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It is essentially impossible to answer the general question of "how does multilinearity come up naturally in physics?" because of the myriad of possible examples that make up the total answer. Instead, let me describe a situation that very loudly cries out for the use of tensor products of two vectors.
Consider the pro... |
I recently learned about irreducible and prime elements in a commutative ring. However, my professor was not quite sure who was the first to make this distinction, or give an example of an irreducible element which is not prime. Was it Dedekind? If so, where did he make this distinction? Could you also give some refere... |
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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 wit... |
Abbreviation:
InRL
An
is a structure $\mathbf{A}=\langle A, \vee, \wedge, \cdot, 1, \sim, -\rangle$ of type $\langle 2, 2, 2, 0, 1, 1\rangle$ such that involutive residuated lattice
$\langle A, \vee, \wedge, \neg\rangle$ is an involutive lattice
$\langle A, \cdot, 1\rangle$ is a monoid
$xy\le z\iff x\le \neg(y(\neg z))... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
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I can't believe I saw Calvin (the math challenge master) walk into my class and talk to my teacher and us O.O
Note by Victor Loh 5 years, 8 months ago
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science relat... |
60J65 Brownian motion [See also 58J65] Refine
We show that the intersection local times \(\mu_p\) on the intersection of \(p\) independent planar Brownian paths have an average density of order three with respect to the gauge function \(r^2\pi\cdot (log(1/r)/\pi)^p\), more precisely, almost surely, \[ \lim\limits_{\var... |
When there are $n$ variables $X_1, \ldots, X_n,$ their mutual covariances can be assembled into a matrix $\Sigma = (\sigma_{ij})$ where
$$\sigma_{ij} = \operatorname{Cov}(X_i,X_j).$$
Note that the diagonal elements $\sigma_{ii} = \operatorname{Cov}(X_i,X_i) = \operatorname{Var}(X_i)$ are the variances. It will be conve... |
skills to develop
To learn what a standard normal random variable is. To learn how to compute probabilities related to a standard normal random variable.
Definition: standard normal random variable
A
standard normal random variable is a normally distributed random variable with mean \(\mu =0\) and standard deviation \(... |
Answer
$90.2$ $ cm^{2}$
Work Step by Step
Using the formula given in the previous exercise, the area of the parallelogram is: $a \times b \times \sin \gamma$ $8 cm \times 12 cm \times \sin 70^{\circ}$$= 90.2$ $ cm^{2}$
You can help us out by revising, improving and updating this answer.Update this answer
After you clai... |
Airspeed is measured with a pitot tube. A pitot tube has two pressure measurement ports. One that measures the total pressure $p_t$. This port is facing the incoming airflow. The other measures the static pressure $p$ and is placed perpendicular to the airflow. The difference between the two pressures is called impact ... |
I have the following statement whith an argumentation which I do not understand.
Fix integers $k,l$ such that $0\leq l\leq k$. Then the identity map on $C^\infty(\mathbb{T}^d)$ extends to the injective continuous operator $$i_{k,l}:H^k(\mathbb{T}^d)\rightarrow H^l(\mathbb{T}^d)$$ of norm one. Moreover, for every $j\in\... |
Skills to Develop
Confidence limits tell you how accurate your estimate of the mean is likely to be. Introduction
After you've calculated the mean of a set of observations, you should give some indication of how close your estimate is likely to be to the parametric ("true") mean. One way to do this is with confidence l... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
The orthogonal group, consisting of all proper and improper rotations, is generated by reflections. Every proper rotation is the composition of two reflections, a special case of the Cartan–Dieudonné theorem.
Yeah it does seem unreasonable to expect a finite presentation
Let (V, b) be an n-dimensional, non-degenerate s... |
There is no joint
density function since the random variable $(U,V,W,Z)$ takes values on a subset $D=\{(f_1^{-1}(x),f_2^{-1}(x),f_3^{-1}(x),f_4^{-1}(x))\mid x\in\mathbb R\}$ of $\mathbb R^4$ which has Lebesgue measure zero.
Informally, $D$ has co-dimension $3$, hence one can compare $D$ to a line in $\mathbb R^4$.Forma... |
Let $N \subset \mathbb N$ denote the set of players and $v : 2^N \to \mathbb R$ , $v(\emptyset) = 0$, the characteristic function. We call $(N,v)$ a cooperative transferable utility (TU) game.
Definition 1. A game $(N,v)$ is called convex, if for all $S,T \subseteq N$ it holds that\begin{align}v(S \cup T) + v(S \cap T)... |
class Gudhi::cubical_complex::Bitmap_cubical_complex< T > Cubical complex represented as a bitmap. More... class Gudhi::cubical_complex::Bitmap_cubical_complex_base< T > Cubical complex represented as a bitmap, class with basic implementation. More... class Gudhi::cubical_complex::Bitmap_cubical_complex_periodic_bounda... |
Suppose that $R$ is a commutative ring (with unity) of characteristic $0$, and that the set $Z$ of zero divisors in $R$ forms an ideal. Does it follow that the characteristic of $R/Z$ is $0$?
Equivalently (with less verbiage), suppose that the ring homomorphism $\iota:\mathbb{Z} \to R$ injects. Does it follows that $\i... |
The idea is to "back off the inf's" and use a "since $\epsilon$ is arbitrary" argument. More precisely,
$1).\ A$ is bounded below, which implies that $A+k$ is also. This means that each has a finite greatest lower bound.
$2).\ $ Set $\alpha=\inf A$ and $\beta=\inf (A+k)$. You want to show that $\beta=\alpha+k.$ As you ... |
Difference between revisions of "SageMath"
m (Jupyter Notebook reference to sagemath kernel package added.)
(Update outdated information)
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* {{Pkg|sage-notebook}} includes the browser-based notebook interface.
* {{Pkg|sage-notebook}} includes the browser-based notebook interface.
−
{{Note|Most
+
{{Note... |
Quadratic programming (QP) involves minimizing or maximizing an objective function subject to bounds, linear equality, and inequality constraints. Example problems include portfolio optimization in finance, power generation optimization for electrical utilities, and design optimization in engineering.
Quadratic program... |
Heavenly Chips is a "new game plus" or "Ascension prestige" mechanic introduced in Cookie Clicker version 1.035. If you ascend by pressing the "Legacy" button, you will gain Heavenly Chips and be sent to the ascension screen. The amount of Heavenly Chips is dependent on your forfeited cookies of all games. Every reset,... |
I am trying to figure out the details on how to implement the structure tensor in Matlab and need some advice!
For an image $\ I(x,y) $ the structure tensor S is given by:
$$ S=\begin{pmatrix} W \ast I_x^2 & W \ast (I_xI_y)\\ W \ast (I_xI_y) & W \ast I_y^2 \end{pmatrix}$$ where W is a smoothing kernel, $\ \ast $ denote... |
Elasticity is the slope after taking a log transform. Throughout this post $\log$ refers to the
natural logarithm. That is, the logarithm with base $e$, the
ln function in Excel. The logarithm transforms multiplication into addition. Log differences are something akin to percent changes (and they're equivalent for smal... |
We prove that the ideal $f^{-1}(P)$ is prime.Suppose that we have $ab\in f^{-1}(P)$ for $a, b\in R$. Then we have $f(ab) \in P$.Since $f$ is a ring homomorphism, we obtain\begin{align*}f(a)f(b)=f(ab)\in P.\end{align*}
Since $P$ is a prime ideal, it follows that either $f(a)\in P$ or $f(b)\in P$.Hence we have either $a\... |
so I found out that SR-71 Blackbird is using what's called "turboramjet" and I find the idea a bit appealing since they say with such engine, the Blackbird is more fuel efficient at it's top speed. I know that the mechanism for such engine is extremely complicated, but what's on my mind is not making an engine like Bla... |
So we are in the midst of solving quadratic equations of the form:\[
{ax}^{2}\hspace{0.33em}{+}\hspace{0.33em}{bx}\hspace{0.33em}{+}\hspace{0.33em}{c}\hspace{0.33em}{=}\hspace{0.33em}{0}
\]
where
a, b, and c are some numbers. So far, we have been looking at equations like this that can be factored so that we can use th... |
Relative efficiency between two unbiased estimators $\widehat{\theta }_{A}$and $\widehat{\theta }_{B}$ of an unknown parameter vector $\theta _{0}\in \mathbb{R}^{K}$ is usually defined as follow (see for instance Ruud, 2001).The estimator $\widehat{\theta }_{A}$ is said to be efficient relative to $\widehat{\theta }_{B... |
ISSN:
1556-1801
eISSN:
1556-181X
All Issues
Networks & Heterogeneous Media
March 2011 , Volume 6 , Issue 1
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Abstract:
We consider the Neumann spectral problem for a second order differential operator, with piecewise constants coefficients, in a domain $\Omega_\varepsilon$ of $R^2$. ... |
ISSN:
1556-1801
eISSN:
1556-181X
All Issues
Networks & Heterogeneous Media
June 2011 , Volume 6 , Issue 2
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Abstract:
We consider solutions to a nonlinear reaction diffusion equation when the reaction term varies randomly with respect to the spatial coordinate. The nonlinearity is th... |
A series of recent works has shown that Principal Ideal-SVP is not always as hard as finding short vectors in general lattices, and some schemes were broken using quantum algorithms --- the Soliloquy encryption scheme, Smart-Vercauteren fully homomorphic encryption scheme from PKC 2010, and Gentry-Garg-Halevi cryptogra... |
In QFT, a representation of the Lorentz group is specified as follows:$$U^\dagger(\Lambda)\phi(x) U(\Lambda)= R(\Lambda)~\phi(\Lambda^{-1}x)$$Where $\Lambda$ is an element of the Lorentz group, $\phi(x)$ is a quantum field with possibly many components, $U$ is unitary, and $R$ an element in a representation of the Lore... |
2 1
##cos(\omega)## is
$$\frac{e^{j \omega } + e^{-j \omega }}{2}$$ ##sin(\omega)## is $$\frac{e^{j \omega } - e^{-j \omega }}{2 j}$$ I also know that ##cos(\omega - \pi / 2) = sin(\omega)##. I've been trying to show this using exponentials, but I can't seem to manipulate one form into the other. Specifically, I can't ... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
In QFT, a representation of the Lorentz group is specified as follows:$$U^\dagger(\Lambda)\phi(x) U(\Lambda)= R(\Lambda)~\phi(\Lambda^{-1}x)$$Where $\Lambda$ is an element of the Lorentz group, $\phi(x)$ is a quantum field with possibly many components, $U$ is unitary, and $R$ an element in a representation of the Lore... |
Google is constantly running experiments to test new search algorithms. For example, Google might test three algorithms using a sample of 10,000 google.com search queries. Table 6.15 shows an example of 10,000 queries split into three algorithm groups.
20 The group sizes were specified before the start of the experimen... |
A Linear Transformation Preserves Exactly Two Lines If and Only If There are Two Real Non-Zero Eigenvalues Problem 472
Let $T:\R^2 \to \R^2$ be a linear transformation and let $A$ be the matrix representation of $T$ with respect to the standard basis of $\R^2$.
Prove that the following two statements are equivalent.
(a... |
I know the BRDF of specular reflection is nonzero only in the reflection direction.
But why it is infinite?
A paragraph on page 36 of Advanced Global Illumination:
Computer Graphics Stack Exchange is a question and answer site for computer graphics researchers and programmers. It only takes a minute to sign up.Sign up ... |
You can take the way SNR is calculated in RGB images as a starting point.
In RGB images, the image SNR is calculated using the familiar formula
$$\frac{\mu}{\sigma}$$
Where $\mu$ is the "whole image" mean and $\sigma$ is the "whole image" standard deviation. To calculate these "whole image" values, each of the RGB chan... |
On p10 of these EFT lecture notes, the "relevance" of operators in a Lagrangian is determined by comparing their mass dimension to the spacetime "d" one considers such that an operator is
Relevant if its dimension is $ < d$
Marginal if its dimension is $ = d$
And irrelevant if its dimension is $ > d$
This means for exa... |
I wonder if someone could provide me with a simple MWE for using TikZ together with
\boxed to produce a colored equation background. If possible with rounded corners.
I am using
\boxed{} inside the
split environment from
amsmath.
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt,... |
If the Quotient Ring is a Field, then the Ideal is MaximalLet $R$ be a ring with unit $1\neq 0$.Prove that if $M$ is an ideal of $R$ such that $R/M$ is a field, then $M$ is a maximal ideal of $R$.(Do not assume that the ring $R$ is commutative.)Proof.Let $I$ be an ideal of $R$ such that\[M \subset I \subset […]
Is the ... |
Exams can be easily created in LaTeX by means of the class
exam.cls. This class makes it straightforward to typeset questions, and it sets a 1in margin in all paper sizes and provides special commands to write and compute grades. This article explains how to edit with exam.cls.
Contents
Let's see a simple working examp... |
Tagged: direct sum Problem 61
Let $V$ and $W$ be subspaces of $\R^n$ such that $V \cap W =\{\mathbf{0}\}$ and $\dim(V)+\dim(W)=n$.
(a) If $\mathbf{v}+\mathbf{w}=\mathbf{0}$, where $\mathbf{v}\in V$ and $\mathbf{w}\in W$, then show that $\mathbf{v}=\mathbf{0}$ and $\mathbf{w}=\mathbf{0}$. (b) If $B_1$ is a basis for the... |
Tagged: nilpotent matrix Problem 582
A square matrix $A$ is called
nilpotent if some power of $A$ is the zero matrix. Namely, $A$ is nilpotent if there exists a positive integer $k$ such that $A^k=O$, where $O$ is the zero matrix.
Suppose that $A$ is a nilpotent matrix and let $B$ be an invertible matrix of the same si... |
A One-Line Proof that there are Infinitely Many Prime Numbers Problem 446
Prove that there are infinitely many prime numbers in
ONE-LINE.
Contents
Background
There are several proofs of the fact that there are infinitely many prime numbers.
Proofs by Euclid and Euler are very popular.
In this post, I would like to intr... |
As the order of the polynomial (the highest power of
x) increases, it usually gets harder to factor. In my last post on this topic, I will cover a way to reduce the order by one for each iteration of the process. If you can get the polynomial to a degree 2, there are many ways to factor these.
A polynomial of degree 2 ... |
I read your question a little differently than the other people who have answered. The role of the Fourier transform in physics is as a bi-directional one-to-one mapping between conjugate variables. The most famous example of a conjugate variable pair is position/momentum, but there are many others. Some examples of co... |
closed as no longer relevant by Robin Chapman, Akhil Mathew, Yemon Choi, Qiaochu Yuan, Pete L. Clark Aug 22 '10 at 9:00
This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicabl... |
Today I am presenting the IPython notebook at the meeting of the Sage Paris group. This post gathers what I prepared.
Installation
First you can install the ipython notebook in Sage as explained in this previous blog post. If everything works, then you run:
sage -ipython notebook
and this will open a browser.
Turn on S... |
So now that you know about matrices, we can use them to add a third way to solve a system of equations. You will need to read my previous 3 posts on matrices if you are unfamiliar with how to multiply matrices.
In the last post on System of Equations, I looked at the system:
2
x + 3 y = 51 3 x + 2 y = 49
And in my last... |
Well, it is indeed an abuse of notation though, by no means you could say (1) is an equality in $L^2(0,T;V')$, because (1) only holds in a finite dimensional subspace. Multiply (1) by the basis of the finite dimensional subspace$$(u_n',w_j) - (\Delta u_n,w_j) = (P_n f,w_j).$$Proper assumption about the boundary conditi... |
203 12 Summary Is there any connection between the new definition of the kilogram based on the Planck constant and the mass-energy equivalence?
Hi,
today I stumbled upon a 2016 article in Scientific American about the (then) possibility of re-defining the kilogram through Planck's constant. The article is really a very... |
For periodic not-necessarily smooth $f$ and a range of $m$, say $0\ldots 31$, I want to compute $\int_{-\pi}^\pi f(t) \cos (mt) dt$ (and maybe the same integral with $\sin$ instead of $\cos$) to machine precision (or close-ish to it).
The obvious thing to do is to evaluate $f$ at an equispaced grid and take a DFT, but ... |
Problem 616
Suppose that $p$ is a prime number greater than $3$.
Consider the multiplicative group $G=(\Zmod{p})^*$ of order $p-1$. (a) Prove that the set of squares $S=\{x^2\mid x\in G\}$ is a subgroup of the multiplicative group $G$. (b) Determine the index $[G : S]$.
Add to solve later
(c) Assume that $-1\notin S$. ... |
Regression is a very fundamental concept in statistics, machine learning and in Neural Network. Imagine plotting the correlation between rainfall frequency and agriculture production in high school. Increase in rainfall generally increases agriculture production. Fitting a line to those points enables us to predict the... |
Sorry for the basic question. But take for example:
$$3x-8\leq 0$$
$$-2+3x-x^2\leq 0$$
If we sum these two inequalities we obtain: $$0\leq x^2-6x+10$$
The solution of this inequality is of course any $x \in \mathbb{R}$. However, we can also attempt to solve them separetly and obtain: $$x \leq 8/3$$ $$(x-2)(x-1)\geq 0$$... |
I'm trying to find a function $u: (0, \infty) \to \mathbb{R}$ which satisfies these conditions:
i) $u$ is bounded.
ii) $u^2$ increases over $(0, \infty)$.
iii) $\dot u(t)$ does not converge to $0$ as $t$ tends to infinity.
I think it's easier to choose first the derivative of $u^2$ and then integrate it. For example, I... |
My question is: How can I integrate $\sqrt{1+\frac{1}{3x}} \, dx$ ? (I don't mind about negative Xs).
I'm aware that there's a theorem which you can use that integrates the function using the points where the function can't be solved or something like that(improper integrals?) but I haven't learned anything but parts a... |
You said it yourself in the question: use L'Hospital's Rule applied to $$\lim_{x\to0^+}\frac{\int_x^1\frac{f(t)}{t^{\alpha+1}}\,dt}{1/x^{\alpha}}$$The numerator and denominator each approach $\infty$, given your conditions on $f$.
EDIT: The denominator approaches $\infty$ simply because $\alpha$ is positive.
If $f(0)$ ... |
In the game I am designing I have to simulate a gold market. A market is, essentially, a place where people buy and sell a specific good, in this case, gold. The prices change, ideally according to offer and demand, in a continuous way. The most well known market is the stock exchange.
I am not an economist, and being ... |
There are several and almost similar inequalities in MSE that some of them can be proved in long page. some of these questions listed below:
For $abc=1$ prove that $\sum\limits_{cyc}\frac{a}{a^{11}+1}\leq\frac{3}{2}.$ For positive $a$, $b$, $c$ with $abc=1$, show $\sum_{cyc} \left(\frac{a}{a^7+1}\right)^7\leq \sum_{cyc... |
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Now showing items 1-10 of 27
Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
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Search for top squark pair production in final states with one isolated lepton, jets, and missing transverse momentum in √s = 8 TeV pp collisions with the ATLAS detector
(Springer, 2014-11)
The results of a search for top squark (stop) pair production in final states with one isolate... |
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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... |
What is the relationship, if any, between Kalman filtering and (repeated, if necessary) least squares polynomial regression?
1. There is a Difference in terms of optimality criteria Kalman filter is a Linear estimator. It is a linear optimal estimator - i.e. infers model parameters of interest from indirect, inaccurate... |
I have perhaps a silly question. I have a set of vectors $\xi_\ell$, with $\ell\in J_k\subset \{1,\ldots,k\}$. Now I want to create a long vector $\xi$ where these individual vectors are stacked on top of each other, and a matrix $\Xi$ of which the columns are these individual vectors.
I am stuck with the proper notati... |
Let us consider the subset\[Z:=\{z\in R \mid zr=rz \text{ for any } r\in R\}.\](This is called the center of the ring $R$.)
This is a subgroup of the additive group $R$.In fact, if $z, z’\in Z$, then we have for any $r\in R$,\begin{align*}(z-z’)r=zr-z’r=rz-rz’=r(z-z’).\end{align*}It follows that $z-z’\in Z$, and thus $... |
According to a review by Legge & Bigelow the arc or degrees of visual angle ($\alpha$) is,
$$\alpha = 57.3 \times S/D,$$
where S is height of object and D is distance to object. [1] $S/D$ is the small angles approximation of $2 \times arctan(S/2D)$ which follows form geometry.
Image 1: the equation comes straight from ... |
It is also useful to be able to compare two means for small samples. For instance, a teacher might like to test the notion that two versions of an exam were equally difficult. She could do so by randomly assigning each version to students. If she found that the average scores on the exams were so different that we cann... |
Let $n$ be a
positive integer and there be $p_1,p_2,p_3,........p_n$ prime numbers such that all of them are greater than $5$. If $6$ divides $p_1 ^2 + p_2 ^2 + p_3 ^2+\ldots +p_n ^2$, prove that $6$ divides $n$. NOTE:- This problem is the $2nd$ question of $1998$ $RMO$ (Regional Mathematical Olympiad). I tried using c... |
Z-Scores
The standard normal distribution is a normal distribution of standardized values called
z-scores. A z-score is measured in units of the standard deviation.
Definition: Z-Score
If \(X\) is a normally distributed random variable and \(X \sim N(\mu, \sigma)\), then the
z-score is:
\[z = \dfrac{x=\mu}{\sigma} \lab... |
The statement is in general false. We give a counterexample.
Let us consider the following $2\times 2$ matrix:\[A=\begin{bmatrix}1 & 2\\2& 1\end{bmatrix}.\]The matrix $A$ satisfies the required conditions, that is, $A$ is symmetric and its diagonal entries are positive.
The determinant $\det(A)=(1)(1)-(2)(2)=-3$ and th... |
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Now showing items 1-9 of 9
Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
Measurements are used to measure something. It is the estimation of ratios of quantity. It is made by comparing a quantity with a standard unit. They are used to find the size, length or amount of something. Measurement Formulas are used to find the distance, area, surface area, volume, circumference etc. They also inc... |
Disclaimer: I admit that the question is not very clear. I think it cannot be helped because the question is very open-ended.
First of all, I present the interested type of circuits. We only consider this structure of Boolean / Arithmetic circuits: a DAG consisting of multiple inputs, 1 output and multiple gates. Each ... |
Before I get to the core of today’s post, I would like to show the details of calculating the standard deviation. From my last post, we have two sets of data: one from Nice David and the other from Evil David. Let’s look a t Nice David’s data which are the last five test scores of his students: 83, 83, 85, 87, and 90.
... |
> Input
> Input
>> 1²
>> (3]
>> 1%L
>> L=2
>> Each 5 4
>> Each 6 7
>> L⋅R
>> Each 9 4 8
> {0}
>> {10}
>> 12∖11
>> Output 13
Try it online!
Returns a set of all possible solutions, and the empty set (i.e. \$\emptyset\$) when no solution exists.
How it works
Unsurprisingly, it works almost identically to most other answe... |
There are many examples where the notation of $\partial{U}$ is used to represent the surface boundary of some volume $U$. For example, the following representation of the Divergence Theorem: $$ \int_U{\nabla \cdot \mathbf{F}}\,dV = \oint_{\partial{U}}\,\mathbf{F}\cdot\mathbf{n}\,dS $$ What is the history and reasoning ... |
Is the electric field between two positively charged parallel infinite plates one with a charge density twice the other effect the electric field on the outside of the plates? I am thinking no, because the field lines cannot cross in the field between the plates since they have positive charges. What does the electric ... |
ISSN:
1937-5093
eISSN:
1937-5077 Kinetic & Related Models
September 2016 , Volume 9 , Issue 3
Issue in memory of Alfredo Lorenzi
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Abstract:
In this paper, we establish a new blowup criterion for the strong solutions in a smooth bounded domain $\Omega\subset\mathbb{R}^3$. In [13], We... |
Running your code, it seems like your pulse looks kinda like this:
(sorry for not adding units to the plots, I used the same as you, i.e. t is in fs and w in rad/fs)
So, the FWHM is not correct (should be 4 fs) and the angular carrier/central frequency is messed up (should be ca. 2.3 / ca. 0.37 per fs). I think there i... |
An $n\times n$ matrix $A$ is said to be idempotent if $A^2=A$.It is also called projective matrix.
Proof.
In general, an $n \times n$ matrix $B$ is diagonalizable if there are $n$ linearly independent eigenvectors. So if eigenvectors of $B$ span $\R^n$, then $B$ is diagonalizable.
We prove that $\R^n$ is spanned by eig... |
ISSN:
1937-5093
eISSN:
1937-5077 Kinetic & Related Models
December 2016 , Volume 9 , Issue 4
Issue on Nonautonomous Dynamics
Select all articles
Export/Reference:
Abstract:
The mathematical description of the interaction between a plasma and a solid surface is a major issue that still remains challenging. In this paper... |
I want to show by a double-counting argument that$${{n+m+1}\brace m}=\sum_{k=0}^mk{{n+k}\brace k}$$for $m,n\in\Bbb N$ (where $0\in\Bbb N$).
Note that ${{n}\brace k}$ is a Stirling number of the second kind (i.e. the number of partitions of $[n]:=\{1,2,\ldots,n\}$ into $k$ blocks). I am just starting to do double-counti... |
Suppose that a wooden cube, whose edge is $3$ inch, is painted red, then cut into $27$ pieces of $1$ inch edge. Find total surface area of unpainted?
First of all, I have tried to draw the cube using MS Paint, below is given picture:
The surface area of cube is $6\cdot a^2$, where $a$ is the length of cube, when cube i... |
Let $A \in Mat_{n,n}(\mathbb C)$.
Let $g_A(t)$ denote $\exp(tA)$ and $\exp(A)$ denote the matrix $g_A(1)$.
Let $\alpha \in \mathbb R$ and $B = \alpha A$.
I've shown $\exp(B) = g_A(\alpha)$ by just substituting $B$ with $\alpha A$ (is this correct?).
I've shown that $\exp(A)$ is invertibel by considering $\exp(-tA)$ and... |
Tagged: determinant Problem 548
An $n\times n$ matrix $A$ is said to be
invertible if there exists an $n\times n$ matrix $B$ such that $AB=I$, and $BA=I$,
where $I$ is the $n\times n$ identity matrix.
If such a matrix $B$ exists, then it is known to be unique and called the
inverse matrix of $A$, denoted by $A^{-1}$.
I... |
Cryptology ePrint Archive: Report 2016/717 Comparison between Subfield and Straightforward Attacks on NTRU Paul Kirchner and Pierre-Alain Fouque Abstract: Recently in two independent papers, Albrecht, Bai and Ducas and Cheon, Jeong and Lee presented two
very similar attacks, that allow to break NTRU with larger paramet... |
I've deduced simple relationships that satisfy each even perfecf number (even numbers $n$ for which $\sum_{d\mid n}d=2n$) and now I wondered about related conjectures.
For each integer $m\geq 1$ we denote the sum of divisors function $\sum_{d\mid m}d$ as $\sigma(m)$, and the Euler's totient function as $\varphi(m)$.
Cl... |
Let $f:\mathbb Z^3\to\mathbb Z^4$ be the group homomorphism given by $$f(a,b,c)=(a+b+c,a+3b+c,a+b+5c,4a+8b).$$ Let $H$ be the image of $f$. Find an element of infinite order in $\mathbb Z^4 /H$ and find the order of the torsion subgroup of that quotient.
This problem certainly has to do with presentation matrices, but ... |
What is the result of $\displaystyle \lim_{n\to \infty}\left(1+\frac{1}{\tan(n)}\right)^{\tan(n)}$ = ?
The limit does not exist as stated by Adam Rubinson. Looks like the requested answer is e but then the question is wrong. What is the correct question to give the answer e? Did answered correctly. But I think this is ... |
I've seen a number of 2D Poisson disc sampling algorithms online that use a grid to accelerate checking for existing points within the minimum radius [![r][r image]][r link] of a candidate point. For example:
They use a grid of squares of side $\frac{r}{\sqrt2}$, which is the same side length that I intuitively came up... |
For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
gmc_nxtman Posts: 1147 Joined: May 26th, 2015, 7:20 pm Kazyan wrote:
Component found in a CatForce result:
Code: Select all
x = 42, y = 67, rule = LifeHistory
A$.2A$2A5$7.A$8.2A$7.2A19$24.2A$24.2A2$39.A$37.A3.A$3... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
Here we want to give an easy mathematical bootstrap argument why solutions to the time independent 1D Schrödinger equation (TISE) tend to be rather nice. First formally rewrite the differential form$$-\frac{\hbar^2}{2m} \psi^{\prime\prime}(x) + V(x) \psi(x) ~=~ E \psi(x) \tag{1}$$into the int...
[Some time travel comme... |
Suppose you have two equtaions: $$2xy + y^2 = 0$$ $$x^2 + 2xy + 1 = 0$$ Subtracting the second from the first yields $y^2 - x^2 - 1 = 0$. Isolating y, we discover that $y = \pm\sqrt{x^2 + 1}$. However, by inspection we can wee that the $2xy$ term in both equations must be negative, which means that a single value of x ... |
skills to develop
To learn how to find, for a normal random variable \(X\) and an area \(a\), the value \(x^\ast\) of \(X\) so that \(P(X<x^\ast )=a\) or that \(P(X>x^\ast )=a\) , whichever is required.
Definition: Left and Right Tails
The left tail of a density curve
Figure \(\PageIndex{1}\): Right and Left Tails of a... |
This is a subtle issue. First let's present a numerical example to see the head-scratching riddle.Assume $$\alpha =1/2 \implies Y = K^{1/2}L^{1/2}$$
and that the exogenously given input prices are
$$r=1/8,\,\, w=4.$$
The f.o.c are
$$\begin{cases} \frac {Y}{2K} = 1/8 \\\\\frac{Y}{2L} = 4 \end{cases} \implies K/4 = 8L \i... |
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