correct.
Instructions
Try your best to answer the questions above. Type your answers into the boxes provided leaving no... |
Applied mathematics is one which is used in day-to-day life, in solving troubles (problems) or in business purposes. Let me write an example:
George had some money. He gave 14 Dollars to Matthew. Now he has 27 dollars. How much money had he?
If you are familiar with day-to-day calculations – you must say that
George ha... |
This module shows how the HP 10bII+ financial calculator can be used to price a call option with the Black-Scholes (1973) model. A key feature of this calculator is the ability to return the normal lower tail probability for the value z. The alternative is often a probability table.
The HP 10bII+ financial calculator i... |
A hypothetical diatomic molecule has a binding length of $0.8860 nm$. When the molecule makes a rotational transition from $l = 2$ to the next lower energy level, a photon is released with $\lambda_r = 1403 \mu m$. At a vibration transition to a lower energy state, a photon is released with $\lambda_v = 4.844 \mu m$. D... |
It's a little unclear exactly what you mean by "contains information about Halting of some turing machines", but under every reasonable interpretation of this I can think of the answer is "yes."
For instance, consider the following:
Definition. A set $X$ has halting information if there is some computable set $C$ of (i... |
@egreg It does this "I just need to make use of the standard hyphenation function of LaTeX, except "behind the scenes", without actually typesetting anything." (if not typesetting includes typesetting in a hidden box) it doesn't address the use case that he said he wanted that for
@JosephWright ah yes, unlike the hyphe... |
The Probability Density Function(PDF) is the probability function which is represented for the density of a continuous random variable lying between a certain range of values. The probability Density function is defined by the formula,
Questions on the probability distribution function Question 1:
The pdf of a distribu... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
Repeated Measures Design
Repeated measures analysis of variance (rANOVA) is one of the most commonly used statistical approaches to repeated measures designs.
Learning Objectives
Evaluate the significance of repeated measures design given its advantages and disadvantages
Key Takeaways Key Points Repeated measures desig... |
Firstly, we must begin by finding out the surface gravity of such a planet as surface gravity is not dependent only on mass but distance from the center, hence the planet's radius, because $$g=G\frac{M}{R^2}$$
$g$ = surface,
$G$ = Gravitational Constant($\approx 6.67408 × 10^{-11}\,m^3\,kg^{-1}\,s^{-2}$),
$M$ = Mass of... |
I know a bunch of different versions of the mean value theorem for integrals, and yet none of them are able to solve my problem, but it sure as heck looks like one of them should.
I have attempted the following versions:
$1)$ let $f$ be a continuous function on $[a,b]$. Then there is $c \in [a,b]$ such that $$\int_a^b ... |
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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 ... |
I'm currently learning mathemetical concepts of distribution and the way to use them in a ray tracer with the book "Physically Based Rendering".
Let's start by uniformly sampling an hemisphere:
As you probably know, a way to generate the uniformly distributed direction is to use the inversion method.
Let us denote by $... |
First of all, the metric tensor is one additional piece of structure one inserts on a smooth manifold to measure lenghts and angles. The metric is indeed not present in all applications of Differential Geometry to Physics (see e.g. Lagrangian Mechanics). In that case, it is important to know also how to deal with manif... |
Are negative incomes (perhaps even negative prices) also allowed? Unless they are, non-horizontal or non-vertical lines are impossible as Engel curves because they have to intersect the negative quadrant of the coordinate system. I will come back to this later.
Without additional restrictions (perhaps a lot of addition... |
I was in the middle of writing the same old geographic distance calculation using the Haversine formula when it occurred to me: shouldn't there be simpler way to do this? Haversine is of course derived from the Law of Cosines. But in thinking about this problem, I ran across Napier's Rules for right-angled spherical tr... |
In order to prove (the non trivial part of) Chang-Los-Suszko's theorem [1], I'm struggling with the following lemma :
Lemma.Let $T$ be a $\mathcal L$-theory and $T_{\forall\exists}$ the set of $\forall\exists$-sentences consequences of $T$. Then for every model $\mathfrak M \models T_{\forall\exists}$, there exists $\m... |
Let $a$, $b$ and $c$ be positive numbers such that $a+b+c=2$. Prove: $$\frac{ab}{\sqrt{2c+a+b}}+\frac{bc}{\sqrt{2a+b+c}}+\frac{ca}{\sqrt{2b+c+a}}\le\sqrt\frac{2}{3}$$
Additional info:I'm looking for solutions and hint that using Cauchy-Schwarz, Hölder and AM-GM because I have background in them.
Things I have tried: I ... |
Is there a standard for how to align three columns of math I could follow? And what is the LaTex for that?
If no standard, how can I nicely format the columns in 3-column math? For example
-1 \leq \sin(t) \leq 1 \int_0^x (-1) dt \leq \int_0^x \cos(t) dt \leq \int_0^x (1) dt-x \leq \cos(x)-1 \leq x
I want the columns to... |
Factors
Factors refer to systematic risks that explain at least partially movements in asset prices. Ross (1976) [1] defines the first multifactor model -- the famous arbitrage pricing theory (APT). The APT states that asset returns are simply linear combinations of factors plus a small idiosyncratic component. Returns... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
Journal of Differential Geometry J. Differential Geom. Volume 102, Number 1 (2016), 67-126. Analytic differential equations and spherical real hypersurfaces Abstract
We establish an injective correspondence $M \to \mathcal{E}(M)$ between real-analytic nonminimal hypersurfaces $M \subset \mathbb{C}^2$, spherical at a ge... |
I think CompEcon covered most of the points that I was going to mention. Just a few last thoughts:1) Why are Epstein-Zin preferences important?The preferences are important because they allow you to separate two of the dimensions along which people care about their allocations; namely, risk aversion and intertemporal s... |
"Abstract: We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, insta... |
Quadratic equation An algebraic equation of the second degree. The general form of a quadratic equation is \begin{equation}\label{eq:1} ax^2+bx+c=0,\quad a\ne0. \end{equation} In the field of complex numbers a quadratic equation has two solutions, expressed by radicals in the coefficients of the equation: \begin{equati... |
If a function is a combination of other functions whose derivatives are known via composition, addition, etc., the derivative can be calculated using the chain rule and the like. But even the product of integrals can't be expressed in general in terms of the integral of the products, and forget about composition! Why i... |
Rotational Impulse-Momentum Theorem
By now we have a very good sense of how to develop the formalism for rotational motion in parallel with what we already know about linear motion. We turn now to momentum. Replacing the mass with rotational inertia and the linear velocity with angular velocity, we get:
The vector \(L\... |
The Landau free energy, also called the Landau-Ginzburg Hamiltonian, is treated in an adhoc and rather confusing manner in a lot of textbooks. But in the modern view, it has a simple interpretation as an effective Hamiltonian attained by integrating out degrees of freedom.
Suppose we have a spin system, such as an Isin... |
SHOGUN 6.1.3
class SGVector< T > shogun vector More... class CQuadraticTimeMMD This class implements the quadratic time Maximum Mean Statistic as described in [1]. The MMD is the distance of two probability distributions \(p\) and \(q\) in a RKHS which we denote by
\[ \hat{\eta_k}=\text{MMD}[\mathcal{F},p,q]^2=\textbf{... |
"A not so simple approach". I may have messed a little bit too much with grouping the terms, do forgive my elementary math skills, it's a side effect of using tools like wolfram and mathematica too much.
Without loss of generality we can assume that the near plane is given as $z=1$ (that is having normal $(0,0,1)$ and ... |
ok, suppose we have the set $U_1=[a,\frac{a+b}{2}) \cup (\frac{a+2}{2},b]$ where $a,b$ are rational. It is easy to see that there exists a countable cover which consists of intervals that converges towards, a,b and $\frac{a+b}{2}$. Therefore $U_1$ is not compact. Now we can construct $U_2$ by taking the midpoint of eac... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
Coupon bonds Exercise: XLF Co has issued a bond with a face value of $100,000 paying an annual coupon of 9%. The bond matures in 10 years from now, the market yield is 8% pa and a coupon has just been paid. Pricing
The price of a bond \(P\) is given by the formula \(P=\sum\limits_{j=1}^T \dfrac{C_j} {(1+i)^{t_j}}\) whe... |
Particle Moving Along y Axis on Surface of Rotating Ellipse
\[xy\]plane. A particle on the surface of the ellipse is made to move on the surface of the ellipse as the ellipse rotates. What will be the velocity and acceleration of the particle?
If the minor and major axes have length
\[b, \; a\]respectively, the coordin... |
what is the molecular mechanism with which thermal conductivity increases by increasing temperature? at least for metals? I know that heat increases the oscillations of the atoms in the crystal. But how that explains the increase in thermal conductivity?
The mechanism for increasing the thermal conductivity is phonon a... |
The problem: Now find a polynomial function $f$ of degree $n - 1$ such that $f(x_i) = a_i$, where $a, \ldots, a_n$ are given numbers.
I found that this question had been asked before, but I did not understand the solution.
Moving on to the actual problem: we are asked to use the formula derived in the previous problem,... |
Building Blocks
Summary
The
dtflearn object makes it easy to create and train neural networks of varying complexity.
Activation Functions¶
Apart from the activation functions defined in tensorflow for scala, DynaML defines some additional activations.
Hyperbolic Tangent 1 val act = dtflearn.Tanh("SomeIdentifier") Cumul... |
In 1202, Leonardo of Pisa (filius Bonacci) published Liber Abaci, or ABAC book. At that time, the book has not attracted attention, because it used arabic numbers.
However, a problem of that book remained famous:
"A certain man put a pair of rabbits in a place surrounded by a wall. How many pairs of rabbits can be prod... |
What is the depreciation rate ($\delta$)?
Assumptions:
$Y_t = K_t^{\alpha} (A_tL_t)^{1-\alpha}$, $\alpha = 0.5$ ($\alpha$ = capital income share), $A_0 =1$ and $g = 0$ ($g$ = growth rate of technology), $s = 0.2$ ($s$ = savings rate), $n = 0.05$ ($n$ = growth rate of the labor force/population).
Capital in the next per... |
Algebra ReviewAlgebra Review
Knowledge of the following mathematical operations is
required for STAT 200: Addition Subtraction Division Multiplication Radicals (i.e., square roots) Exponents Summations \(\left( \sum \right) \) Factorials (!)
Additionally, the ability to perform these operations in the appropriate order... |
There is the standard argument, using the definition of the inner product; that $\langle f|A|g\rangle =\langle g|A|f\rangle ^{*}$ for a Hermitian operator $A$, given any wave vectors $|f\rangle,~ |g\rangle$.
Also consider the following:
Consider the infinite dimensional one dimensional position space, with a column vec... |
On the Kuratowski measure of noncompactness for duality mappings Abstract
Let $(X,\Vert \cdot\Vert ) $ be an infinite dimensional real Banach
space having a Fréchet differentiable norm and $\varphi\colon \mathbb{R}_{+}\rightarrow \mathbb{R}_{+}$ be a gauge function. Denote by $J_{\varphi}\colon X\rightarrow X^{\ast}$ t... |
You're right about the second one, but your reasoning for both is sketchy. The definition of $f(n)=O(g(n))$ is that there exist constants $c,N$ both greater than zero such that $f(n)\le c\cdot g(n)$ for all $n\ge N$.
Trying a single value for $n$ won't generally give anything in the way of an answer. Consider, though, ... |
In an economy with two agents whose utility functions are $$ U_A(x_1,x_2) = \alpha \cdot x_1 + x_2 \hskip 20pt U_B(y_1,y_2) = y_1 \cdot y_2. $$
The given allocations are bundle (4,0) for A and bundle (1,5) for B.
Consider the following question
Taking into consideration the respective utilities for the bundles, we have... |
Let $S$ be a bounded and closed star domain of $\mathbb{R}^n$, $n>1$ with not empty interior and with an inner a "good" star-center $x_0$.
I define "good" star-center as a star-center $x_0$ such that for every $x \in S$, the straight line $\overline{x_0 x}$ that crosses $x_0$ and $x$, also intersects $\partial S$ only ... |
11.3.1 - Example: Gender and Online Learning
A sample of 314 Penn State students was asked if they have ever taken an online course. Their genders were also recorded. The contingency table below was constructed. Use a chi-square test of independence to determine if there is a relationship between gender and whether or ... |
Suppose we have a population of voters, each of them casting a vote in some (not necessarily deterministic) voting system.
Let w be the winning candidate.
Consider the following experiment:
Fix some number N. Draw a sample of N voters with replacement (i.e. you may draw the same voter more than once). Run the election ... |
I'm wondering where the following equality came from: $$ \langle x , y \rangle = \|x \| \| y \| \cos \theta$$
where the thing on the LHS is the inner product and $\|\cdot\|$ is the norm induced by $\langle \cdot, \cdot \rangle$. Do we need the Cauchy Schwarz inequality to prove this? I'm asking because I'm reading my n... |
I'm trying to follow a proof of the fact that if $g$ is an element of a hyperbolic group $G$ with infinite order, then $\langle g \rangle$ is an undistorted subgroup of $G$. The proof relies on the following lemma:
If $[p,q] \cup [q,r] \cup [r,s] \cup [s, p]$ is a geodesic quadrangle in a $\delta$-hyperbolic space $X$,... |
Advance warning: If you’re familiar with Bayesian reasoning it is unlikely this post contains anything new unless I’m making novel mistakes, which is totally possible.
Second advance warning: If taken too seriously, this article may be hazardous to your health.
Let me present you with a hypothetical, abstracted, argume... |
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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... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
A series has a constant difference between terms. For example, 3 + 7 + 11 + 15 + ….. + 99. We name the first term as
a1. The common difference is often named as “ d”, and the number of terms in the series is n.
We can find out the sum of the arithmetic series by multiplying the number of times the average of the last a... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
The Poisson Random Variable
The Poisson random variable is a discrete random variable that counts the number of times a certain event will occur in a specific interval.
Learning Objectives
Apply the Poisson random variable to fields outside of mathematics
Key Takeaways Key Points The Poisson distribution predicts the d... |
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