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Polar Coding Notes: A Simple Proof
For any B-DMC $W$, the channels $\{W_N^{(i)}\}$ polarize in the sense that, for any fixed $\delta \in (0, 1)$, as $N$ goes to infinity through powers of two, the fraction of indices $i \in \{1, \dots, N\}$ for which $I(W_N^{(i)}) \in (1 − \delta, 1]$ goes to $I(W)$ and the fraction fo... |
Avinash Singh
Articles written in Pramana – Journal of Physics
Volume 29 Issue 5 November 1987 pp 509-516 Condensed Matter Physics
The spin-correlation length is used to set up a RG analysis of the Hubbard model (within RPA). We demonstrate that an identical critical behaviour is obtained by performing the macroscopic ... |
M Fabiane
Articles written in Pramana – Journal of Physics
Volume 72 Issue 6 June 2009 pp 979-988 Research Articles
We consider corrections to scaling within an approximate theory developed by Mazenko for nonconserved order parameter in the limit of low $(d \rightarrow 1)$ and high $(d \rightarrow \infty)$ dimensions. ... |
This is the first part of a series on bubbles in the U.S. Equity Market I will be publishing this summer.
Introduction
The problem with writing about bubbles is that bubbles are hard to define. More troubling is that bubbles are almost always identified ex-post. For example, some claim there was a bubble in the U.S. ho... |
2018-09-11 04:29
Proprieties of FBK UFSDs after neutron and proton irradiation up to $6*10^{15}$ neq/cm$^2$ / Mazza, S.M. (UC, Santa Cruz, Inst. Part. Phys.) ; Estrada, E. (UC, Santa Cruz, Inst. Part. Phys.) ; Galloway, Z. (UC, Santa Cruz, Inst. Part. Phys.) ; Gee, C. (UC, Santa Cruz, Inst. Part. Phys.) ; Goto, A. (UC,... |
Title:
Time duration for the yellow traffic light
Post by:
Fu-Kwun Hwang on July 12, 2008, 01:59:37 pm
A yellow light at a traffic intersection should last long enough that a car traveling at the suggested speed can either
apply the brakes and decelerate to a stop prior to reaching the front of the intersection, or
mai... |
Identically Distributed (i.i.d.)
Consider a sequence of random variables: . The are mutually independent if for any finite subset and any finite sequence of numbers :\begin{equation}P \left[ \bigcup\limits_{i=1}^{n} (X_i\leq a_i) \right] = \prod\limits_{i=1}^{n} P(X_i\leq a_i)\end{equation}This may look more familiar i... |
The only meaning I can attach to $\overline{xxxx}$ is that you expect a result made of 4 equal digits (I can't read your source since it seems in Arabic or something similar).
If $n$ is our middle odd number, the sum of the square of 3 consecutive odd numbers is $$(n-2)^2 +n^2+(n+2)^2 = 3n^2+8$$and we want this to be e... |
Let $X$ be a Hausdorff locally compact in $x \in X$. Show that for each open nbd $U$ of $x$ there exists an open nbd $V$ of $x$ such that $\overline{V}$ is compact and $\overline{V} \subset U$.
My work:
Since $X$ is Hausdorff and locally compact then $X$ is regular. Let $U$ be an open nbd of $x$. By assumption $X$ is l... |
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... |
I am facing some problems in understanding what is the importance of a Killing vector field? I will be grateful if anybody provides an answer, or, refer me to some review or books.
In terms of classical general relativity: Einstein's equations $$ G_{ab} = 8\pi T_{ab} $$ can be formulated, in local coordinates, as a sys... |
High Productivity Close to Maths
SAC aims to help application programmers' productivity. The abstraction facilities in SAC enable programs that closely reflect the underlying mathematics of scientific problems. As an example, consider naive n-body simulation. Using $m$ for planet masses, $p$ for positions (in 3D space)... |
Here I have a free abelian group $A$ on $\Sigma$ and a grouping operator $()$ on $\Sigma^*$ which turns it into a magma. The grouping could mean arguments to a function (later) in which case this is just regular group cohomology. I came up with these formulas. We do have $d^3 \circ d^2 = 0$ but not for the higher ones ... |
TLDR;
The equations:
$$r_{B} = \sqrt{\frac{F}{2.46\times 10^{-14}}}$$
or rearranging for$$F = r_{B}^{2} \times 2.46\times 10^{-14}$$
Where $F$ is the fraction of light blocked ($F=0.01$ gives your $1\%$) and $r_{B}$ is the radius of your satellite in meters which will achieve this.
For one percent reduction, using the ... |
Difference between revisions of "NTS ABSTRACTSpring2019"
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Your score is simply the sum of difficulties of your solved problems. Solving the same problem twice does not give any extra points. Note that Kattis' difficulty estimates vary over time, and that this can cause your score to go up or down without you doing anything.
Scores are only updated every few minutes – your sco... |
This question already has an answer here:
Let $G$ be an abelian group with all proper subgroup finite, then is $G$ finite or at least finitely generated ?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up... |
My book gives the following definition:
Let $A$ be a $(n\times n)$-matrix with real components. A nonzero vector $v\in\mathbb R^n$ is an eigenvector of $A$ if there exists $\lambda\in\mathbb R$, such that $A\cdot v=\lambda v$. This value $\lambda$ is the eigenvalue that belongs to eigenvector $V$.
The way I interpret t... |
The book I am using for my Introduction of Topology course is
Principles of Topology by Fred H. Croom.
Show that Hilbert Space is not locally compact at any point.
This is what I understand:
A space $X$ is compactprovided that every open cover of $X$ has a finite subcover. A space $X$ is locally compact at a point$x$ i... |
ISSN:
1935-9179
eISSN:
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Abstract:
A compact Riemannian manifold may be immersed into Euclidean space by using high frequency Laplace eigenfunctions. We study the geometry of the manifold viewed as a metric space endowed with the distance functio... |
when we have a covering $p:Y\to X$ choose $x\in X$ and we have two actions on the fiber $p^{-1}(x)$:
1) The monodromy action of $\pi_1(X,x)$ defined as follows: $[\gamma].\tilde x=\tilde \gamma (1)$ that is; the action gives the endpoint of the unique lift of $\gamma$ starting at $\tilde x$.
2)The Deck group action of ... |
In lecture, we went through solving a Taylor error bound for arcsine. I followed most of it except for where it talks about the odds divided by the evens divided by $2n+1$ gaining in accuracy by a factor of 1/10 for each successive term (see bolded sentence below), which comes from this part of the series:
$$ \sum_{x=1... |
Given a curve in a frictionless environment with parameterization $\displaystyle \mathbf{r}(\theta)=x(\theta)\hat{\mathbf{i}}+y(\theta)\hat{\mathbf{j}}$ for $\theta\in[0,\theta_f]$, how can I find the position of a particle, which starts at $\mathbf{r}(0)$ and which slides down $\mathbf{r}$ under only the force of grav... |
Actually, I think you can take the limit just fine.
Consider $\lim_{E_i\to 0} (O_i-E_i)^2/E_i$ under two cases:
Case 1: $O_i > 0$. In this case the term goes off to infinity in the limit, and the overall chi-square statistic goes with it.
Case 2: $O_i = 0$. In this case the term equals $E_i^2/E_i = E_i$, which goes to ... |
Last time I wrote about different ways of calculating distance in a vector space — say, a two-dimensional Euclidean plane like the streets of Portland, Oregon. I showed three ways to reckon the distance, or norm, between two points (i.e. vectors). As a reminder, using the distance between points
u and v on the map belo... |
Value and Momentum
Two of the most discussed effects in the asset pricing literature are Value and Momentum.Let’s start with the definitions:
1) Value Effect: Stocks with high book-to-market have historically outperformed stocks with low book-to-market
Book-to-Market: (book value of common equity + deferred taxes and i... |
In this class, we will deal only with integrals of complex functions of a real variable integrated with respect to the real variable. This is identical to integration of real functions of real variables. The $j$ is simply treated as a constant in all these cases. In this class, we are typically interested in time $t$ o... |
There are numerous mathematically equivalent formulations of quantum mechanics. One of the oldest and most commonly used formulations is the transformation theory proposed by Cambridge theoretical physicist Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics, matrix mechanics (i... |
Home Publications all years 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 theses techreports presentations edited volumes conferences Awards Research Teaching BLOG Miscellaneous Full CV [pdf] Events Past Events Publications of Torsten Hoefler
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The documents distributed... |
Here's my two cents worth.
Why Lie Algebras?
First I'm just going to talk about Lie algebras. These capture almost all information about the underlying group. The only information omitted is the discrete symmetries of the theory. But in quantum mechanics we usually deal with these separately, so that's fine.
The Lorent... |
Mohammed Alatif, Puttaswamy, Laplacian Minimum Boundary Dominating Energy of Graphs, Asia Pac. J. Math., 3 (2016), 99-113.
R. A. Rashwan, H. A. Hammad, Random Fixed Point Theorems for Random Mappings, Asia Pac. J. Math., 3 (2016), 114-135.
K.P.R. Rao, Md. Mustaq Ali, A.S. Babu, Coincidence Point Theorem for Two Pairs o... |
Orbit
Personal Recommendation
Two novels for the price of one. The second may be a little weaker than the first, but Larry Niven does not produce any bad writing. In common with the rest of his work, these contain rock hard science. Take a neutron star, put a planet round it and you have the recipe for a gas torus — a ... |
This is an exercise (1.4.11) from Marker. Fix a language $\mathcal L$ and $\mathcal L$-structure $\mathcal M$. For a subset $A \subseteq M$, an element of $M$ is
algebraic over $A$ if it is a member of a finite $A$-definable subset of $M$. Let $\bar A$ denote the set of algebraic elements over $A$. We would like to sho... |
This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by showing an implementation of how the parameters of a real pure tone can be calculated from just two DFT bin values. The equations from previous articles are used in tandem to first calculate the frequency, and then ca... |
[
Disclaimer: I give my answer, however I am not an expert so feel free to comment/edit if I have made some mistake ;-) ]
Mathematically, you can think of evolution in classical mechanics as a (symplecto)morphism on the cotangent bundle $T^*M$ of some smooth $n$-dimensional manifold $M$.
The cotangent bundle $T^* M$ is... |
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... |
On my calculator, I usually get a $0$ when I divide something by $2$, a lot of times if that makes sense, but I was just wondering why does $2^{-329} = 0?$
It doesn't. Your calculator can't handle a number of such a small magnitude. Specifically, $2^{-329}\approx 9.14\times 10^{-100}$, and I'm guessing that your calcul... |
This is the second post in a series on bubbles in the U.S. Equity Market. The first part can be found here.
Testing for Multiple Bubbles 1: Historical Episodes of Exuberance and Collapse in the S&P 500, Phillips, Shi and Yu, 2013 Summary
As mentioned previously, most bubbles are identified ex-post. This presents a prob... |
The axiom of well-ordered choice, or $\sf AC_{\rm WO}$, is strictly weaker than the axiom of choice itself. If we start with $L$ and add $\omega_1$ Cohen reals, then go to $L(\Bbb R)$, one can show that $\sf AC_{\rm WO}$ holds, while $\Bbb R$ cannot be well-ordered there.
Pincus proved in the 1970s that this is equival... |
prettify-symbols-mode is a recent feature of Emacs and it’s very nice. And it looks like it can replace TeX-fold-mode in the future. But, at the time of writing, prettify-symbols-mode doesn’t seem to work well with AUCTeX unless you enable two workarounds together.
Tested versions:
AUCTeX 11.89.7 (latest version from G... |
Starting with the boundary conditions for parallel E and B fields for emr normal to an interface, i am trying to derive reflection coefficient with refractive indices.
I have got as far as
$E_1=E_2\qquad \qquad $ (parallel $\vec E$ fields are equal)
$E_{0i}+E_{0r}=E_{0t}\qquad \qquad $ Eq.(a)
$\frac{B_1}{\mu_1} = \frac... |
@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... |
My question is about the
challenge space size in Schnorr protocol. To be precise, I feel I've read all the Internet (twice) and I still don't understand why is it bad to allow challenge space to be large (say, why one shouldn't let $\text{Challenge} \in \mathbb{Z}_q$)
I'm interested only in situation of honest prover $... |
Yesterday I started to write a paper about the reformulation of the Riemann Hypothesis.
My idea was to map the function such that all of the trivial zeros are outside of the unit disk, and the non-trivial zeros are on the circle. Iff RH is true, then the radius of convergence (the distance to the closest singularity fr... |
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Now showing items 1-10 of 26
Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
Ratio of Volume of Sphere Inside a Cube Inside a Sphere
If the side of the cube is
\[2x\]the the innermost sphere has radius
\[x\].
The radius of the larger sphere is the distance from the centre of the cube to one of its vertices, and is equal to
\[\sqrt{x^2+x^2+x^2} = \sqrt{3x^2} = x \sqrt{3}\]
Then
\[\frac{Volume \:... |
Last Updated: May 11, 2019 Keywords Boussinesq approximation, closure problem, Reynolds averaging Reynolds Average
It is computationally expensive to resolve the wide range of time and length scales observed in turbulent flows. We now consider decomposing a flow property \(f\), such as velocity and pressure, into a mea... |
The ladder operator method is used to solve the one-particle Schrodinger equation with a harmonic potential.
What other potentials for the one-particle Schrodinger equation may be solved with the ladder operator method?
Physics Stack Exchange is a question and answer site for active researchers, academics and students ... |
3GPP 5G has been focused on structured LDPC codes known as quasi-cyclic low-density parity-check (QC-LDPC) codes, which exhibit advantages over other types of LDPC codes with respect to the hardware implementations of encoding and decoding using simple shift registers and logic circuits.5G NR QC-LDPC Circulant Permutat... |
In the ACKS2 polarizable force field paper, I found a thing called the atom-condensed softness matrix. In another paper, I found this expression for it:
$$ \chi_{kl} = 2 \sum_{i}^{\text{occ MOs}} \sum_{j}^{\text{unocc MOs}} \frac{\langle\psi_{i}|g_{k}|\psi_{j}\rangle\langle\psi_{j}|g_{l}|\psi_{i}\rangle}{\epsilon_{i} -... |
Following the excellent answer here, it is stated that
Connection: Let $P^X(\cdot\mid\cdot)$ be a regular conditional probability of $P$ given $X$. Then for any $A \in \mathcal{F}$ we have $$ {\rm E}[1_A\mid X]=\varphi(X), $$ where $\varphi(x) = P^X(A\mid x)$. In short we write ${\rm E}[1_A\mid X]=P^X(A\mid X)$.
I'm tr... |
I would like to clarify something and I will take the example of the $SO(2)$ Lie group.
A Lie group is a manifold with a group structure. Thus we can define maps on it to be able to move on the manifold.
In $SO(2)$, I can write the matrices as :
$$ \begin{pmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\th... |
@ José Hdz. Stgo.:
Thank you for this great answer. I think I should add a few comments on the related materials I collected from different books. (Since I am neither a native speaker of German language nor well-versed in it, sometimes I need google translation or deepL translation for a better understanding on all the... |
Algebraic Geometry Seminar Fall 2016
The seminar meets on Fridays at 2:25 pm in Van Vleck B305.
Here is the schedule for the previous semester.
Contents Algebraic Geometry Mailing List Please join the AGS Mailing List to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is... |
No, I don't think auto-regulation explain much in the population sizes of predators. Group selection may explain such auto-regulation but I don't think it is of any considerable importance for this discussion.
The short answer is, as @shigeta said
[predators] tend to starve to death as they are too many!
To have a bett... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
Based on the Bekenstein-Hawking Equation for Entropy, hasn't the relationship between quantum mechanics and gravity already been established.
The macroscopic Beckenstain-Hawking entropy formula
$$ S_{BH} = \frac{k A}{4 l_p^2} $$
with the Planck length given by
$$ l_p = \sqrt{\frac{G\hbar}{c^3}} $$
gives a hint that qua... |
ISSN:
1531-3492
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Discrete & Continuous Dynamical Systems - B
September 2011 , Volume 16 , Issue 2
A special issue
Dedicated to Qishao Lu on the occasion of his 70th birthday
Select all articles
Export/Reference:
Abstract:
This issue of Discrete and Continuous Dynamical Systems–Series B, is de... |
in an exercise I was asked to prove that
(a) The structures $(\mathbb{R}^+,1,\cdot)$ and $(\mathbb{R},0,+)$ are elementarily equivalent.
(b) The two structures $(\mathbb{N},<)$ and $(\mathbb{Q},<)$ are not elementarily equivalent.
(c) The structure $(\mathbb{R},0,1,+,\cdot )$ is not an elementary substructure of the st... |
Theorem 2.27: If $X$ is a metric space and $E \subset X$, then $\bar E$ (the closure of $E$) is closed.
The proof says: If $p \in X$ and $p \not \in \bar E$ then $p$ is neither a point of $E$ nor a limit point of $E$. Hence $p$ has a neighborhood which does not intersect $E$. The complement of $\bar E$ is therefore ope... |
Let's say we write a standard call option on $S_t$ which pays $Max[0, S_t-K] \,\forall \, t \in T $. Given that $\frac{dS}{S} = \mu \,dt + \sigma \,dW_t$, and, $V_T = (S_T -K)_+$, we can solve this under the Black-Scholes framework as:
$$V_t[S_t,K,\sigma_S,r,t] = S_t \varPhi[d_1] - K e^{-r (T-t)} \varPhi[d_1 - \sigma \... |
I have been doing quite a lot of reading recently about the theory of atoms in molecules and think that I have semi-satisfactory answers to your questions, so I will share them here and perhaps others will add complementary answers as there actually seems to be quite an extensive literature on this subject, but there i... |
I am trying to understand the definition of point process when reading its Wikipedia article:
Let $S$ be locally compact second countable Hausdorff space equipped with its Borel σ-algebra $B(S)$. Write $\mathfrak{N}$ for the set of locally finite counting measures on $S$ and $\mathcal{N}$ for the smallest σ-algebra on ... |
Let$\ \sigma(n)$ be the sum-of divisors function, with the divisors raised to$\ 1$. If the Riemann Hypothesis is false, Robin proved there are infinitely many counterexamples to the inequality$$\ \sigma(n)<e^\gamma n \log \log n.$$ There are 27 small counterexamples, but the conjecture is that it holds for every$\ n>50... |
I've always wondered why do one use squared or absolute returns to determine if volatility modeling is required for the return series? We understand that there are various tests for its autocorrelation and conditional heteroskedasticity. However, I don't quite grasp the concept behind it. Can anyone kindly explain what... |
2019-09-12 16:43
Pending/LHCb Collaboration Pending LHCB-FIGURE-2019-008.- Geneva : CERN, 10 详细记录 - 相似记录 2019-09-10 11:06
Smog2 Velo tracking efficiency/LHCb Collaboration LHCb fixed-target programme is facing a major upgrade (Smog2) for Run3 data taking consisting in the installation of a confinement cell for the gas ... |
First, I propose to rewrite your original system (by multiplyingnumerator and denominator by $x\,y$) as\begin{align} x' &= \frac{d_2 r_1\,x + (r_1 a_{22} - r_2 a_{12})\,x\,y}{a_{12}a_{21}\, x\, y - (d_1 + a_{11}\,x)(d_2 + a_{22}\,y)}, \tag{1a}\\ y' &= \frac{d_1 r_2\,y + (r_2 a_{11} - r_1 a_{21})\,x\,y}{a_{12}a_{21}\,x\... |
Given a matrix $F \in \mathbb{C}^{m \times n}$ such that a $m>n$ and other matrix $A$ (non-symmetric matrix) of size $n \times n$ and spectral norm as:
$$\|A-F^*\operatorname{diag}(b)F\|_2 = \sigma_{\max}(A-F^*\operatorname{diag}(b)F) = \sqrt{\lambda_{\max} \left( (A-F^*\operatorname{diag}(b)F)^* (A-F^*\operatorname{di... |
Shortcomings of the MAPE
The MAPE, as a percentage, only makes sense for values where divisions and ratios make sense. It doesn't make sense to calculate percentages of temperatures, for instance, so you shouldn't use the MAPE to calculate the accuracy of a temperature forecast.
If just a single actual is zero, $A_t=0$... |
If the integral kernel $k(x, y)$ of an operator $T : C^\infty_c(M) \to \mathcal{D}'(M)$ is symmetric ($M$ is a compact manifold), then the operator $T$ is symmetric. Is the converse true? That is, given a self-adjoint $T$ which has an integral kernel $k(x, y)$, is $k(x, y) = k(y, x)$? A reference would be really apprec... |
Edited: Just realised my first post was somewhat misleading and not precise. Thanks to the two commetators that pointed it out.
I am working on an article and ended up wondering for which values of $\gamma>0$ does the following inequality hold:
$$\frac{\sum_iN_ic_{i,t}^\gamma}{\left(\sum_iN_ic_{i,t}\right)^\gamma}<\fra... |
$$\int_0^\pi x \ln(\sin (x))dx $$
I tried integrating this by parts but I end up getting integral that doesn't converge, which is this $$ \int_0^\pi \dfrac{x^2\cos (x)}{\sin(x)} \ dx$$ So can anyone help me on this one?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and p... |
Before answering the question more or less directly, I'd like to point out that this is a good question that provides an object lesson and opens a foray into the topics of
singular integral equations, analytic continuation and dispersion relations. Here are some references of these more advanced topics: Muskhelishvili,... |
Chapter 01: Number System
Notes (Solutions) of Chapter 01: Number System, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.
Contents & summary Rational numbers and irrational numbers Properties of real numbers Complex numbers Operation on complex numbers ... |
Hello, I've never ventured into char before but cfr suggested that I ask in here about a better name for the quiz package that I am getting ready to submit to ctan (tex.stackexchange.com/questions/393309/…). Is something like latex2quiz too audacious?
Also, is anyone able to answer my questions about submitting to ctan... |
$\textit{Square Root}$
Until now, the exponents (indices) have all been integers. In theory, an exponent (index) can be any number. We will confine ourselves to the case of exponents (indices) which are the rational number (fractions).
The symbol $\sqrt{x}$ means square root of $x$. It means, finds a number that multip... |
Standard Gibbs free energy of formation of liquid water at 298 K is −237.17 kJ/mol and that of water vapour is −228.57 kJ/mol. Therefore, $$\ce{H2O(l)->H2O(g)}~~\Delta G=8.43~\mathrm{kJ/mol}$$
Since $\Delta G>0$, it should not be a spontaneous process but from common observation, water
does turn into vapour from liquid... |
Silver is not as inert as gold. Tarnish is the name we give to the phenomenon when silver metal is oxidized and becomes a salt. Surfaces made of silver tend to disinfect themselves pretty quickly. As for disinfecting water poured into a silver cup, I imagine that would take a little longer since you have to wait for si... |
Assume that we have an already assigned Multiplicative Cyclic Group $\mathbb Z_p^*$ with order $q=p-1$, and $p$ is a prime number, is it possible to create a bilinear function $\hat{e}: \mathbb Z_p^* \times \mathbb Z_p^* \rightarrow \mathbb G_2$ with the property that follows:
$$\hat{e}(g^{a},g^{sb})=\hat{e}(g^{b},g^{s... |
Archive For The “Number Theory” Category
By DC Ipsen
The purpose of this publication is to teach how a whole figuring out of devices and dimensions presents an easy foundation for explaining features of actual description that differently could appear complicated or mysterious. the best way devices and dimensions behav... |
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Now showing items 11-20 of 165
Multiplicity dependence of the average transverse momentum in pp, p-Pb, and Pb-Pb collisions at the LHC
(Elsevier, 2013-12)
The average transverse momentum <$p_T$> versus the charged-particle multiplicity $N_{ch}$ was measured in p-Pb collisions at a collision energy per nucleon-nu... |
What about this we have two people A and B both born in February. I will make four cases:
Case1:Both born in a year with February with 28 day. this year has the probability 3/4 Hence we have the set which present their birthday day $\{(1,1) , (1, 2) , \cdots (28 , 28)\}$ This set has $28 \cdot 28$ days and $28$ element... |
We draw (and don't put them back) balls in a box that has $r$ red balls, $y$ yellow balls, $g$ green balls, $b$ blue balls and $w$ white balls. The game stop when we took twice balls of the same color. We are interested on the even
A : "The game stop after $k$ drawn and we drawn two red balls."
What is the probability ... |
Prove that the equation $n^a + n^b = n^c$, with $a,b,c,n$ positive integers, has infinite solutions if $n=2$, and no solution if $n\ge3$.
So this is fermats last theorem upside down? It occurs to me if we have two binary numbers we may add them to get another power of two,
1000000 1000000+ -------- 10000000
but if we h... |
For instance in Blumenhagen's CFT, there is a standard argument which determines that globally defined conformal transformations on the Riemann sphere where
$$l_n = -z^{n+1} \partial_z$$ is an element of the Witt algebra. In this argument we note that $l_n$ is non-singular at $z=0$ only for $n\geq -1$. Also substitutin... |
Quantum integer Set
context $f:{\mathbb N}\to{\mathbb R}$ definiendum $[n]_q \in \mathrm{it}$ inclusion $[n]_q:{\mathbb N}\to{\mathbb C}^*\to{\mathbb R}$ definition $[n]_q:=q^{-f(n)/2}\frac{1-q^n}{1-q}$ Discussion
These are $q$-deformations of integers, so that arithmetic coincides at $q=1$.
$[n]_{q} = q^{-f(n)/2}q^{-1... |
Definition:Morphism Property
Jump to navigation Jump to search
Some sources call this property the
Definition Then $\circ$ has the morphism property under $\phi$ iff: $\forall x, y \in S: \phi \left({x \circ y}\right) = \phi \left({x}\right) * \phi \left({y}\right)$ Also known as
Some sources call this property the
hom... |
I Am trying to derive the expression for the GRS test of the CAPM. I am following the book: The Econometrics Of Financial Markets by Campbell, Lo, McKinley (1997).
Define $Z_t$ as an $N×1$ vector of excess returns for N assets. We assume that the excess returns can be described by the following excess-return market mod... |
Both panel data and mixed effect model data deal with double indexed random variables $y_{ij}$. First index is for group, the second is for individuals within the group. For the panel data the second index is usually time, and it is assumed that we observe individuals over time. When time is second index for mixed effe... |
Here is a report of the Ray Tracer written by myself Christopher Chedeau. I've taken the file format and most of the examples from the Ray Tracer of our friends Maxime Mouial and Clément Bœsch. The source is available on Github.
Check out the
demo, or click on any of the images. Objects
Our Ray Tracer supports 4 object... |
This might look like a copy of another question, but what I'm about to propose here is new. There's this question,
Find the least positive integral value of n for which $(\frac{1+i}{1-i})^n = 1$
While solving, if we multiply what is within the bracket, by the conjugate of denominator and divide by the same thing, we ge... |
So I'm following Szabo's book "An Introduction to String Theory and D-brane Dynamics (2nd ed, 2011); still on the canonical treatment in chapter 3. After doing a mode expansion, we get (up to a constant) a set of nice ladder operators \begin{equation}[\alpha_m^\mu, \alpha_n^\nu] = m\delta_{m+n}\eta^{\mu\nu}\end{equatio... |
I decided to write this article from a question I saw in stackoverflow.com
Here the link to the question.
The questioner tries to write an algorithm to identify whether a “word” is a palindrome or it is not. The algorithm is written using the Java programming language
I do not want to analyze the algorithm proposed by ... |
Here's the work i've done to find the Maclaurin series. However, I'm having a very hard time finding a representation for the series using sum, n for the nth term, and x from g(x).
One way to get the "${+}{+}{-}{-}$" pattern is with $(-1)^{n(n-1)/2}$.
To alternate between $\sin(2)$ and $\cos(2)$: $$\sin(2)\frac{(-1)^n+... |
I am trying to understand Rømer's determination of the speed of light ($c$). The geometry of the situation is shown in the image below. The determination involves measuring apparent fluctuations in the orbital period of Io. (Jupiter's moon)
The Earth starts from point A. $r(t)$ is the distance between the Earth and Jup... |
Discussion on Bangladesh Mathematical Olympiad (BdMO) National
Moon Site Admin Posts: 751 Joined: Tue Nov 02, 2010 7:52 pm Location: Dhaka, Bangladesh Contact: Problem 10:
Consider a function $f: \mathbb{N}_0\to \mathbb{N}_0$ following the relations:
$f(0)=0$ $f(np)=f(n)$ $f(n)=n+f\left ( \left \lfloor \dfrac{n}{p} \ri... |
Given that $f\colon [-1,1] \to \mathbb{R}$ is a continuous function such that $ \int_{-1}^{1} f(t) \ dt =1$, how do I evaluate the limit of this integral: $$\lim_{n \to \infty} \int_{-1}^{1} f(t) \cos^{2}{nt} \,dt$$
What I did was to write $\cos^{2}{nt} = \frac{1+\cos{2nt}}{2}$ and substitute it in the integral so that... |
Don't be intimidated, semiclassical quantization is very simple, and it can be straightforwardly understood from a few examples which lead to the general case.
Consider a particle in a box. The classical motions are reflections off the wall. These make a box in phase space, as the particle goes left, hits the wall, goe... |
Welcome to the Kancolle Wiki! Currently account creation is by request only. Once you submit your request please wait 1-2 days for our administrators to process your request. You can also visit our IRC channel at #kancollewikito directly contact an administrator. Difference between revisions of "Sandbox/Plane Proficien... |
Calculate a value for the standard enthalpy of formation for liquid ethanethiol, $\ce{C2H5SH}$. Use the equation given below and enthalpy of combustion data from the following table.
Just assume values and comment the methods to solve the problem, I'll try solving it.
Edit: I'm not sure whether you're supposed to use
$... |
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