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One of the main lessons of category theory is that whenever you think about some kind of mathematical gadget, you should also think about maps
between gadgets of this kind. For example, when you think about sets you should also thin... |
I've heard a lot of definitions given for structural estimation. But it's never seemed entirely clear to me. Some times I've heard that what one person might call "reduced form" estimation should actually be called structural estimation. Sorry I don't have an example to illustrate, but I was wondering if somebody could... |
AliPhysics 1168478 (1168478)
Scripts used in the analysis Algorithms Corrections Monte-carlo code Mid-rapidity tracklet code for dN/deta Tasks Topical
file AliAODForwardMult.h Per-event \( N_{ch}\) per \((\eta,\varphi)\) bin. file AliFMDEventPlaneFinder.h file AliForwardUtil.h Various utilities used in PWGLF/FORWARD. f... |
Every geometry textbook has formulas for the circumference (\(C = 2 \pi r\)) and area (\(A = \pi r^2\)) of a circle. But where do these come from? How can we prove them?
Well, the first is more a definition than a theorem: the number \(\pi\) is usually
defined as the ratio of a circle’s circumference to its diameter: \... |
Evaluating the Determinant of a 2×2 Matrix
A determinant is a real number that can be very useful in mathematics because it has multiple applications, such as calculating area, volume, and other quantities. Here, we will use determinants to reveal whether a matrix is invertible by using the entries of a
square matrix t... |
Consider a static, complete information game with 2 players.
Strategy sets are $S_1=\{U,D\},S_2=\{l,m,r\}$.
Payoffs are irrelevant to this question as I am trying to get the concept of rationalizability correct.
Suppose I want to verify whether $m$ is a rationalizable strategy for player 2.
Then, I want to ask the foll... |
1. The rupee/coin changing machine at a bank has a flaw. It gives 10 ten rupee notes if you put a 100 rupee note and 10 one rupee coins if you insert a 10 rupee note but gives 10 hundred rupee notes when you put a one rupee coin!Sivaji, after being ruined by his rivals in business is left with a one rupee coin and disc... |
Abstract
The differential branching fraction of the decay Λ0b→Λμ+μ− is measured as a function of the square of the dimuon invariant mass, q2. A yield of 78±12 Λ0b→Λμ+μ− decays is observed using data, corresponding to an integrated luminosity of 1.0\,fb−1, collected by the LHCb experiment at a centre-of-mass energy of 7... |
Thermalization Time Bounds for Pauli Stabilizer Hamiltonians 103 Downloads Citations Abstract
We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of
N-qubits, serve as on... |
To round off our series on round objects (see the first and second posts), let’s compute the sphere’s surface area. We can compute this in the same way we related the area and circumference of a circle two weeks ago. Approximate the surface of the sphere with lots of small triangles, and connect these to the center of ... |
Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\beta_2\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.
Basis of coefficient ring in terms of a root \(\nu\) of \(x^{3}\mathstrut -\mathstrut \) \(x^{2}\mathstrut... |
What 'exactly' is power spectral density for discrete signal? I was always under the assumption that taking the Fourier transform of the signal, and then the ratio of desired freq range magnitude over entire freq range gives the power ratio for that freq range which is the same as power spectral density. Is that wrong?... |
I am trying to diagonalize hubbard model in real and K-space for spinless fermions. Hubbard model in real space is given as: $$H=-t\sum_{<i,j>}(c_i^\dagger c_j+h.c.)+U\sum (n_i n_j)$$ I solved this Hamiltonian using MATLAB. It was quite simple. t and U are hopping and interaction potentials. c, $c^\dagger$ and n are an... |
[latex]
\quicklatex{color=”#000000″ size=100}
{A^{d}\alpha}\oint_r u_i \cdot T!}
[/latex]
Yesterday, I published a post about opamps here on the blog. This post utilized a new feature here at Adafruit: rendered LaTeX equations. For those that are unfamiliar, LaTeX is a markup language for the TeX system, originally dev... |
1.
Nope. For example, in Minkowski spacetime, consider the vector $(v^\mu)=(1,0,0,1)$, which is a null vector. The vector $ (u^\mu)=(0,1,0,0) $ is orthogonal to it, yet, it is not a null vector.
2.
I don't understand this question.
3.
Consider a null geodesic with tangent vector $u^\mu$ ($u^\mu u_\mu$=0). Let $\lambda$... |
Your confusion really just comes down to understanding the notation that is widely used for partial derivatives.
For simplicity, I'll restrict the discussion to a system with one coordinate degree of freedom $x$. In this case, the Lagrangian is a real valued function of two real variables which we suggestively
label by... |
A friend of mine asked me a question, which I considered trivial at first, but after a while gave rise to some doubts.
For instance, we have a potential well in 1 dimension defined by $$ V(x)= \begin{cases} +\infty &\text{if}& x<0 \text{ and } x>L\\ 0 &\text{if} &0\leq x\leq L \end{cases} $$ We know the wave function t... |
I am trying to understand the solution of the optimization problem in geometric PCA. In my lecture notes I have the following:
Given $$\{x_{1}, ..., x_n\}\in\mathbb{R}^{D}$$ we seek a low-dim representation $$\{y_1, ..., y_n\}\in\mathbb{R}^d$$ such that: $$x_i=Uy_i+\epsilon_i\ \ where\ \ U=[u_1, ..., u_d]\in\mathbb{R}^... |
1)
Off-shell vs. on-shell action. What may cause some confusion is that Noether's theorem in its original formulation only refers to the off-shell action functional
$$\tag{1} I[q;t_i,t_f]~:=~ \int_{t_i}^{t_f}\! {\rm d}t \ L(q(t),\dot{q}(t),t), $$
while Feynman's proof [1]$^1$ mostly is referring to the
Dirichlet on-she... |
Imagen de los τ-Productos Author
Calderón Gómez, José Emilio
AdvisorOrtiz Albino, Reyes M. CollegeCollege of Arts and Sciences - Art DepartmentDepartment of Mathematics TypeThesis Degree LevelM.S. Date2019-05-15 MetadataShow full item record Abstract
The theory of $\tau$-factorizations, also known as theory of generali... |
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 ... |
Can ordinary least squares estimation be considered an optimization technique? If so, how can I explain this?
Note:
From an AI perspective, supervised learning involves finding a hypothesis function $h_\vec{w}(\vec{x})$ that approximates the true nature between predictor variables and the predicted variable. Let some s... |
Definition:Path-Connected/Topology Contents Definition
Let $T = \left({S, \tau}\right)$ be a topological space.
Let $a, b \in S$ be such that there exists a path from $a$ to $b$.
That is, there exists a continuous mapping $f: \left[{0 \,.\,.\, 1}\right] \to S$ such that $f \left({0}\right) = a$ and $f \left({1}\right) ... |
I saw this lovely tweet from PGS yesterday:
Our basin studies team spotted this on fast-track imaging from Republic of Guinea. A 7.5 km diameter depression, with no salt or mobile shale, nor dissolution of fluid escape. We interpreted the structure as a complex meteorite impact crater. https://t.co/Z4TUOtsv54 #meteorit... |
Relation concatenation Set
context $ R \in \text{Rel}(X,U) $ context $ S \in \text{Rel}(V,Y) $
definiendum $ \langle x,y \rangle \in S\circ R $
postulate $ \exists m.\ \langle x,m \rangle \in R \land \langle m,y \rangle \in S $ Discussion
Concatenations/compositions are associative.
A mayority of uses of the relation c... |
Question
Let $R$ be the complex plane with the non positive real axis taken out.
Find explicitly a conformal mapping $f$ of $R$ onto the unit disc $U$ such that $f(1)=0$ and $f'(1)\gt 0$
solution:
We know that all automorphism of the unit disk are of the form:
$$f(z)=e^{i\theta}\frac{z-\alpha}{1-\overline{\alpha}}$$ fo... |
L # 1
Show that
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
Last edited by krassi_holmz (2006-03-09 02:44:53)
IPBLE: Increasing Performance By Low... |
k-partite graph
Set
context $k\in\mathrm N$ context $V$ … set
definiendum $\langle V,E\rangle \in \mathrm{it}(E,V) $
inclusion $ \langle V,E\rangle $ … undirected graph
range $ i,j\in\{1,\dots,k\} $ range $ \bigcup_i X_i=V $ range $ \forall i,j.\ X_i\cap X_j=\emptyset $ range $ v,w\in V $
postulate $\exists X_1,\dots,X... |
It is "well known" that
on the hand there is a "cubical line bundle" governing the fine structure of the Chern-Simons term in 11-dimensional supergravity/M-theory;
on the other hand just such "cubical lines" on elliptic curves induce the elliptic cohomology refinement of the partition function of the heterotic string.
... |
[This is the 6th post in the current series about Wythoff’s game: see posts #1, #2, #3, #4, and #5.
Caveat lector: this post is a bit more difficult than usual. Let me know what you think in the comments!]
Our only remaining task from last week was to prove the mysterious Covering Theorem: we must show that there is ex... |
Atoms on the corners, edges, and faces of a unit cell are shared by more than one unit cell.
An atom on a face is shared by two unit cells $\implies$ half an atom belongs to each unit cell.
An atom on the edge is shared by four unit cells
and an atom on the corner is shared by eight unit cells
What does this have to do... |
GEOMETRY
GEOMETRY
Geometry is derived from two greek words "Geo" means "Earth" metron means "Measurement". That means measurement of Earth is called geometry.
Basics terms of geometry
There are three basics undefined terms of geometry.
(i) Point (ii) Line (iii) Plane
Point: Point is a mark of position, it is made by sh... |
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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 ... |
Measure Theory Notes by Anwar Khan
Name Measure Theory: Notes Provider Mr. Anwar Khan Pages 169 pages Format PDF (see Software section for PDF Reader) Size 7.75 MB Partial contents Algebra on $X$ Sigma Algebra i.e. $\sigma-$algebra on $X$ Trivial $\sigma-$algebra; Largest $\sigma-$algebra Increasin & sequence of sets D... |
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Session 67 - Stars: Evolution, Atmospheres, Intrinsic.
Display session, Thursday, June 11
Atlas Ballroom,
We report on a rich set of observations of the K0 III star \beta Geminorum (Pollux) with the Goddard High-Resolution Spectrograph (GHRS). The dataset consists of low-dispersion spect... |
Complex Networks Toolbox (NetLogo) Introduction Interface Scripts Generators Global Measures Utilities Dynamics Input/Output
This NetLogo model is a toy tool to launch experiments for (small)
Complex Networks.
It provides some basic commands to generate and analyze small networks by using the most common and well-known... |
In some of Boundary value problems involving ordinary differential equations,, subsidiary conditions are imposed locally. In some other cases, nonlocal conditions are imposed.
In this paper: Existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem Byszewski studied ... |
Notes of Introduction to Statistical Learning
=====================================
## Statistical Learning
- basic concepts
- two main reasons to estimate f: prediction and inference
- trade-off: complex models may be good for accurate prediction, but it may also be hard to interpret
- reducible vs. irreducible error
... |
I'm in trouble with the exercise problem iii.12.3 in Hartshorne's AG.
Let $X_{1}$ be a rational normal curve in $\mathbb{P^4}$ ( = image of 4th veronese embedding of $\mathbb{P^1}$).
$X_{0}$ be a rational quartic curve in $\mathbb{P^3}$ with parametrization $[t^4, t^3u, tu^3, u^4]$.
Construct flat family $X$ using proj... |
In the end, the choice of a single specific number comes from the necessity to standardize.However, we can make some physical observations to understand why that final choice had to fall in a certain range.
Why a standard?
First of all, why do we even need a standard?Can't individual appliances convert the incoming ele... |
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History and Feedback Elliott Fletcher 2 years, 2 months ago
This is a really good question, i just have a couple of comments
Main Parts
a) and b) i would use a \displaystyle before the fractions in the questions to make the fractions look bigger.
Advice
a) in the ve... |
Hask Note todo: objects are types arrows are extensionally identified Haskell functions identity morphism: for each object, the identity morphism is the instance of the polymorphic identity for that type The identity for a type 'a' is '(id :: a→a)' and concatenation is 'f . g', defined as '\x → f (g x)'. Discussion
Has... |
Event detail Probabilistic Operator Algebra Seminar: An introduction to monotonic independence
Seminar | October 2 | 3:45-5:45 p.m. | 748 Evans Hall
Ian Charlesworth, NSF Postdoctoral Fellow UC Berkeley
One may think of an "independence relation" as a prescription for building joint distributions of (non-commutative) r... |
Asymptotic expansion of the mean-field approximation
1.
CMLS, Ecole polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau Cedex, France
2.
International Research Center on the Mathematics and Mechanics of Complex Systems, MeMoCS, University of L'Aquila, Italy
We consider the $ N $-body quantum evolution of a pa... |
Chandrasekhar Venkat Raman
Chandrasekhar Venkat Raman, also known as Sir CV Raman, was a Physicist, Mathematician and a Nobel Laureate. Venkat (his first name) was a Tamil Brahmin and was the second of the eight children of his parents. He was born at Thiruvanaikaval, near
Tiruchirappalli on 7th November 1888. He was t... |
@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... |
Positive measurable numerical function Set
context $ \langle X,\Sigma_X\rangle\in \mathrm{MeasurableSpace}(X) $
postulate $f\in \mathcal M^+$
context $f\in \mathrm{Measurable}(X,\overline{\mathbb R})$
$x\in X$
postulate $f(x)\ge 0$ Discussion
For the definition of the integral, it's crucial to know that for every $f\in... |
I love comments and feedback. I always wait for a comment to be appeared on my dashboard and the things to pop in my mailbox. Below are some easy guidelines to comment better:
Be polite. Write to the topic. You may not use objectionable words, however critics and spicy comments are always welcomed. If you didn’t unders... |
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Now showing items 1-2 of 2
Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
It looks like you're new here. If you want to get involved, click one of these buttons!
One of the main lessons of category theory is that whenever you think about some kind of mathematical gadget, you should also think about maps
between gadgets of this kind. For example, when you think about sets you should also thin... |
It looks like you're new here. If you want to get involved, click one of these buttons!
I've spent four lectures on the logic of partitions; you may be wondering why. One reason was to give you examples illustrating this important fact:
Theorem. Left adjoints preserve joins and right adjoints preserve meets. Suppose \(... |
On wikipedia I can find that a de Sitter-space has maximal symmetry and a constant curvature. Recently the interest of de Sitter spaces has increased as it could serve as a model for the universe, an universe which has (almost) no matter density, however a sensible non-zero value of the cosmological constant (large amo... |
Stability of ground states for logarithmic Schrödinger equation with a $δ^{\prime}$-interaction
Department of Mathematics, IME-USP, Cidade Universitária, CEP 05508-090, São Paulo, SP, Brazil
$δ^{\prime}$
$i{\partial _t}u + \partial _x^2u + {\rm{ }}{\gamma ^\prime }(x)u + u{\mkern 1mu} {\rm{Log|}}u|2 = 0,(x,t) \in \math... |
Maybe a little sketch maybe helpful here.
Consider a one dimensional case first
$$\ln y = \alpha_0 + \alpha_1 \ln x + \frac{1}{2}\beta_{11}\ln^2x \tag{1}$$
At first order (that is, ignore $\ln^2 x$), note that
$$\frac{{\rm d}\ln y}{{\rm d}\ln x} = \alpha_1 \tag{2}$$
i.e. $\alpha_1$ is just the logarithmic slope of the ... |
Lipschitz function
Let a function $f:[a,b]\to \mathbb R$ be such that for some constant M and for all $x,y\in [a,b]$ \begin{equation}\label{eq:1} |f(x)-f(y)| \leq M|x-y|. \end{equation} Then the function $f$ is called Lipschitz on $[a,b]$, and one writes $f\in \operatorname{Lip}_M[a,b]$.
The concept can be readily exte... |
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... |
If you are aware of elementary facts of geometry, then you might know that
the area of a disk with radius $ R$ is $ \pi R^2$ .
The radius is actually
the measure(length) of a line joining the center of disk and any point on the circumference of the disk or any other circular lamina. Radius for a disk is always same, ir... |
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Now showing items 1-10 of 26
Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
If you only need to pick 5 out of 10 and want equal weights then just enumerate all 252 possibilities (as pointed out above) and compute the portfolio volatility
$(\textbf{1}'K^{(i)}\textbf{1})^{1/2} = \left( \sum_{ij}K^{(i)}_{ij} \right)^{1/2}$,
where $K^{(i)}$ is the covariance matrix for the $i$th subset. Then use w... |
What is Variance in Statistics?
Variance meaning – It is a measure of how data points differ from the mean. According to layman’s terms, it is a measure of how far a set of data( numbers) are spread out from their mean (average) value.
For the purpose of solving questions, it is,
Var (X) = E[ ( X – \(\mu\)))
2]
Put int... |
One can construct a Chebyshev series approximation to the integrand for an interval, such as
-5 <= x <=5 mentioned in the comments, and integrate it to get a series expansion for the integral. It is well known that Chebyshev series representation have numerical advantages over power series. I saw a comment about a NPU-... |
I've been reading up on the internet as to why the sky is blue. The answer usually cites Rayleigh scattering that I've checked on wikipedia: https://en.wikipedia.org/wiki/Rayleigh_scattering:
$$ I=I_0 \frac{1+\cos^2\theta}{2R^2}\left(\frac{2\pi}{\lambda}\right)^4\left(\frac{n^2-1}{n^2+2}\right)^2\left(\frac{d}{2}\right... |
№ 9
All Issues Volume 60, № 9, 2008
Ukr. Mat. Zh. - 2008. - 60, № 9. - pp. 1155-1156
Ukr. Mat. Zh. - 2008. - 60, № 9. - pp. 1157–1167
We study the relationship between the (min, max)-equivalence of posets and properties of their quadratic Tits form related to nonnegative definiteness. In particular, we prove that the T... |
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Session 12 - Cosmology, Large-Scale Structure and Distance Scales.
Display session, Monday, June 10
Great Hall,
The production of LiH in the postrecombination epoch was previously investigated by Stancil et al. (1996, ApJ, 458, 401) who incorporated quantal rate coefficients for the (spo... |
The integral formula for the Moyal/Groenewold $*$ product in Ref. 1 reads
$$\tag{1} (f * g)(y)~=~\int_{\mathbb{R}^4} \! d^2u~d^2v~ \exp \left[i u_{\alpha} \epsilon^{\alpha\beta} v_{\beta}\right]f(y+u)g(y+v).$$
Remark: The argument $u_{\alpha} \epsilon^{\alpha\beta} v_{\beta}$ inside the exponential of the integral form... |
Analytic Signal
In communication theory and modulation theory we always deal with two phases: In-phase (I) and Quadrature-phase (Q). The question that I will discuss in this blog is that why we use two phases and not more.
Any real band-limited signal along with its Hilbert transformed pair form an analytic signal. We ... |
Ten Little Algorithms, Part 2: The Single-Pole Low-Pass Filter
Other articles in this series:
Part 1: Russian Peasant Multiplication Part 3: Welford's Method (And Friends) Part 4: Topological Sort Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method Part 6: Green’s Theorem and Swept-Area Detection
I’m wri... |
AI News, MachineLearning MachineLearning
So for example, it may have 25 inputs which are gray-levels of a 5x5 image and a single output that should, for example, tell whether a cat is in the image or not.
If you are familiar with linear algebra you will notice that this can be done with the dot product of the normal ve... |
I would like to solve the following nonlinear PDE:
$$ \frac{\partial^2 \phi}{\partial x^2} - \frac{\partial^2 \phi}{\partial t^2} = \lambda |\phi|^2 \phi $$
I was trying:
NDSolve[{D[f[x, t], x, x] - D[f[x, t], t, t] == f[x, t]^3, f[x, 0] == Sin[2*Pi*x], f[0, t] == 0, f[1, t] == 0}, f, {x, 0, 1}, {t, 0, 1}]
but, I am co... |
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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 ... |
What is Fluid Dynamics?
What is computational fluid dynamics? Applications of fluid dynamics
Fluid Dynamics can be applied in the following ways:
Fluid dynamics is used to calculate the forces acting upon the aeroplane. It is used to find the flow rates of material such as petroleum from pipelines. It can also be used ... |
Intersection Set
context $X,Y\in\mathfrak U$ definiendum $ x\in X \cap Y $ postulate $ x\in X \cap Y \Leftrightarrow (x\in X\land x\in Y) $ Discussion
$ X \cap Y $ is commutative and idempotent.
The intersection and union are associative and distributive with respect to another.
Reference
Wikipedia: Intersection |
Many of us are familiar with the word problem, but are we aware of the fact and problems related to variables and constants? When we say 5 it means a number but what if we say x=5 or 5y or something like that?
This is where algebra came into existence algebra is that branch of mathematics which not only deals with numb... |
We have discussed how to calculate the probability that an event will happen. Sometimes, we are interested in finding the probability that an event will
not happen. The complement of an event [latex]E[/latex], denoted [latex]{E}^{\prime }[/latex], is the set of outcomes in the sample space that are not in [latex]E[/lat... |
Suppose a fashion designer traveling to Milan for a fashion show wants to know what the temperature will be. He is not familiar with the
Celsius scale. To get an idea of how temperature measurements are related, he asks his assistant, Betty, to convert 75 degrees Fahrenheit to degrees Celsius. She finds the formula
and... |
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I've spent four lectures on the logic of partitions; you may be wondering why. One reason was to give you examples illustrating this important fact:
Theorem. Left adjoints preserve joins and right adjoints preserve meets. Suppose \(... |
I'm wondering is that possible to get insignificant beta estimates in the time-series context, but highly significant risk premium associated with that beta in the cross-sectional regression?
Any help would be greatly appreciated!
Quantitative Finance Stack Exchange is a question and answer site for finance professiona... |
The scalar QED Lagrangian in your question is for a complex scalar field $\psi(x)$ interacting with an electromagnetic field given by potential $A_{\mu}(x)$. At any point $x$, the scalar field is a complex number. We model this situation by constructing a space - a
vector bundle $V$ - which is isomorphic to $M \ X \ \m... |
I like to think of QFT Weinberg-style: particles come first, and fields come later; and the latter are constructed so as to describe the former. Fields are not to be thought of as fundamental, but only as convenient tools to study particles.
In this setting, what justifies the postulate that a fermion particle must be ... |
This is a question that I have thought about myself, but I'm struggling a bit regarding how to answer it.
This is my question:
Imagine we have a universe with 3 bodies. Out of these 3, 2 are identical and massive, and 1 is small and insignificant. The 2 identical celestial bodies are literally identical in every way po... |
There is a saying “a good compromise makes no one happy”. As distressing as that may be, I guess most people still think it is a good idea to seek the best agreement. The problem though, is to define the measure in which the word “best” gets a meaning. Let us consider $n$ people, each with a firm belief on $m$ differen... |
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1. Measurement of exclusive γγ→ℓ+ℓ− production in proton–proton collisions at s=7 TeV with the ATLAS detector
Physics Letters B, ISSN 0370-2693, 10/2015, Volume 749, Issu... |
I notice if I put heat under a laser beam it will cause the beam to shimmer. The heated air is causing a disturbance in the air which affects the light. Yet, I can blast a stream of air from a compressor across the beam and there is no effect on the light. What’s going on?
Heat ripples the light beam because the temper... |
I am trying to compute the dBFS value of a group of samples (stereo wave file), according to this formula:
$$p_{RMS} = \sqrt{\frac{ x_1^2 + x_2^2 + \ldots}n } $$ $$dbFS = 20\log_{10}\frac{ p_{RMS}}{p_{max}}$$
The value I get is wrong, and not stable (I am using a stereo constant -18dbFS 1000H sinewave audio file). I kn... |
One thing you should learn, is that analysts like to think of functions as power series (or at worst Laurent series) In this sense, L'Hopital's rules is essentially saying that "When we have a function $ \frac {(x-7)f(x)}{(x-7)g(x)}$, then we can 'fill in' the hole and carry along our own merry way".
So, if we don't ha... |
SolidsWW Flash Applet Sample Problem 1
Line 6: Line 6:
</p>
</p>
<p style="background-color:#93BED2;border:black solid 1px;padding:3px;">This applet and WeBWorK problem are based upon work supported by the National Science Foundation under Grant Number DUE-0941388.</p>
<p style="background-color:#93BED2;border:black so... |
Given $q = e^{2\pi i \tau}$ and the Eisenstein series $E_{2k}(\tau)$, i.e.,
$$E_2(\tau) = 1-24\sum_{n=1}^\infty \frac{n q^n}{1-q^n}$$
$$E_4(\tau) = 1+240\sum_{n=1}^\infty \frac{n^3 q^n}{1-q^n}$$
and so on. Define the function,
$$F_{2k}(\tau) = \frac{E_{2k}(\tau)}{\left(E_2(\tau)-\frac{3}{\pi\; \Im(\tau)}\right)^k}$$
fo... |
1.A watch is sold for Rs.440 cash or for Rs.200 cash down payment together with Rs.244 to be paid after one month. Find the rate of interest charged in the installment scheme.
a. 10%
b. 15%
c. 20%
d. 25%
Answer: C
Explanation:
Principal for the next month = 440 - 200 = 240 Amount paid after next month = 244 Therefore i... |
> **Puzzle 71.** Can you make the complex numbers, ℂ, into a commutative monoidal poset with the usual + and 0 and some concept of ≤? If so, how many ways can you do this?
We can always just do \\(x \preceq_1 y \iff \mathfrak{Re}(x) \leq \mathfrak{Re}(y)\\) where \\(\mathfrak{Re}(x)\\) is the real component of \\(x\\).... |
Denote $[r]\triangleq\{1,2,\ldots,r\}$.
Consider a game with $n$ players, $[n]$, each has $m$ strategies, $[m]$.
Each player $i$ has an associated payoff function, which considers only his selected strategy, and the number of players selected the same strategy: $$U_i:[m]\times[n]\to[0,1]$$
Furthermore, the utility func... |
broall wrote:
EgmatQuantExpert wrote:
What is the product of all values of x that satisfies the equation: \(\sqrt{5x} + 1= \sqrt{(7x - 3)}\) ?
A. 9 B. 11 C. 49 D. 99 E. None of the above
First, make sure that \(\sqrt{5x}\) and \(\sqrt{7x-3}\) have real value so \(x \geq 0\) and \(x \geq \frac{3}{7}\). Hence \(x \geq \f... |
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Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c ... |
Geophysicists often assume that the earth is
isotropic. This word comes from 'iso', meaning same, and 'tropikos', meaning something to do with turning. The idea is that isotropic materials look the same in all directions — they have no orientation, and we can make measurements in any direction and get the same result. ... |
Specifically, we offer a choice of FHE schemes based on the learning with error (LWE) or ring-LWE (RLWE) problems that have $2^\secparam$ security against known attacks. For RLWE, we have:
1. A leveled FHE scheme that can evaluate $L$-level arithmetic circuits with $\tilde{O}(\secparam \cdot L^3)$ per-gate computation ... |
Difference between revisions of "Stiffened equation of state"
(fixed typo in las formula)
Line 20: Line 20:
It is useful to notice that, given this equation of state, the [[adiabatic]] law is modified from its ideal form:
It is useful to notice that, given this equation of state, the [[adiabatic]] law is modified from ... |
Equivalence Class of Element is Subset
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Theorem $\forall x \in S: \eqclass x {\mathcal R} \subseteq S$ Proof
\(\displaystyle y\) \(\in\) \(\displaystyle \eqclass x {\mathcal R}\) \(\displaystyle \leadsto \ \ \) \(\displaystyle \tuple {x, y}\) \(\in\) \(\displaystyle \mathcal R\) Definit... |
In last week’s discussion of proofs by contradiction and nonconstructive proofs, we showed:
Theorem: There exist irrational numbers \(x\) and \(y\) with the property that \(x^y\) is rational.
However, our proof was
nonconstructive: it did not pinpoint explicit values for \(x\) and \(y\) that satisfy the condition, inst... |
I would like to monitor step by step running of ECDSA.
Parameters I am working on:
The elliptic curve satisfies the equation: $y^2 = x^3 + x + 1$. I picked up the base point $G$ as: $(0, 1)$ Finally, the modulo $p$ is $977$
My private key is $19$. Thereby, my public key is equal to $19\times G$ and its coordinates are ... |
Use Inclusion-Exclusion to determine the number of integer solutions to the equation
$$x_1+x_2+x_3+x_4=14$$
Where $0{\leq}x_1{\leq}8; 0{\leq}x_2{\leq}5; x_3, x_4{\geq}0$.
My thought process:
I can disregard the last two restrictions because those two are given since the combination gives the number of nonnegative integ... |
Single mode
Suppose I have two $LC$ oscillators, one with $L_1$ and $C_1$, and the other with $L_2$ and $C_2$. If uncoupled, each oscillator has resonant frequency $\omega \equiv 1/\sqrt{LC}$. Using the flux in the inductor as the coordinate, the equation of motion for each oscillator is
$$\ddot{\Phi} = -\omega^2 \Phi ... |
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