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Mathematics CIIT: LaTeX Resources
This page contains LaTeX template of CIIT Mathematics, MSc Project and MS Thesis templates.
Templates
Download a zip file given below and extract it by right clicking on the file.
The latest templates are available at http://www.mathcity.org/cui
Installing latex
Three separte software ... |
Let us now take a closer look at the
hex-fractal we sliced last week. Chopping a level 0, 1, 2, and 3 Menger sponge through our slanted plane gives the following:
This suggests an iterative recipe to generate the hex-fractal. Any time we see a hexagon, chop it into six smaller hexagons and six triangles as illustrated ... |
[Sophie wrote](https://forum.azimuthproject.org/discussion/comment/18107/#Comment_18107):
> > in other words, we have \\((x, y) \le (x', y')\\) iff \\(x \le x' \land y \le y'\\)
>
> I assume you used \\(\land\\) to mean "and" and not "join". Is that correct?
I can definitely see how that's ambiguous! I did mean "and". ... |
I think there are two legitimate sources of complaint. For the first, I will give you the anti-poem that I wrote in complaint against both economists and poets. A poem, of course, packs meaning and emotion into pregnant words and phrases. An anti-poem removes all feeling and sterilizes the words so that they are clear.... |
does this series converge/diverge conditionally or absolutly
$\sum_{n=2}^{\infty} (-1)^n \cdot \frac{\sqrt{n}}{(-1)^n + \sqrt{n}} \cdot \sin(\frac{1}{\sqrt{n}})$
i can use the facts that:
$\lim_{x\to0}\frac{\sin x}{x} =1 $;
$\sin(\frac{1}{\sqrt{n}})$ is monotone decreasing
my problem is the alternating $-1$'s in the de... |
This feat is notorious for its poor wording. The “+100%” phrasing is completely unique within D&D 3.5e as far as I know, for example. Ultimately, I can’t imagine any other interpretation here than adding again the number subtracted from your attack rolls, and it does have the nice feature of specifying the “normal” dam... |
Team Member Jaehyun Bae Contents
Motivation
This project is motivated by DARPA Warrior Web Program.
There has been a lot of research into exoskeletons over the years to alleviate heavy loads that soldiers carry, but strapping a person into a robotic outfit just isn't practical in a combat zone yet. DARPA's Warrior Web ... |
ä is in the extended latin block and n is in the basic latin block so there is a transition there, but you would have hoped \setTransitionsForLatin would have not inserted any code at that point as both those blocks are listed as part of the latin block, but apparently not.... — David Carlisle12 secs ago
@egreg you are... |
What is the fluorescence lifetime?
The fluorescence lifetime - the average decay time of a fluorescence molecule's excited state - is a quantitative signature which can be used to probe structure and dynamics at micro- and nano scales. FLIM (Fluorescence Lifetime Imaging Microscopy) is used as a routine technique in ce... |
It's hard to say just from the sheet music; not having an actual keyboard here. The first line seems difficult, I would guess that second and third are playable. But you would have to ask somebody more experienced.
Having a few experienced users here, do you think that limsup could be an useful tag? I think there are a... |
Energy balance are used to account the needs of energy to run a process.
There are several different types of energy forms:
Indipendently to the form, is defined as:
energy is the capacity to perform work or heat.
The unit of measure of energy is
joule (symbol: $\si{\joule}$, pronounce: "jul").
Thus, standard units for... |
This is inspired by ... an article by G. A. Krasinsky and V. A. Brumberg, "Secular Increase of Astronomical Unit from Analysis of the Major Planet Motions, and its Interpretation."
Pitjeva and Pitjev (1) provide a simple explanation of the very large secular change in the astronomical unit found by Krasinsky and Brumbe... |
Given the sample mean $\bar{x}$ and the sample variance $s^2$ of a random variable $X$, is it possible to estimate the shape $\sigma^2$ and log-scale $\mu$ of the log-normal distribution, with probability density function $$f_X(x;\mu,\sigma^2) =\frac{1}{x \sqrt{2 \pi \sigma^2}}\, \mathrm{exp}\left( {-\frac{(\ln x - \mu... |
Shapes of constant width Yes - there are shapes of constant width other than the circle. No - you can't drill square holes. But saying this was not just an attention catcher. As the applet below illustrates, you can drill holes that are almost square - drilled holes whose border includes straight line segments!
Now the... |
Mensuration (Perimeter & Area, Review of Earlier Concepts)
Category : 6th Class
MENSURATION (Perimeter and Area, Review of Earlier Concepts)
FUNDAMENTALS
(a) Perimeter of a square \[=4\,\,\times \]side.
Elementary question-1: Find perimeter of a square kabaddi field each of whose side is 20 metres Ans. Perimeter \[4\ti... |
In my population genetics book (see reference at bottom) they define them as:
Nucleotide polymorphism (θ): proportion of nucleotide sites that are expected to be polymorphic in any sample of size 5 from this region. Of the genome. $\hat{θ}$ equals the proportion of nucleotide polymorphism observes in the sample (S) div... |
First let me say that what is intuitive to a physicist may be not be so to a geometer and vice-versa. To many physicists a connection is the potential of a field satisfying a gauge invariance. For this point of view I refer to vol. 1, Chap. 6 sect 41 of the three volume book by Dubrovin-Fomenko-Novikov: Modern Geometry... |
Fussy spacing issues
These are issues that won't affect the correctness of formulas, but might make them look significantly better or worse. Beginners should feel free to ignore this advice; someone else will correct it for them, or more likely nobody will care.
Don't use
\frac in exponents or limits of integrals; it l... |
Activity monitoring for seniors living alone Identifying Critical Events
If a sensor uses water within an observation period, but the water does not flow all the time, there is probably nothing to worry about. Critical cases are those in which no water flows or water flows for a long time (see cases A and B). To identi... |
Chapter 03: General Theorem, Intermediate Forms
Rolle's theorem Geometrical interpretation of Rolle's theorem The mean value theorems Another form of mean value theorem Increasing and decreasing functions Cauchy's mean value theorem Extended mean value theorem Indeterminate form The form $\frac{0}{0}$ The form $\frac{\... |
NCERT Solutions For Class 7 Maths Chapter 5 Lines and Angles, are given here in a simple and detailed way. These solutions are provided for students to clear the concepts covered in chapter 5 and make them understand on the basis of each question and its solution, in an easy manner. The solutions are prepared by our ex... |
For this univariate linear regression model $$y_i = \beta_0 + \beta_1x_i+\epsilon_i$$ given data set $D=\{(x_1,y_1),...,(x_n,y_n)\}$, the coefficient estimates are $$\hat\beta_1=\frac{\sum_ix_iy_i-n\bar x\bar y}{n\bar x^2-\sum_ix_i^2}$$ $$\hat\beta_0=\bar y - \hat\beta_1\bar x$$ Here is my question, according to the bo... |
I am taking a course on Monte Carlo methods and we learned the Rejection Sampling (or Accept-Reject Sampling) method in the last lecture. There are a lot of resources on the web which shows the proof of this method but somehow I am not convinced with them.
So, in the Rejection Sampling, we have a distribution $f(x)$ wh... |
@0celouvskyopoulo7 Anyways, I don't think so: the initial topology $\mathfrak{T}_{\lVert \cdot\rVert}$ on a Banach space is finer than the weak topology $\sigma(X,X')$, and therefore $f\in C((X,\mathfrak{T}_{\lVert \cdot\rVert}),T)$ may very well be discontinuous in $(X,\sigma(X,X'))$, and almost surely not even semico... |
Terms sourced from: http://iupac.org/publications/pac/68/12/2223/
"Glossary of terms used in photochemistry (IUPAC Recommendations 1996)", Verhoeven, J.W.,
Pure and Applied Chemistry 1996, 68(12), 2223
absorbance \(A\)absorptance \(\alpha\)absorption absorption coefficient absorption cross-section \(\sigma\)absorptivit... |
Assume $$X\sim \frac{e^{-\beta Nf(x)}}{Z_{\beta}}$$ where $$ f(x) = -hx -x^2 + \frac{1}{\beta N}(1-x)\ln(1-x) + (1+x)\ln(1+x) $$ and $Z_{\beta}$ is the appropriate normalization factor. The support of $X$ is the lattice $\Gamma_N = \{-1,-1+2/N,\ldots,1-2/N,1\}$ and $N$ is some large positive integer and $\beta>1$.
I wo... |
I am asked to prove that
an O(1)-pass randomized streaming algorithm that solves s-t connectivity problem in a simple directed graph $G=(V,E)$ with $|V|=n$ vertices, with sucess possibility $>\frac{1}{2}$, has space lower bound of $\Omega(n^2)$ bits, using techniques in communication complexity theory.
I believe what t... |
The formula you quote gives the Gibbs energy of a system [single liquid droplet plus vapor of same chemical species].
You say "we are not at constant pressure". This is true in the sense that pressure of liquid inside the droplet is different from pressure of vapor just above the droplet.
The formula you quote actually... |
Introduction
Built at the Jet Propulsion Laboratory by an Investigation Definition Team (IDT) headed by John Trauger, WFPC2 was the replacement for the first Wide Field and Planetary Camera (WF/PC-1) and includes built-in corrections for the spherical aberration of the HST Optical Telescope Assembly (OTA). The WFPC2 wa... |
I know ooids form in high energy water, by rolling and building layers around a nucleation site, but I don't understand what limits their size.
What keeps these such a regular, small size?
Earth Science Stack Exchange is a question and answer site for those interested in the geology, meteorology, oceanography, and envi... |
12.3.3 - Hypothesis Testing
We can use statistical inference (i.e., hypothesis testing) to draw conclusions about how the population of \(y\) values relates to the population of \(x\) values, based on the sample of \(x\) and \(y\) values.
The equation \(Y=\beta_0+\beta_1 x\) describes this relationship in the populatio... |
12.3.4 - Confidence Interval for Slope
We can use the slope that was computed from our sample to construct a confidence interval for the population slope (\(\beta_1\)). This confidence interval follows the same general form that we have been using:
General Form of a Confidence Interval \(sample statistic\pm(multiplier)... |
So the first time I tried to recolor this insertion case from memory, I ended up with the right-hand side recoloring; of course the left recoloring is more efficient as the loop ends at this point. If however, we check in the right case for whether the grandparent of
a is the root (color it black) and otherwise continu... |
For a student of Karnataka Board 1st Year PUC class, mathematics can be a challenging subject as it deals with a wide range of topics from sets, relations and functions to complex numbers and quadratic equations, sequences and series, mathematical reasoning and so on. If a student needs to get a good foundation in clas... |
$$\sec2\theta=\csc2\theta$$
My attempt:
$$\begin{align} \cos2\theta &= \sin2\theta \tag{1}\\ \cos^2\theta+\sin^2\theta-2\cos\theta\sin\theta &=0 \tag{2}\\ (\cos\theta-\sin\theta)^2 &=0 \tag{3}\\ \cos\theta-\sin\theta &=0 \tag{4}\\ \cos\theta &=\sin\theta \tag{5}\\ \tan\theta &=1 \tag{6}\\ \theta &=180^\circ n+45^\circ ... |
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Now showing items 1-5 of 5
Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
11.2.1.2- Cards (Equal Proportions) Research question Section
When randomly selecting a card from a deck with replacement, are we equally likely to select a heart, diamond, spade, and club?
I randomly selected a card from a standard deck 40 times with replacement. I pulled 13 hearts, 8 diamonds, 8 spades, and 11 clubs.... |
There are two prominent uses of the term "average" in algorithm analysis.
Average-case as a special case of expected costs
Here, "average case" just means "expected case w.r.t. uniform distribution". Since we
usually analyse with uniform inputs in mind (everything else is hard, and there's not much reason to prefer one... |
11.2.1.3 - Roulette Wheel (Different Proportions) Research Question Section
An American roulette wheel contains 38 slots: 18 red, 18 black, and 2 green. A casino has purchased a new wheel and they want to know if there is any evidence that the wheel is unfair. They spin the wheel 100 times and it lands on red 44 times,... |
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Now showing items 1-10 of 27
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 ... |
The best intuitive analogy I've heard is with classical sound waves. Consider a musical instrument playing a pure sine wave of frequency $\nu$ and amplitude $A$, and no other harmonic frequencies at all. Graphing this in frequency-amplitude space ($x$-axis=frequency, $y$=amplitude) gives you a $\delta$-function-like po... |
The geodesic equation is
$$ {d^2 x^\mu \over {ds}^2}+\Gamma^\mu {}_{\alpha \beta}{d x^\alpha \over ds}{d x^\beta \over ds}=0\ $$
for some scalar parameter of motion
s and connection coefficients of the second kind $\Gamma^\mu {}_{\alpha \beta}$. It's straightforward to show this reduces to
$$ \frac{d^2 x^n}{{dt}^2} = -... |
Given a set of $n$ points in $R^d$, the goal is to cover them with (finitely many) unit balls such that following conditions satisfy:
1) Minimizing the number of balls that are required to cover all the points.
2) Maximizing the
inter-clusters separation between clusters, which is define as follows:
For clusters $C_i$ ... |
Developed in 1945 by the statistician Frank Wilcoxon, the signed rank test was one of the first "nonparametric" procedures developed. It is considered a nonparametric procedure, because we make only two simple assumptions about the underlying distribution of the data, namely that:
(1) the random variable
X is continuou... |
Symbols:Abbreviations/P/PGF
Jump to navigation Jump to search
Abbreviation: PGF or p.g.f.
Let $p_X$ be the probability mass function for $X$.
The probability generating function for $X$, denoted $\map {\Pi_X} s$, is the formal power series defined by: $\displaystyle \map {\Pi_X} s := \sum_{n \mathop = 0}^\infty \map {p... |
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... |
Please assume that this graph is a highly magnified section of the derivative of some function, say $F(x)$. Let's denote the derivative by $f(x)$.Let's denote the width of a sample by $h$ where $$h\rightarrow0$$Now, for finding the area under the curve between the bounds $a ~\& ~b $ we can a...
@Ultradark You can try d... |
We consider two different methods to estimate the parameters of a factor model:
Principal Component Method Maximum Likelihood Estimation
A third method, principal factor method, is also available but not considered in this class.
Principal Component Method Section
Let \(X_i\) be a vector of observations for the \(i^{th... |
I was asked to calculate the limit: $$\lim_{(x,y)\to (0,0)} \frac{x^3 \sin y}{x^6+2y^3} $$
I believe it has no limit so I tried to place some other functions that goes to $(0,0)$ and prove they don't goes to $0$ (I found some functions that does go to zero).
I've tried with $y=x^2$ and I find out it goes to infinity, i... |
Example 12-1: Continued... Section
The communalities for the \(i^{th}\) variable are computed by taking the sum of the squared loadings for that variable. This is expressed below:
\(\hat{h}^2_i = \sum\limits_{j=1}^{m}\hat{l}^2_{ij}\)
To understand the computation of communulaties, recall the table of factor loadings:
F... |
In the paper "A Duality Web in 2+1 Dimensions and Condensed Matter Physics"
https://arxiv.org/abs/1606.01989 on page 34, the action for electromagnetic field in Lorentzian signature is given by
$$S=\int d^{4}x\sqrt{-g}\left(\frac{-1}{4g^{2}}F_{\mu\nu}F^{\mu\nu}+\frac{\theta}{32\pi^{2}}\epsilon^{\mu\nu\alpha\beta}F_{\mu... |
Infinite series is one of the important concept in mathematics. It tells about the sum of series of numbers which do not have limits.
The sum of an infinite series can be denoted as $\sum_{0}^{\infty}r^{n}$. The formula for infinite series is given by,
\[\large \sum_{0}^{\infty}r^{n}=\frac{1}{1-r}\]
Solved Examples Que... |
Through Riemann sum, we find the exact total area that is under a curve on a graph, commonly known as integral. Riemann sum gives a precise definition of the integral as the limit of a series that is infinite. For approximating the area of lines or functions on a graph is a very common application of Riemann Sum formul... |
The Hénon equation with a critical exponent under the Neumann boundary condition
Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea
$ -Δ u + u = |x|^{α}u^{p}, \; u > 0 \;\text{in} \; Ω,\ \ \frac{\partial u}{\partial ν} = 0 \; \text{ on }\;\partial Ω,$
$Ω \subset B(0,... |
I'm trying to solve the one-dimensional heat equation using Fourier series:
$$\frac{\partial T}{\partial t}=-\alpha\frac{\partial^2T}{\partial x^2}$$
I know that:
$$T = k_n\cos{(nx-\varphi_n)}e^{-\alpha n^2t}$$
is a solution that satisfies the PDE, but doesn't necessary satisfy the initial, or boundary conditions. Howe... |
In Classical Mechanics to describe symmetries like translations and rotations we use diffeomorphisms on the configuration manifold. In Quantum Mechanics we use unitary operators in state space. We impose unitarity because we don't want the action of the symmetry to interfere with the normalization of the states.
Now, e... |
We know that two fields commute - by locality and causality -
iff there is spacelike separation
$\left[\phi_l^k(x) , \phi_m^{k'}(y)\right] = 0$ for $(x-y)^2<0$
In the canonical quantization of the Dirac field, if $b_\alpha(k)$ is the annihilation operator and $b^\dagger_\alpha(k)$ is the creation operator for a particl... |
I'm attempting to solve the 1D Schrodinger Equation, approaching a potential barrier defined as follows:
$$V(x) = \begin{cases}-V_0&\quad\text{for}\quad x<0 \\0&\quad\text{for}\quad x>0\end{cases}$$
where the inbound particle has energy $-V_0 < E < 0$ (Approaching from the left).
I've started the solution, as I would n... |
The integrability of negative powers of the solution of the Saint Venant problem 2014 (English)In: Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, ISSN 0391-173X, E-ISSN 2036-2145, Vol. XIII, no 2, p. 465-531Article in journal (Refereed) Published Abstract [en]
We initiate the study of the fini... |
First, note that the growth rate of $\mu$ is defined as $\dot\mu = \frac{ d\mu }{ \mu }$. Therefore, you will have to
take the total differential of the equation; and divide by $\mu$.
For the first step, as in your previous question, simply use the rules of total differentials, specifically the product rule that states... |
The rigorous way to solve this would be to solve the differential equation, get an expression for $P(t)$ and then take the limit $\lim_{t \to \infty}P(t)$.
But if you start out by assuming the limit exists, then at the limit, $\frac{dP}{dt}=0$ (i.e. loosely speaking, "P stops changing").
So solve $3P(4-P) = 0$ giving $... |
To find the maximum likelihood a generic approach is to write down the likelihood function as a starting point.
In this example, $Y_i\sim\mathcal{N}(\mu,\sigma_i^2)$ means that$$L(\mu,\sigma_1,\ldots,\sigma_n) = \prod_{i=1}^n \dfrac{\exp\{-(y_i-\mu)^2/2\sigma_i^2\}}{\sqrt{2\pi}\sigma_i}$$or$$\ell(\mu,\sigma_1,\ldots,\s... |
I have a recollection of seeing an identity connecting polylogarithm and polygamma functions of arguments $\frac14$ and $\frac34$. But I don't remember details, and searching my books and the Internet for an hour did not give any results. Could you please remind me this identity (if it exists)?
I have not found a sourc... |
I'd appreciate some help in squaring this thermodynamic circle (which may exist only in my mind, but I digress ...)
Let's consider pure water in a two-phase(liquid/vapour) state. Within the vapour dome, the density of water can be determined from mass and volumetric balances according to
$$\rho = \Bigg[\frac{x}{\rho_V(... |
11.3 - Chi-Square Test of Independence
The chi-square (\(\chi^2\)) test of independence is used to test for a relationship between two categorical variables. Recall that if two categorical variables are independent, then \(P(A) = P(A \mid B)\). The chi-square test of independence uses this fact to compute expected valu... |
Mathematics - Part 2
This tutorial builds on the basic foundations presented in the previous tutorial. If you often include a lot of maths in your documents, then you will probably find that you wish to have slightly more control over presentation issues. Some of the topics covered make writing equations more complex -... |
Write a program which can encode text to avoid reusing characters, and convert back.
Both normal and encoded forms are restricted to a particular character set: the space character
with code point 32, the tilde character
~ with code point 126, and all characters between. This is 95 total characters. It's a printable su... |
Here we will only answer OP's two first question(v1). Yes, Newton's Shell Theorem generalizes to General Relativity as follows. The Birkhoff's Theorem states that a spherically symmetric solution is static, and a (not necessarily thin) vacuum shell (i.e. a region with no mass/matter) corresponds to a radial branch of t... |
Tutorial: K Nearest Neighbors in Python
In this post, we’ll be using the K-nearest neighbors algorithm to predict how many points NBA players scored in the 2013-2014 season. Along the way, we’ll learn about euclidean distance and figure out which NBA players are the most similar to Lebron James. If you want to follow a... |
2019-05-20 15:18 Record dettagliato - Record simili 2019-01-23 09:13
nuSTORM at CERN: Feasibility Study / Long, Kenneth Richard (Imperial College (GB)) The Neutrinos from Stored Muons, nuSTORM, facility has been designed to deliver a definitive neutrino-nucleus scattering programme using beams of $\bar{\nu}_e$ and $\ba... |
The Binomial Formula
The binomial distribution is a discrete probability distribution of the successes in a sequence of [latex]\text{n}[/latex] independent yes/no experiments.
Learning Objectives
Employ the probability mass function to determine the probability of success in a given amount of trials
Key Takeaways Key P... |
I'm trying to proove $NP$-membership for a problem from the following certificate. I have $n$ sets of integers : $$(S_i)_{i \in \{1,\dots,n\}}$$ Each set has a number $m_i$ of integers. I make "combination" from those sets by taking at most one element in each set. A "combination" has between $0$ and $n$ elements (assu... |
In the book that I am using,
Linear Algebra Done Right, the proof for the Steinitz exchange lemma (which can be found here) left me unconvinced.
The proof refers to the linear independence lemma. This is where my problem lies, the proof says that 'one of the vectors in this list is in the span of the previous ones'. I ... |
This is not easy for general $G$, but we can immediately produce some crude bounds (on the minimal number $\mu(G)$ such that $G$ embeds into $S_{\mu(G)}$):
If we have an embedding $G \hookrightarrow S_n$, we must trivially have $|G| \leq |S_n| = n!$. Of course, this is sharp in the sense that equality holds for $G = S_... |
Mainly trying to determine where I'm going wrong. Here is what I have done so far:
$$r = 1 + cos(\theta)$$
We know that: $x = r cos(\theta)$ and $y = r cos(\theta)$
So:
$$x = (1 + cos(\theta))cos(\theta)$$ $$x = cos(\theta) + cos^2(\theta)$$ $$\frac{dx}{d\theta} = -sin(\theta)-2cos(\theta)sin(\theta)$$
Set $\frac{dx}{d... |
I have some questions about homotopy. Before starting here a definition:
A topological space $X$ is called contractible if $X$ is homotopy equivalent with a one-point-space Suppose $X$ a toplogical space, $Y\subset X$. A retraction $r:X\rightarrow Y$ is a continu function such that $r_{|Y}=id_Y$, thus r(y)=y $\forall y... |
The Riemann Hypothesis is true if and only if Robin's Inequality is true for all n>5040. It has also been shown by Akbary and Friggstad that the smallest counterexample greater than 5040, if it exists, must be a Superabundant Number.
These two facts suggest that Robin's Inequality might provide a more elementary way to... |
There are $x^n$ possible lists of $n$ objects, where there are $x$ different possible objects. So on average, over all possible such lists, a (non-lossy, optimal) compression algorith will give a file of size $n\log_2 x$ bits.
Of course, many decent algorithms will either know which objects are common in general, and m... |
Water, as simple as it might appear, has quite a few extraordinary things to offer. Most does not seem to be as it appears.
Before diving deeper, a few cautionary words about hybridisation. Hybridisation is an often misconceived concept. It only is a mathematical interpretation, which explains a certain bonding situati... |
EDIT There was an essential step left out in the proof. Thanks to Al Jebr for pointing it out.
Since I've muddled the matter with my comments, I'll post an answer, although you only asked for a hint. I'll try to phrase it as a sequence of hints, so you can stop reading when you want.
First, this seems to have something... |
Meshing Considerations for Linear Static Problems
In this blog entry, we introduce meshing considerations for linear static finite element problems. This is the first in a series of postings on meshing techniques that is meant to provide guidance on how to approach the meshing of your finite element model with confiden... |
Now that I'm ridiculously behind in the Stanford Online Statistical Learning class, I thought it would be fun to try to reproduce the figure on page 36 of the slides from chapter 3 or page 81 of the book. The result is a curvaceous surface that slices neatly through the data set.
I’m not sure what incurable chemical im... |
Introduction
In earlier parts we discussed about the basics of integral equations and how they can be derived from ordinary differential equations. In second part, we also solved a linear integral equation using
trial method. Now we are in a situation from where main job of solving Integral Equations can be started. Bu... |
I need to find the Fourier series of $$ f(x)=\begin{cases}a,& 0<x<\frac{\pi}{3}\\ 0,&\frac{\pi}{3}<x<\frac{2\pi}{3}\\-a,& \frac{2\pi}{3}<x<\pi\\ \end{cases} $$ $$ f(x)= a_0+\sum_{n=1}^{\infty}a_n\cos\frac{n\pi x}{L}+\sum_{n=1}^{\infty}b_n\sin\frac{n\pi x}{L}, $$ $$ a_0 = \frac{1}{2\pi} \int_{-\pi}^{\pi} f(x) dx $$ $$ a... |
Sure, in principle it could be used to separate the levels of $\mathsf{PH}$...the key thing is to find polynomial families complete for the relevant classes (or, at least polynomial families $f, g$ such that $f$ is in the larger class and is conjectured to not be in the smaller class, and such that showing that $f$ is ... |
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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 ... |
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Now showing items 21-30 of 182
The new Inner Tracking System of the ALICE experiment
(Elsevier, 2017-11)
The ALICE experiment will undergo a major upgrade during the next LHC Long Shutdown scheduled in 2019–20 that will enable a detailed study of the properties of the QGP, exploiting the increased Pb-Pb luminosi... |
The Lane-Riesenfeld algorithm subdivides the control polygon of a B-spline to create a new control polygon with the same limit spline. It's made up of two steps: first, duplicating all of the control points $P_i$ into $P^\prime_{2i}$ and $P^\prime_{2i+1}$; then, moving each point to the midpoint between it and the next... |
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Now showing items 1-1 of 1
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
It sounds like both Griffiths and your lecturer are trying to come up with a mechanical rule for what you should say about states and measurement results instead of an explanation. I could be wrong about that since I have only your report to go on, but the appropriate explanation follows.
Say you have a state $\psi = a... |
Many users have tried to do a seasonal decomposition with a short time series, and hit the error “Series has less than two periods”.
The problem is that the usual methods of decomposition (e.g.,
decompose and
stl) estimate seasonality using at least as many degrees of freedom as there are seasonal periods. So you need ... |
Thursday, 30 March 2017
In a recent
Science paper, Eric Loken and Andrew Gelman discuss an interesting statistical nuance relevant to measurement error. Loken and Gelman begin by pointing out statisticians/econometricians/people with data and computers have the mindset that measurement error in one of our covariates bi... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
There have been a number of cases where efficient hidden subgroup algorithms have been found for specific non-Abelian groups with very specific structures. Why haven't we found any efficient quantum algorithm to find a hidden subgroup in a symmetric group even when the structure of the hidden subgroup is heavily restri... |
I want to estimate the distribution/variance of the ratio $WTP=\frac{\gamma}{\alpha}$. The problem is, both $\gamma$ and $\alpha$ are random coefficients. In other words, both are random to begin with (please note that here their true values are random; this is different from the usual regression models where the true ... |
I am trying to use a finite difference scheme to numerically solve sixth order parabolic equations such as
\begin{equation} u_t = u_{xxxxxx} \end{equation}
with symmetry conditions \begin{equation} u_x(0,t) = u_{xxx}(0,t) = u_{xxxxx}(0,t) = 0. \end{equation}
On the vast majority of grid points, the central difference s... |
Note: While I am interested in typesetting the Euler constant raised to the power of a matrix, I am more interested in understanding why the second version inserts a square dot, and why the third doesn't compile.
First, what works: I have adapted the answer here, (defining a new command). Second, when I try incorporati... |
It is not an answer, but maybe some information which could be useful :
In an other post, it has been also noticed that the commutators of the $R$-symmetry generators with supercharge generators are:
$[R^a_b,Q^c_{\alpha}]=\delta^c_bQ^a_{\alpha}-\frac{1}{4}\delta^a_bQ^c_{\alpha}$
So, taking the trace (on $a,b$), with $\... |
Stephen Merity, Bryan McCann, Richard Socher Motivation: Better baselines Fast and open baselines are the building blocks of future work ... yet rarely get any continued love. Given the speed of progress within our field, and the many places progress arises, revisiting these baselines is important important Baseline nu... |
Today in class I showed some ways for dealing with the classical integral $\int_{0}^{2\pi}\frac{d\theta}{(A+B\cos\theta)^2}$ under the constraints $A>B>0$, including
Symmetry and the tangent half-angle substitution; Relating the integral to the area enclosed by an ellipse, via the polar form of an ellipse with respect ... |
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