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To describe the evolution of a (in this example non-relativistic) fluid system, the evolution equations for all relevant variables, conservation laws, the second law of thermodynamics, and appropriate (a)n appropriate equation(s) of state have to be considered.
The evolution equation for momentum is the Navier-Stokes e... |
Let's assume, we have standard model singlet particle $s$, that mixes after electroweak symmetry breaking with an exotic, vectorlike neutral lepton $N$. The relevant part of the Lagrangian reads
$$ L \supset h^c s N + h s N^c + M N N^c, $$
where $h$ is the standard model higgs and $M$ is a superheavy mass. Moreover, we... |
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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... |
Lecture: HGX208, F 9:55-11:35
Section: HGX208, T 18:30-20:10
Lecture: H5116, F 8:00-9:40
Section: HGW2403, F(e) 18:30-20:10
Textbook: https://doi.org/10.1017/CBO9781107050884
Lecture: HGX205, M 18:30-21
Section: HGW2403, F 18:30-20 Exercise 01 Prove that \(\neg\Box(\Diamond\varphi\wedge\Diamond\neg\varphi)\) is equival... |
I came across Shimura (1971) notes about cosets representatives of the congruence subgroups $ \Gamma_0(N) $. He firstly proves that its index in the modular group $\Gamma$ is
\begin{equation} [\Gamma : \Gamma_0(N)]=N \cdot \prod_{p|N} (1+p^{-1} ) \end{equation}
Then he comes up with a sets of cosets representatives for... |
Ex.14.1 Q4 Statistics Solution - NCERT Maths Class 10 Question
Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarised as follows. Find the mean heart beats per minute for these women, choosing a suitable method.
Number of heart beats per minute \(65 – ... |
If you haven’t seen the previous blog, or not familiar with Hoeffding bounds, I suggest you read about it. This blog goes head first into the continuation of the previous blog here.
A hypothesis, can be
thought of as a function. However, it’s not necessary. A function maps something to something else, like $f: \Re^n \t... |
the measurement affects the position of the body
To be clear a so called measurement doesn't reveal some preexisting value, it is an interaction that happens continuously over time and leaves the resulting state in one of many fixed final states. Each of which has a real number associated with it.
mean that the positio... |
In order to prove a certain function to be partially computable, I need to show an $\mathbb S$-program that computes it. I could really use the predicate $X \in B$ in my program to draw my conclusion. To give you the idea of what I am dealing with here it is one of my problems:
Give an infinite set $B$ such that $\Phi(... |
Here's a more compact and mathematical description of what is going on. Let $a$ and $b$ be the input, already reduced modulo $m$, so $a < m$ and $b < m$. (Code-wise, this means after the
b %= m line.) We want to calculate $ab \mod m$, which is to say, setting $x=ab$, we want to find $r_x$ such that $x = q_xm + r_x$ for... |
Regularity of 3D axisymmetric Navier-Stokes equations
School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
In this paper, we study the three-dimensional axisymmetric Navier-Stokes system with nonzero swirl. By establishing a new key inequality for the pair $(\frac{ω^{r}}{r},\frac{ω^{θ}}{r})$, we... |
So, here's a question and a solution to part b). I do not understand why they make $y^{1/2}$ belong to interval $[0,1)$ and then
separately to the interval $[1,3)$.
You have $X\sim \mathcal U(-1;3)$ and $Y=X^2$
Now $Y\in(0;1)$ when $X\in(-1;0)$ and also when $X\in(0;1)$. So this interval for $Y$ is mapped to by two int... |
Let's assume the basic nouns of our language to describe the physical world are the members of Lie groups. Okay, this is a pompous-sounding statement and somewhat arbitrary, but my justification is that these objects describe all the
continuous symmetries there can be, and almost every clarification of physics using ma... |
I am trying to follow the proof of Lemma 9.2 (Certain prerequisite lemma to prove a maximum principle) of the Book of Gilbarg and Trudinger and I am having certain difficulties with an assertion in the proof. It is the following
Let's take a function $u:\Omega\subset\mathbb{R}^n\rightarrow \mathbb{R}$ belonging to the ... |
When I was trying to find closed-form representations for odd zeta-values, I used $$ \Gamma(z) = \frac{e^{-\gamma \cdot z}}{z} \prod_{n=1}^{\infty} \Big( 1 + \frac{z}{n} \Big)^{-1} e^{\frac{z}{n}} $$ and rearranged it to $$ \frac{\Gamma(z)}{e^{-\gamma \cdot z}} = \prod_{n=1}^{\infty} \Big( 1 + \frac{z}{n} \Big)^{-1} e^... |
Suppose $A$ and $B$ are two $R-$algebras, where $R$ is a commutative ring with $1$. There are natural algebra homomorphisms $\ a \to a \otimes 1 \ $ and $ \ b \to 1 \otimes b \ $ from $A$ and $B$ to $A \otimes_{R} B$.
Are these homomorphisms injective?
Consider the first homomorphism. If $a_1 \neq a_2$ then we want $(a... |
I'm having a trouble understanding the concept. Can you give me a math example where $P\Rightarrow Q$ Is true but $P\Leftrightarrow Q$ is false? Thank you.
Set theory example: let be $A\subset B$ with $A\ne B$. $$x\in A\implies x\in B$$ but $$x\in B\kern.6em\not\kern -.6em \implies x\in A.$$
Almost all the examples of ... |
This shows you the differences between two versions of the page.
monoidal_t-norm_logic_algebras [2010/07/29 15:46]
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Line 4: Line 4: ====Definition==== ====Definition==== - A \emph{monoidal t-norm logic algebra} is a [[ FL$_{ew]]$-... |
2019-10-09 06:01
HiRadMat: A facility beyond the realms of materials testing / Harden, Fiona (CERN) ; Bouvard, Aymeric (CERN) ; Charitonidis, Nikolaos (CERN) ; Kadi, Yacine (CERN)/HiRadMat experiments and facility support teams The ever-expanding requirements of high-power targets and accelerator equipment has highligh... |
No. String theory's resolution of the old paradox is a sign of the hidden cleverness of string theory. After he read some of my essays on the electron's spin, Tom W. Larkin asked an interesting question: Does string theory resolve the paradox of (post-)classical physics that the electron, if imagined as a spinning ball... |
Would a high voltage ( of the order of a few score kV ) drive electrolysis?
Or, does it require a large current and low voltage? Alternatively, does electrolysis require both large voltage & large current?
Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the fi... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
It is known that the spiral phyllotactic pattern is common in Nature, especially in Botany.
It consists of two group of clockwise and anticlockwise spirals, starting from the center. In most cases the number of those spirals are two consecutive Fibonacci numbers: $F_n, F_{n+1}$. Also there are patterns where number of ... |
Schützenberger promotion, studied (for example) in Richard Stanley,
Promotion and Evacuation, 2009, is a permutation of the set of all linear extensions of a finite poset. Since one can identify the linear extensions of a poset with saturated chains of order ideals in that poset, this allows one to also view Schützenbe... |
I want to find analog of following two statements.
Let $G$ be a discrete group, $M$ is representation of $G$. Local systems on $BG$ are the same as $G$ representations (because $\pi_1 (BG) =G$). Let $\mathscr{M}$ be a local system corresponding to $M$. $$ H^{\bullet}_{Grp} (G, M) = H^{\bullet} (BG, \mathscr{M})$$
Let $... |
We would have to know more about the ice we want to build the wall with.
For example, for ice in icesheets, you have an ice which effectively reaches a plastic region of the stress strain curve at around $0,5 MPa$. I am not a geologist, but I believe that the glaciers can be only thicker than $\sim 50 m$ thanks to it's... |
Linear mixed fluid-structure interaction system¶
This tutorial demonstrates the use of subdomain functionality and show how to describe a system consisting of multiple materials in Firedrake.
The model considered consists of fluid with a free surface and an elastic solid. We will be using interchangeably notions of flu... |
Since moving to a Mac a bit over a year ago, I've had only a few reasons to look back (the business with the HP LJ1022 printer being one of them). I'm now rather close to the end of my tether, and the reason is fonts.
As an academic and a computer scientist, I end up writing quite a lot of papers and presentations with... |
Yes, it is possible to render the process stationary regardless of whether thenon-stationary cycles are related to real or complex roots.
For example, the following seasonal random walk:
$$y_t = y_{t-4} + \epsilon_t \quad \epsilon_t \sim NID(0, \sigma^2) \,,$$
contains four unit roots: $\pm 1, \pm i$ (i.e., 2 real and ... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
I'm trying to write a module. Its input is a matrix (tensor), the module should return new tensor with increased rank with 1. The new tensor is defined as$$O \Rightarrow N_{\alpha \beta \ldots \sigma}^{\gamma \delta \ldots}=\frac{\partial}{\partial x^{\sigma}} O_{\alpha \beta \ldots}^{\gamma \delta \ldots}$$ where $O$ ... |
This shows you the differences between two versions of the page.
congruence_regular [2010/08/20 20:14]
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congruence_regular [2010/08/20 20:14] (current)
jipsen
Line 2: Line 2: An algebra is \emph{congruence regular} if each congruence relation of the algebra is An algebra is \emph{congruence regular} if ea... |
OpenCV 3.4.8-dev
Open Source Computer Vision
In this chapter,
In last chapter, we saw that corners are regions in the image with large variation in intensity in all the directions. One early attempt to find these corners was done by
Chris Harris & Mike Stephens in their paper A Combined Corner and Edge Detector in 1988... |
Consider the following properties for a subset $A$ of $\mathbb{N}$:
(1) $A$ is large: $\sum_{n \in A}$$ 1\over n$$=\infty,$ (2) $A^\infty=\limsup \frac{|A \cap \{ 1, \dots, n\}|}{n} >0$, (3) $A_\infty=\liminf \frac{|A \cap \{ 1, \dots, n\}|}{n} >0.$
By a conjecture of Erdős-Turán, if $A$ is large, then it contains arit... |
In Python, objects can declare their textual representation using the
__repr__ method. IPython expands on this idea and allows objects to declare other, rich representations including:
A single object can declare some or all of these representations; all are handled by IPython's
display system. This Notebook shows how ... |
Say you consider spherical waves (momentum eigenstates) propagating outwards from some starting point $r = r_{0} $ (not defined for $r < r_{0}$) with $k \in \mathbb{R} $:
\begin{equation} \psi\left(r, t\right) = \left( A {e^{ikr} \over r} + B {e^{-ikr } \over r } \right) e^{-ikt} \end{equation}
We have boundary conditi... |
Let us for simplicity discuss RHF formalism. For $2n$-electron system we have $n$ Hartree-Fock equations written for $n$ spatial orbitals $\{ \phi_{k} \}_{k=1}^{n}$ $$ \newcommand{\mat}[1]{\boldsymbol{\mathbf{#1}}} $$ \begin{equation} \hat{F}(1) \phi_{k}(1) = \varepsilon_{k} \phi_{k}(1) \, , \quad k = 1, 2, \dotsc, n \... |
Give a convincing argument that the following inequalities are true: $$\int_1^n \log x\mathrm dx \leq \log1 + \log2 + ... \log n \leq \int_1^{n+1}\log x \mathrm dx$$ for any $n \geq 1 $ . We are given the hint to observe that: $$\int_{k-1}^k \log x\mathrm dx \leq \log k \leq \int_k^{k+1}\log x\mathrm dx $$
Update 1
BRI... |
Of course, most of you will, upon reading the title, exclaim "But isn't that the definition of the continuum hypothesis?" So I need to be a little more careful about the exact definitions.
Let ${\sf CH}(\frak m)$ be the statement that either $\frak m$ is a finite cardinal or there is no cardinality $\frak n$ such that ... |
In Python, objects can declare their textual representation using the
__repr__ method. IPython expands on this idea and allows objects to declare other, rich representations including:
A single object can declare some or all of these representations; all are handled by IPython's
display system. This Notebook shows how ... |
I am trying to calculate the tension in a string in the configuration shown in the diagram below. Here is a verbal description of the setup: The string is fixed at one end with the other end connected to a spring. The spring, with constant $K$, is limited to only vertical movement. The string begins with a tension $T$,... |
Ex.4.3 Q10 Quadratic Equations Solutions - NCERT Maths Class 10 Question
An express train takes \(1\) hour less than a passenger train to travel \(132 \,\rm{km}\) between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of express train is \(11\,... |
IAMCS Workshop in Large-Scale Inverse Problems and Uncertainty Quantification – Texas A&M University College Station, TX Stephen W. Hawking Auditorium George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy (MIST) Bruce Fryxell, University of Michigan Calibration and Prediction in a Radiati... |
xcorr function (of Matlab) computes the cross-correlation between two sequences $x[n]$ and $y[n]$ of length $M$ each. If $x$ and $y$ are random processes (jointly WSS) then xcorr returns an estimate $$\hat{r}_{xy}[m] = \frac{1}{M} \sum_{n=0}^{M-1} x[n]y[n+m]^*$$ computed over the two random vectors $x$ and $y$, of the ... |
If $C$ is any additive category then every object has a unique structure as an abelian group object so $Ab(C)=C$; but typically $C$ is not abelian. For example, this applies to the category of free abelian groups. One can also think about triangulated categories, which are usually not abelian, although a nice theorem o... |
How can I calculate the $\alpha$ and $\beta$ parameters for a Beta distribution if I know the mean and variance that I want the distribution to have? Examples of an R command to do this would be most helpful.
I set$$\mu=\frac{\alpha}{\alpha+\beta}$$and$$\sigma^2=\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}$$and... |
Given a million data points in say 100d,is there a way to generate an optimal filter bank of say 20 filtersfrom an SVD of the data ?
Call the 100d space $F$ (as in Frequency), with coordinates $[f_1, f_2 ... f_{100}]$. There are many bases $V_i$ of $F$, that split the 1M $\times$ 100 data array $ A \approx \sum_{i=1}^{... |
This question already has an answer here:
I'm trying to understand what frequency domain is. I found general explanations on the Internet, for example:
frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies Fourier transformrefers to both the frequency doma... |
I have been working this problem almost 3 days, I would appreciate any help or idea:
Let (M,h) be a Riemannian manifold. For every $ p \in M $ and $ (e_1 , ... , e_n)$ basis of $T_pM$. There exists an orthonormal frame in an neighborhood of p $(E_1, ... , E_n)$ , with $E_i (p) = e_i$ and $\nabla E_i (p) = 0 $
Hint: Fix... |
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,... |
In my talk at 2018 Chinese Mathematical Logic Conference, I asked if \((V,\subset,P)\) is epsilon-complete, namely if the membership relation can be recovered in the reduct. Professor Joseph S. Miller approached to me during the dinner and pointed out that it is epsilon-complete. Let me explain how.
Theorem
Let \((V,\i... |
Consider the function $e^x$ on the reals. I want to show that $e^x$ is continuous at the any point $t \in \mathbb{R}$. Is the following argument valid?
(1) Let $\{t_n\}$ be an arbitrary sequence of reals s.t. $t_n \to t$ and $t_n \ne t$.
(2) Then $\lim\limits_{t_n \to t}$ $e^{t_n} = \lim\limits_{t_n \to t}1 + \frac{{t_... |
[I'll ask this in the one-dimensional setting, and (if the answer is
yes) I'll leave as open what possible extensions to more general settings one might wish to discuss.]
Let $K \subset \mathbb{R}$ be a compact nowhere dense set. Suppose that for each $x \in K$ we have a sequence $(U_n^x)_{n \in \mathbb{N}}$ of connect... |
I'm writing a paper and I used them as an example, but then reconsidered . . . maybe I'm not getting it right! thanks!
At first, I had written that they certainly could have, given that blackbody radiation had been fairly well analyzed since the early 1900's and Wien's law would have been common knowledge among physici... |
I am currently simulating particle trajectories in Kerr spacetime numerically with $M=1$ and $a=1$.
In the picture above, I am calculating the geodesic in Boyer-Lindquist coordinates. I was messing around with the simulation a little bit and I wanted to transform to a local lorentz frame by use of a vierbein (tetrad) $... |
No, sadly.
This is an unfortunate consequence we have in our notation, we write $r$ when we mean the function $(r\cdot)$ which multiplies a function by $r$, and we write $A B$ when we mean the composition of functions $A\circ B$. So when we write something like $$r^{-2}\frac{\partial}{\partial r} \left(r^2 \frac{\parti... |
The length of a vector is defined as:
$$ ||\mathbf{v}||^2=\mathbf{v}\cdot \mathbf{v} $$
In the case that $\mathbf{v}:=a\hat{x}+b\hat{y}$ is expressed in an orthogonal basis using $\hat{x}$ and $\hat{y}$ as the generators of a Clifford algebra $Cl_{0,2}(\mathbb{R})$, then $||\mathbf{v}||^2=a^2+b^2$
For a poly-vector (sa... |
When $m^2 + n^2$ is large, the contribution from $1 - \frac{\mathrm{exp}(-(m^2+n^2))}{m(m^2+n^2)}$ is roughly $1$ because the fraction goes to zero as $m^2 + n^2 \to \infty$. If your series would converge, since clearly$$\sum_{m,n \ge 1} \frac{\mathrm{exp}(-(m^2+n^2))}{m(m^2+n^2)}$$converges, it would imply that $$\sum... |
Solvers for ordinary differential equations (ODEs) belong to the best-studied algorithms of numerical mathematics. An ODE is an implicit statement about the relationship of a curve $x:\mathbb{R}_{\geq 0}\to\mathbb{R}^N$ to its derivative, in the form $x'(t) = f(x(t),t)$, where $x'$ is the derivative of curve, and $f$ i... |
Lecture: HGX205, M 18:30-21
Section: HGW2403, F 18:30-20 Exercise 01 Prove that \(\neg\Box(\Diamond\varphi\wedge\Diamond\neg\varphi)\) is equivalent to \(\Box\Diamond\varphi\rightarrow\Diamond\Box\varphi\). What you have assumed? Define strategyand winning strategyfor modal evaluation games. Prove Key Lemma: \(M,s\vDas... |
OpenCV 3.0.0
Open Source Computer Vision
This class is used to perform the non-linear non-constrained minimization of a function,. More...
#include "optim.hpp"
virtual void getInitStep (OutputArray step) const =0 Returns the initial step that will be used in downhill simplex algorithm. More... virtual void setInitStep ... |
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Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
Eigenvalues are properly one of the most important metrics which can be extracted from matrices. Together with their corresponding eigenvector, they form the fundamental basis for many applications. Calculating eigenvalues from a given matrix is straightforward and implementations exist in many libraries. But sometimes... |
The
amsmath package provides a handful of options for displaying equations. You can choose the layout that better suits your document, even if the equations are really long, or if you have to include several equations in the same line.
Contents
The standard LaTeX tools for equations may lack some flexibility, causing o... |
I was asked to calculate all the possible groups for elliptic curves and their order in $\mathbb{F}_5$. There are $p^2-p$ groups that respect $\Delta \neq 0$, so there are $20$ groups.
Some of them may be isomorphic. I have to look for the ones with the same order.
For example: are the ones defined by $x^3+4x+2$ and $x... |
I have a point $P_0 = [x_0, y_0, z_0]'$. I want to rotate the axes so that the new coordinates will be $P_1 = [x_1, y_1, z_1]'$. Define the following rotation matrices:
$R_x = \left[\matrix{ 1 & 0 & 0\\ 0 & \cos\alpha & - \sin\alpha\\ 0 & \sin\alpha & \cos\alpha} \right]$, $R_y = \left[\matrix{ \cos\beta & 0 & \sin\bet... |
In mathematics, especially in applications of linear algebra to physics, the
Einstein notation or Einstein summation convention is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving notational brevity. As part of mathematics it is a notational subset of Ricci calculu... |
Design open well staircase. Draw the plan showing flight details, mid-landings etc. Draw reinforcement details in a flight. Grade of concrete is M20 and steel Fe415.
Civil Eng > Sem 8 > Design and Drawing of Reinforced Concrete structure
Design open well staircase. Draw the plan showing flight details, mid-landings etc... |
Bunuel wrote:
\(a\) and \(b\) are integers. \([x]\) is an integer less than or equal to \(x\). Is \([\frac{a}{b}] \geq {1}\)? Harshgmat
(1) \(ab = 64\) (2) \(a=b^2\)
Yes the question is a bit confusing because we have been dealing with such questions with a bit different wordings.
Had it been \([x]\) is the GREATEST in... |
What does it mean for the ratio of the lengths of the sides of a rectangle to be
rational, say $\frac{5}{3}$? It means that if the long side of the rectangle is divided into five equal parts, and if one counts out three of those parts, then the length of the resulting line segment equals the length of the short side of... |
I am measuring voltages and currents of a 3-phase electrical machine and I need to calculate the power. Every interrupt (frequency between 30-70kHz) I get values (voltages, currents) from analogue-digital converter and I need to do a simple calculation to determine power. However, I was told to use averaging with a fir... |
Practical and theoretical implementation discussion.
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Hi,
I have a simple question as in the title. Why is volumetric emission proportional to absorption coefficient? I often see the volumetric emission term is written as I can also see another representation, volumetric emittance functio... |
Let $x[n]$ be real signal and $y[n]=\exp(j3\pi n)$ be a complex signal
Would the convolution between those two signals be $$x[n] * \Re(y[n]) + jx[n]*\Im(y[n])$$?
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It only takes a... |
Here is a string of comments which might be helpful.
UPDATE at the end I conjecture an upper bound $a(n) \leq \lfloor (\frac{n-1}{2})^2 \rfloor$ which satisfies a stronger property.
Consider instead cases of $$\prod_1^k(x_i+a)= \prod_1^k(y_i+a) \tag{*}$$ where the multisets $\{x_1,\cdots ,x_k\}$ and $\{y_1,\cdots ,y_k\... |
A measure of concordance between two random variables based on ranks.
Kendall's tau is a measure of concordance for two random variables. It is based on ranks, and has many properties in common with Spearman's rho.
We say that $(y_{i,1},y_{i,2})$ and $(y_{j,1},y_{j,2})$ are concordant if:
$$(y_{i,1} - y_{j,1}) \times (... |
A simple question about notation of Moore Nekrasov and Shatashvili which makes me confused. Page 3, the authors rearranged the action into a novel form.
For D=3+1,5+1,9+1 respectively, the path integral is $$ I_D=(\frac{\pi}{g})^{\frac{(N^2-1)(D-3)}{2}} \frac{1}{{\rm{Vol(G)}}}\int d^DXd^{\frac{D}{2}-1}\Psi e^{-S} $$ wh... |
Let $L$ be a finite lattice with least element $\hat{0}$, greatest element $\hat{1}$, and Möbius function $\mu$.
Question 1: What class of lattices the following property characterizes? $$\mu(\hat{0},a)=\mu(\hat{0},\hat{1})\mu(a,\hat{1}), \ \forall a \in L$$ It follows that $\mu(\hat{0},\hat{1}) = \pm1$. Remark: It is ... |
I am having trouble grasping the concept of vorticity. Above is a picture of fluid element under deformation (rotational). Say we ignore the vertical motion, which is $\frac {\partial {v}}{\partial x} = 0$. Which can be considered the case in the boundary layer close to a flat plate.
Assume flow is incompressible, and ... |
When dealing with wave propagation problems such as electromagnetic waves passing from one medium to another we set up boundary conditions to ensure the field is continuous and the flux is continuous as the waves pass from the first medium into the other.
Similarly in the case of acoustic waves passing from, say, a reg... |
Is there sparse representation for stationary noise and nonstationary noise? How can I learn dictionary for each noise class? (my mean of noise is noises with which speech signals are often contaminated such as white gaussian noise, car noise, babble noise, impulsive noise....)
Let's think about it in a different way -... |
Last edited: April 20th 2016
The objective of this module is to use the method of forward shooting to determine numerically the eigenenergies of the quantum harmonic oscillator in one dimension. In other words, we are looking for eigenvalues of the time-independent Schrödinger equation$$ \qquad\left[-\frac{\hbar^2}{2m}... |
Difference between revisions of "Using Gamma-ray Counts to Calculate Element Concentration"
Line 23: Line 23:
'''''<math>\frac{w_{p}}{w_{s}}=\frac{R_{xp} \cdot e^{\lambda_{x} \cdot t_{dx}}}{R_{xs} \cdot e^{\lambda_{x} \cdot t_{ds}}}</math>'''''<br><br>
'''''<math>\frac{w_{p}}{w_{s}}=\frac{R_{xp} \cdot e^{\lambda_{x} \c... |
##plugins.themes.bootstrap3.article.main## Abstract
For an arbitrary fixed element $\beta$ in $\{1; 2; 3; ...; \omega\}$ both a sequent calculus and a natural deduction calculus which axiomatise simple paracomplete logic $I_{2;\beta}$ are built. Additionally, a valuation semantic which is adequate to logic $I_{2;\beta}... |
In Python, objects can declare their textual representation using the
__repr__ method. IPython expands on this idea and allows objects to declare other, rich representations including:
A single object can declare some or all of these representations; all are handled by IPython's
display system. This Notebook shows how ... |
Ex.5.3 Q13 Arithmetic Progressions Solution - NCERT Maths Class 10 Question
Find the sum of first \(15\) multiples of \(8.\)
Text Solution What is Known?
Multiples of \(8\)
What is Unknown?
Sum of first \(15\) multiples of \(8,\) \({S_{15}}\)
Reasoning:
Sum of the first \(n\) terms of an AP is given by \({S_n} = \frac{... |
Our new book (NAT)
Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids, EMS Tracts in Mathematics vol 15
uses mainly cubical, rather than simplicial, sets. The reasons are explained in the Introduction: in strict cubical higher categories we can easily express
algebraic inverse... |
A Spearman rank correlation is a number between -1 and +1 that indicates to what extent 2 variables are monotonously related.
Spearman Correlation - Example Spearman Rank Correlation - Basic Properties Spearman Rank Correlation - Assumptions Spearman Correlation - Formulas and Calculation Spearman Rank Correlation - So... |
I am trying to understand the LSM algorithm applied to grayscale image segmentation.
There are essentially 2 things that are blocking me:
1) From my point of view - the level sets - i.e. ''moving'' the 3D surface (that is, conceptually visualizing the grayscale image (say 8 bits/pixel) as a surface whose height is give... |
Your task is to take an array of numbers and a real number and return the value at that point in the array. Arrays start at \$\pi\$ and are counted in \$\pi\$ intervals. Thing is, we're actually going to interpolate between elements given the "index". As an example:
Index: 1π 2π 3π 4π 5π 6πArray: [ 1.1, 1.3, 6.9, 4.2, ... |
setting constant of integration \\chi for initial conditions
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Hello, I have a question about how [tex]\chi[/tex] is determined in CAMB. I know that it is set to [tex]-1[/tex], but see below.
\begin{equation} \label{1} \mathcal{R} = \pm (\Delta_{\mathcal{R}})^{1/2} = \pm \sqrt{A_s} \end{eq... |
The Warsaw circle $W$ http://en.wikipedia.org/wiki/Continuum_%28topology%29 is a counterexample for quite a number of too naive statements.
The Warsaw circle can be defined as the subspace of the plane $R^2$ consisting of the graph of $y = \sin(1/x)$, for $x\in(0,1]$, the segment $[−1,1]$ in the $y$ axis, and an arc co... |
The speed of sound is defined as $c^2 = \frac{\partial p}{\partial \rho}$, which for an ideal gas becomes $c^2 = \gamma \frac{p}{\rho}$.
For a real gas, the relationship to an ideal gas can be found through the compressibility factor $z$. This is a measure of how much a real gas deviates from an ideal gas. It shows up ... |
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 \(\nu = \zeta_{18} + \zeta_{18}^{-1}\):
\(\beta_{0}\) \(=\) \( 1 \) ... |
ExB in BICEP2
Anze Slosar
Posts: 183 Joined: September 24 2004 Affiliation: Brookhaven National Laboratory Contact:
I am having arguments with some colleagues of mine about the following:
To me, the fact that ExB and TxB are (mostly) consistent with zero is a good argument in favour of BICEP2 seeing primordial fluctuat... |
Here is Artin's proof:
First we need to prove a lemma.
Lemma: Let $\gamma$ be a path in an open set $U$. There there exists a rectangular path $\eta$ with the same end points, and such that $\gamma,\eta$ are close together in $U$. In particular, $\gamma$ and $\eta$ are homologous in $U$, and for any holomorphic functio... |
You get $2^\kappa$ many models for any uncountable $\kappa$. This follows immediately from the fact that $\mathsf{ZFC}$ (trivially) defines an infinite linear order, and this is all that's needed to ensure unstability.
(The same argument shows that already much weaker theories, such as $\mathsf{PA}$, are unstable.)
Thi... |
Protein Synthesis
Category : NEET
Protein Synthesis
Formation of protein from mRNA is called translation is also known as polypeptide synthesis or protein synthesis. It is unidirectional process. The ribosomes of a polyribosome are held together by a strand of mRNA. Each eukaryotic ribosome has two parts, smaller 40S s... |
$$\mathrm{molarity} = \frac{\text{amount of solute}}{\text{volume of solution}} $$ and amount of substance is based on quantity (larger mass means larger amount), so how come it is an intensive property. Shouldn't it be an extensive property?
Concentration is an intensive property. The value of the property does not ch... |
Refine
Despite their very good empirical performance most of the simplex algorithm's variants require exponentially many pivot steps in terms of the problem dimensions of the given linear programming problem (LPP) in worst-case situtation. The first to explain the large gap between practical experience and the disappoi... |
In Spivak's
Calculus, he asks for a proof that $\lim_{x\to a}f(x)=\lim_{h\to 0}f(a+h)$.
He first shows that the existence of $\lim_{x\to a}f(x)$ implies the existence and equivalence of $\lim_{h\to0}f(a+h)$, and then he says the argument for the other direction is "similar," but I am having a hard time replicating it (... |
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