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Image Dimensions Contents Describing the fields of the Canvas Properties Dialog
The user access the image dimensions in the Canvas Properties Dialog.
The Other tab
Here some properties can simply be locked (such that they can't be changed) and linked (so that changes in one entry simultaneously change other entries as ... |
2017-04-19 08:09
Flavour anomalies after the $R_{K^*}$ measurement / D'Amico, Guido (CERN) ; Nardecchia, Marco (CERN) ; Panci, Paolo (CERN) ; Sannino, Francesco (CERN ; Southern Denmark U., CP3-Origins ; U. Southern Denmark, Odense, DIAS) ; Strumia, Alessandro (CERN ; Pisa U. ; INFN, Pisa) ; Torre, Riccardo (EPFL, Laus... |
In the case that $V$ and $W$ are finite-dimensional, here is a "non-intrinsic" way to see this isomorphism. If $V$ is finite-dimensional, then every $\operatorname{End}(V)$-module is semisimple, and moreover every simple $\operatorname{End}(V)$-module is isomorphic to $V$:
Choose a basis $\{e_i\}$ for $V$ and define $P... |
Is there a way to make all three lines of math in the code below take up the same amount of length by use of font expansion? I know too little about
microtype to even see if it could offer a solution. I don't care too much about the exact math environment that'll be used in the end (
gather is not too bad a solution if... |
Hmm;
\textbackslash (mentioned by others) isn't in my reference book (Kopka and Daly).
At any rate, math mode provides
\sim,
\backslash, and
\setminus (the latter two appear to look the same and differ only by spacing in math mode).
My LaTeX book – which, as you would expect, features the \ extensively – seems to use t... |
So I was thinking about my high variance strategies post and I realised that there was a case I hadn’t considered which is kinda important.
Which is that often you’re not very interested in how good your best solution is, only that it’s at least this good for some “this good” bar. e.g. you don’t care how cured cancer i... |
Inflation is a rapid stretching which result in cosmic smoothness and uniformity on large scales; as such, inflation is a key component of almost all fundamental cosmological scenarios. Not only does inflation explain the overall uniformity of the universe, but quantum fluctuations during inflation plant the seeds that... |
Text: Bayesian Data Analysis 3E by Gelman, section 3.6
Let $y | \mu, \Sigma \sim \text{MVN}(\mu, \Sigma),$ where
$\mu$ is a column vector of length $d$ $\Sigma$ is a $d \times d$ symmetric, positive definite, variance matrix both unknown
The conjugate prior for $(\mu, \Sigma)$ is the normal-inverse-Wishart distribution... |
Special Functions of Mathematics
Special mathematical functions related to the beta and gamma functions.
Keywords math Usage
beta(a, b)lbeta(a, b)gamma(x)lgamma(x)psigamma(x, deriv = 0)digamma(x)trigamma(x)choose(n, k)lchoose(n, k)factorial(x)lfactorial(x)
Arguments a, b non-negative numeric vectors. x, n numeric vecto... |
Overview
The ideas we have developed for linear momentum and impulse apply to rotational motion as well. But first, we will need to develop the rotational analogs of the various variable and constructs we have been using. Force, momentum, velocity, impulse all have rotational analogs. The concept that impulse equals ch... |
It is well known (Fricke ?) that $ E_4^{1/4}$ and $ E_6^{1/6}$ can be represented as Gauss hypergeometric functions of $ 1728/j$ and $ 1728/(1728-j)$ respectively. The same result is true in levels $ 2$ , $ 3$ , and $ 4$ for instance, in which case $ E_4$ , $ E_6$ , and $ j$ must be replaced by analogous modular functi... |
You might find this short note helpful ($\LaTeX$ code available [1] if the binary link breaks). I am reproducing the relevant part below:
Theorem. (Folklore) Learning an unknown distribution over a known domain of size $n$, up to total variation $\varepsilon\in(0,1]$, and with error probability $\delta\in(0,1]$, has sa... |
I would like to find the poles and residues of $$ f(z) = \frac {1}{z^2 \sin(\pi (z + \alpha))} $$ Where $0<\alpha<1$.
I found the first pole, which is a double pole at $z=0$, and then also there are poles at $z=n-\alpha$.
To find the residues I used the Laurent expansion, so for the residue of $z_0 = n - \alpha$
$$ f(z... |
@SARAHAI 🏆Gauntlet Run🏆 🏃🏃🏃🏃🏃🏃🏃🏃🏃🏃🏃🏃 🗿Run Rock’s Run🗿 He’s going the distance!Read More @SARAHAI It was a pleasure to have met you. I LOVE YOU
💓💓💓https://youtu.be/sIaT8Jl2zpI💓💓💓 #JESUS For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him. 2 ... |
There are 3 actions of the Galilean group on the free particle: On the configuration space, on the phase space and on the quantum state space (wave functions). The Galilean Lie algebra is faithfully realized on the configuration space by means of vector fields, but its lifted action on Poisson algebra of functions on t... |
A prime $p$ of the form $p = 2q+1$ for another prime $q$ allows a number of shortcuts in calculating a generator for the multiplicative group of $\mathbb{Z}/p\mathbb{Z}.$ That multiplicative group has order $2q,$ so all of its elements have order $1,2,q$ or $2q$.
If we exclude $1$ and $-1$, every other element has orde... |
This problem is $NP$-complete. Reduce from
Exact Cover by $3$- Sets ( X3C).
Given an
X3C instance, its ground set is $\mathcal{U}=\{e_1,e_2,\cdots,e_n\}$. Its collecion of $3$-subsets is $\mathcal{C}=\{s_1,s_2,\cdots,s_m\}$.
For each element in the ground set and each subset in the collection,
we create a new vertex (w... |
A while back I was messing around with representations of finite fields and found this problem above while doing so. I'll explain below how I came to this point but my question is:
Question:How would one show $$F_{\frac{p^2+1}{2}}\equiv p-1 \pmod{p}$$ when $p\equiv \pm 2 \pmod{5}$ and $p\equiv 3 \pmod{4}$?
Here $F_n$ r... |
Let an elliptic curve $ E(a,b )$ $$E(a,b ) = \{(x,y)\,|\,y^2=x^3+ax + b\}$$Where the points of the line $xm + n$:$$P =(x_1, y_1),\, Q =(x_2, y_2),\, R =(x_3, y_3) \in E(a, b)$$
How can you calculate the product between them? $$Q\cdot P =\, ?$$
Let an elliptic curve $ E(a,b )$ $$E(a,b ) = \{(x,y)\,|\,y^2=x^3+ax + b\}$$W... |
i have this question : in an example of the compact embedding, the autor gives a demonstration of : the sobolev space $W^{1,1}(\mathbb{R}^n)$ is not compactly embedded in $L^1(\mathbb{R}^n)$
So let $F\in D(\mathbb{R}^n)$(=the space of smooth functions with a compact support in $\mathbb{R}^n)$ ., not identically equal t... |
I already asked a (stupid) question about this problem here thinking I wouldn't have problems to continue it but I was pretty wrong. I'm finding several more problems trying to solve it. I'll try to summarize what I've done so you don't get bored. The problem is:
Let X be a random absolutely continuous variable with pr... |
Projection¶ class
Projection(
spin=None, atoms=None, l_quantum_numbers=None, m_quantum_numbers=None)¶
Initialize the class by defining the orbitals to include in the projection.
Parameters: spin(None |
Spin.Up|
Spin.Down|
Spin.Sum|
Spin.X|
Spin.Y|
Spin.Z) – Spin components to include in the projection.
Default:
Spin.Su... |
Suppose there is a person standing in a Merry go Round, which is rotating at a constant angular velocity $\vec \omega$. He experiences, of course, a centripetal acceleration $\vec a_{cen}$ and has some tangental velocity $\vec v_{tan}$.
This person now starts to walk in a circular path against the direction of rotation... |
Suppose I have the following Lagrangian density:
$$ \mathcal L = -\frac{1}{2} \sum_{i = 1}^N \left [ \partial_\mu \phi_i\partial^\mu \phi^i +m^2 \phi_i^2\right ] + \frac{g}{2N}\sum_{i=1}^N \sum_{j=1}^N \phi_i^2 \phi_j^2 $$
where the $\phi$'s are real scalar fields. Then we can see that, as $N \to +\infty$, the coupling... |
Ozer, O., Khammash, A. (2017). On the real quadratic fields with certain continued fraction expansions and fundamental units. International Journal of Nonlinear Analysis and Applications, 8(1), 197-208. doi: 10.22075/ijnaa.2017.1610.1420
Ozen Ozer; Ahmed Khammash. "On the real quadratic fields with certain continued fr... |
How do I calculate the infinite sum of this series?
$$\sum_{n=1}^{\infty}n^2q^n = -\frac{q(q+1)}{(q-1)^3}\ \text{when}\ |q| < 1.$$
How does wolfram alpha get this result?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a m... |
Modeling Metallic Objects in Wave Electromagnetics Problems
Metals are materials that are highly conductive and reflect an incident electromagnetic wave — light, microwaves, and radio waves — very well. When using the RF Module or the Wave Optics Module to simulate electromagnetics problems in the frequency domain, the... |
2017-04-19 08:09
Flavour anomalies after the $R_{K^*}$ measurement / D'Amico, Guido (CERN) ; Nardecchia, Marco (CERN) ; Panci, Paolo (CERN) ; Sannino, Francesco (CERN ; Southern Denmark U., CP3-Origins ; U. Southern Denmark, Odense, DIAS) ; Strumia, Alessandro (CERN ; Pisa U. ; INFN, Pisa) ; Torre, Riccardo (EPFL, Laus... |
I am interested in finding pressure of neutron star! So. Please could any tell me how to choose central density for the inner and outer core of neutron Star. What numeric value should me in both core. Also what should be the polytropic index gamma for outer core.
The central density of a neutron star is unknown, but pr... |
I'm interested in using the horseshoe prior (or the related hierarchical-shrinkage family of priors) for regression coefficients of a traditional multilevel regression (e.g., random slopes/intercepts). Horseshoe priors are similar to lasso and other regularization techniques, but have been found to have better performa... |
I am trying to prove:
$$\lim _{ x \rightarrow 1 }{ \frac { x^{ 2 }-1 }{ x-1 } } = 2$$
So I began to work on proving it using epsilon-delta:
$$\left| \frac { x^{ 2 }-1 }{ x-1 } -2 \right| <\epsilon \\ -\epsilon <\frac { x^{ 2 }-1 }{ x-1 } -2<\epsilon \\ -\epsilon +2<\frac { x^{ 2 }-1 }{ x-1 } <\epsilon +2$$
And then I'm... |
Let $a,b$ be the major and minor axes of the ellipse.
Let $x_0,y_0$ be the coordinates of the center on the ellipse.
Let $x_1,y_1$ be the coordinates of the one point on the ellipse.
First, we write the equation of the ellipse, those major axis is parallel to the $x$ axis of the coordinate system (which is at this poin... |
A very partial answer :
$$\left(\frac{\partial T}{\partial t}\right)^2 - \frac{1}{t^2}\left(\frac{\partial T}{\partial r}\right)^2 = 1 \qquad\qquad [1]$$
Change of function : $\qquad \cosh\left(f(r,t)\right) =\frac{\partial T}{\partial t} \qquad\implies\qquad t\:\sinh\left(f(r,t) \right)=\frac{\partial T}{\partial r}$
... |
2013-10-10 15:39
Status of the NA62 liquid krypton electromagnetic calorimeter Level 0 trigger processor / Bonaiuto, V (IAS, Rome ; Rome U.,Tor Vergata) ; Federici, L (IAS, Rome ; Rome U.,Tor Vergata) ; Fucci, A (INFN, Rome2) ; Paoluzzi, G (INFN, Rome2) ; Salamon, A (INFN, Rome2) ; Salina, G (INFN, Rome2) ; Santovetti,... |
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J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
OpenCV 3.1.0
Open Source Computer Vision
Here, the matter is straight forward. If pixel value is greater than a threshold value, it is assigned one value (may be white), else it is assigned another value (may be black). The function used is
cv2.threshold. First argument is the source image, which should be a grayscale ... |
Definition:Epsilon Relation/Restriction
Jump to navigation Jump to search
The
Definition
Let $S$ be a set.
The
restriction of the epsilon relation on $S$ is defined as the endorelation $\Epsilon {\restriction_S} = \left({S, S, \in_S}\right)$, where: $\in_S \; := \left\{{\left({x, y}\right) \in S \times S: x \in y}\righ... |
Assessment | Biopsychology | Comparative |Cognitive | Developmental | Language | Individual differences |Personality | Philosophy | Social |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology | Cronbach's $ \alpha $ (alpha) is a statistic. It has an important use as a mea... |
Hello one and all! Is anyone here familiar with planar prolate spheroidal coordinates? I am reading a book on dynamics and the author states If we introduce planar prolate spheroidal coordinates $(R, \sigma)$ based on the distance parameter $b$, then, in terms of the Cartesian coordinates $(x, z)$ and also of the plane... |
In this answer the following lemma is proved:
Lemma
Let $X$ be a Hausdorff space and $C \subset X$ have a compact
neighbourhood $K$. Then $C$ is a component of $X$ if and only if
$C$ is a component of $K$
Also:
Let $X$ be a compact Hausdorff space, $Y$ an open subspace and $Z$ a closed
subspace.
Let $C$ be a connected ... |
Let $B = \left\{ A \cup \mathbb{N}_\text{even} : A\subseteq \mathbb{N}_\text{odd} \right\}$
I need to show $\left|B\right| = \mathfrak{c}$
by using an equivalence function (bijection) to another set with the same cardinality.
Any idea? Thanks.
Mathematics Stack Exchange is a question and answer site for people studying... |
In this article I’m about to present the process of decoding previously recorded FSK transmission with the use of Python, NumPy and SciPy.
The data was gathered using SDR# software and it is stored as a wave file that contains all the IQ baseband data @ 2.4Msps
The complete source code for this project is available her... |
How to Build Gear Geometries in the Multibody Dynamics Module
Realistic gear geometries are useful for multibody dynamics simulations when coupled with other physical phenomena. Rather than manually building these geometries, we can use built-in parts available in the Part Library. With these highly parameterized gear ... |
I‘ll ignore $q$ and $v$ in the following, so that $\gamma$ is a unit speed geodesic and $u(t)=exp_p^{-1}(\gamma(t)).$ Furthermore let $\sigma(t)=exp_p(tu(1)).$
Then by the Gauss Lemma\begin{equation}\langle u‘(t),u(0)\rangle=\langle (dexp_p)_{u(0)}(u‘(0)),\sigma‘(1)\rangle=\langle \gamma‘(0),\sigma‘(1)\rangle.\end{equa... |
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 ... |
Topological Methods in Nonlinear Analysis Topol. Methods Nonlinear Anal. Volume 46, Number 1 (2015), 223-246. Index 1 fixed points of orientation reversing planar homeomorphisms Abstract
Let \(U \subset {\mathbb R}^2\) be an open subset, \(f\colon U \rightarrow f(U) \subset {\mathbb R}^2\) be an orientation reversing h... |
Bill Dubuque raised an excellent point here: Coping with *abstract* duplicate questions.
I suggest we use this question as a list of the generalized questions we create.
I suggest we categorize these abstract duplicates based on topic (please edit the question). Also please feel free to suggest a better way to list the... |
Define $f:\mathbb{R} \rightarrow \mathbb{R}$. For any fixed closed interval $[a,b] $,$f(x) $ is $Riemann$ integrable on $[a,b].$
Show that $\forall a,b;c,d\in\mathbb{R},a<b,c<d.$$\int_{a}^{b}dx\int_{c}^{d}f(x+y)dy=\int_{c}^{d}dy\int_{b}^{a}f(x+y)dx.$
If $f (x+y) $ is $Riemann$ integrable on $\mathcal{R}=[a,b]\times [c,... |
If I understand correctly the equation for kinetic energy in relativity is $$ E_k= mc^2 \left(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1\right) \;,$$ and the equation for escape velocity in General Relativity is the same as in Newtonian Physics so $v_e=\sqrt{\frac{2GM}{r}}$ and when something is moving at escape velocity the... |
I am working through the NLP notes for Naive Bayes' classification here: https://web.stanford.edu/~jurafsky/slp3/6.pdf
Below $c$ is the class of the observation and $w_i$ is the $i$th word of a text document.
In developing the maximum likelihood estimate for the conditional probability of the feature (word) $w_i$ given... |
As far as your added question goes, no, I'm afraid your thought process is invalid. You are essentially using a classic misapplication of the Divergence Test.
Divergence Test. If the limit of $a_n$ as $n\to\infty$ is not equal to $0$ (either does not exist, or exists and is not equal to $0$), then the series
$$\sum a_n... |
The following words reflect my understanding(an elementary one) of the divergent series. We first define an infinite series as follows:
$L = \sum_{n=0}^{\infty}a_n \Leftrightarrow L = \lim_{k \rightarrow \infty} S_k.$
Where $S_k$ is the partial sum of the infinite series from $a_0$ to $a_k$. A series whose limit exists... |
To understand the concept
intuitively, ask the question of why it is needed. And start from a simpler question, why is the variance computed as $V = \frac 1 {N-1} \sum (x_i-\bar x)^2$ with a $N-1$ as denominator.
The fact is that you are interested in the variance of the population, not of the one of sample. Now obviou... |
CentralityBin () CentralityBin (const char *name, Float_t low, Float_t high) CentralityBin (const CentralityBin &other) virtual ~CentralityBin () CentralityBin & operator= (const CentralityBin &other) Bool_t IsAllBin () const Bool_t IsInclusiveBin () const const char * GetListName () const virtual void CreateOutputObje... |
Suppose the curve is given in parametric form $$ C: \vec{r} = \langle x(t), y(t) \rangle$$
At any time $t_0$, a point on the curve is given by
$$ P(x_0,y_0) = \langle x(t_0), y(t_0) \rangle $$
The vector tangent to $C$ at $P$ is $$ \vec{v} = \langle \dot x(t_0), \dot y(t_0) \rangle $$
The direction vector of the line $... |
I am currently attempting to calculate the heat transfer when compressed air is flowing isothermally through a pipe with frictional losses. I realise this might seem like an odd question, but I am aiming to demonstrate the difference between assuming isothermal flow and isentropic on the calculated pressure drop and wi... |
You might want to look at
https://scilearn.sydney.edu.au/fychemistry/prelab/e12.shtml
and the related page
https://scilearn.sydney.edu.au/fychemistry/calculators/lattice_energy.shtml
which has a nice lattice energy calculator that allows you to play with the parameters and see how the lattice energy varies, but I'll tr... |
I'm trying to locate my four zeroes of a complex-valued function, in order to apply the Residue Theorem.
After using the quadratic formula, I am left with $$z^2 = [-3 \pm i\sqrt7] / 2$$
writing the left side in exponential form, I get: $$z^2 = 2exp(\pm i\theta)/2$$
which gives $$z=\pm \sqrt2exp(\pm i\theta/2)/2$$
these... |
Steric hinderance is a major component in determining the feasibility and the rate of a chemical reaction. Wouldn't it be useful to measure it quantitatively then? This would make it easier to compare the property of two molecules. Are there currently ways to measure steric hindrance, or is it not possible for some rea... |
The examples we just worked through have shown how we can use the steady-state energy density model to calculate various fluid flow or charge flow parameters given sufficient details about the physical situation. Now we extend this analysis to complete “circuits.” There is not any really new physics in what we are abou... |
Strong Acids
In water, strong acids completely dissociate into free protons and their conjugate base.
Learning Objectives
Calculate pH for solutions of strong acids.
Key Takeaways Key Points Strong acids can catalyze chemical reactions. Strong acids are defined by their pKa. The acid must be stronger in aqueous solutio... |
... counterclockwise 45 degrees with respect to z axis means that you look along the +z direction from the origin. The plane of the loop then lies along the same direction as $B$ so $\mu$ and $B$ are now perpendicular. Torque is now a maximum. (See diagram below.)
The magnitude of $\mu$ is still the same ($0.016 Am^2$)... |
The general Solution to the Equation A more general way to write this equation that emphasizes its applicability to all cases of SHM is as follows: We will arbitrarily use the symbol “y”, but we just as well have used \( \theta \), or x, or any other symbol.
\[ \dfrac{d^2}{dt^2} y(t) = \left(\dfrac{- 2 \pi} { T} \right... |
I solved one question in a book of analysis, and although I used an informal method to check it, I'd like to know more about what should be done. The question was the following:
$A\subset X$ and $ B \subset X$;
If $A\subset Y$ and $ B\subset Y$, then $X\subset Y$.
Prove that $X=A\cup B$.
Looking at the second line, we ... |
Armed with only a basic knowledge of vectors and knowing the required length proportions for an equilateral triangle and a regular tetrahedron, here is a plodding derivation of the coordinates for your circumscribing tetrahedron.
I start with a unit cube with corners at $(0,0,0)$ and $(1,1,1)$ for convenience.
As noted... |
Steric hinderance is a major component in determining the feasibility and the rate of a chemical reaction. Wouldn't it be useful to measure it quantitatively then? This would make it easier to compare the property of two molecules. Are there currently ways to measure steric hindrance, or is it not possible for some rea... |
Physicists prefer to work with conservative forces because this results in path independence. What this means is that the net work done by a system over a closed path goes to zero:
\begin{equation}W = \oint_C \vec{F}\cdot d\vec{r} = 0\end{equation}
This can only be true if the force $F$ does not depend explicitly on th... |
I have a small confusion over describing the cutoff point for the critical region in a likelihood ratio test when the null hypothesis is composite. Take this exercise in particular:
Let $(X_1,X_2,\ldots,X_n)$ be a random sample from a shifted exponential distribution with density $$f_{\theta}(x)=e^{-(x-\theta)}\mathbf1... |
Introduction
Built at the Jet Propulsion Laboratory by an Investigation Definition Team (IDT) headed by John Trauger, WFPC2 was the replacement for the first Wide Field and Planetary Camera (WF/PC-1) and includes built-in corrections for the spherical aberration of the HST Optical Telescope Assembly (OTA). The WFPC2 wa... |
The Particle In Cell example posted previously was based on a uniform, Cartesian mesh. Such meshes are common in PIC simulations for a good reason. The PIC method requires interpolation of properties between particles and the mesh. As such, it is important to be able to quickly find the containing cell and compute the ... |
Hello guys! I was wondering if you knew some books/articles that have a good introduction to convexity in the context of variational calculus (functional analysis). I was reading Young's "calculus of variations and optimal control theory" but I'm not that far into the book and I don't know if skipping chapters is a goo... |
The goal of this section is simply to extend the naive discussion of energy and temperature we have running so far to include phase changes. I use the word naive in the sense that, at this point in the course, we still don't understand what the underlying mechanisms in thermal phenomena really are. There were a lot of ... |
I recently looked up J. van Hoorn's question on How to color delimiters in Math Mode, and so I decided to test my LaTeX knowledge by trying to define a new appropriate command:
\leftcolor{color}<delim symbol> and
\rightcolor{color}<delim symbol>.
The MWE is as follows:
\documentclass{article}\usepackage{amsmath}\usepac... |
$\mathop {\lim }\limits_{x \to {0^ + }} \left( {\frac{1}{x} - \frac{1}{{\sqrt x }}} \right) = \mathop {\lim }\limits_{x \to {0^ + }} \frac{{1/\sqrt x - 1}}{{\sqrt x }} = \mathop {\lim }\limits_{x \to {0^ + }} \frac{{ - \frac{1}{2}{x^{ - 3/2}}}}{{\frac{1}{2}{x^{ - 1/2}}}} = \mathop {\lim }\limits_{x \to {0^ + }} \left( ... |
Why does delocalization of electrons generally make compounds more stable (e.g. in carboxylate anions, where the lone pair on the negatively charged oxygen is delocalised into the C=O π* orbital)? Is there any proper explanation involving quantum mechanics?
A simple QM explanation I can think of would invoke Hückel the... |
This question already has an answer here:
Is there an exact form of $$f(s)=\sum_{n=0}^\infty {\frac{(-1)^n}{(2n+1)^s}}=1-\frac{1}{3^s}+\frac{1}{5^s}-\frac{1}{7^s}+\dots$$ when $s$ is odd?
Discussion
I have been exploring infinite series and will be spending my evening looking for patterns in this particular class. I in... |
Approximation
This article
needs additional citations for verification. (April 2013) (Learn how and when to remove this template message)
An
approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usageEdit
The word
approximation is derived from Latin approximatus,... |
A sequence which is either non-decreasing or non-increasing is said to be monotone, this is the definition we have been given. But if a sequence is strictly increasing or strictly decreasing then that doesn't mean it is monotone so monotone is only if it is non-decreasing or non-increasing. Am I correct or not?
A seque... |
Here is a well-known interview/code golf question: a knight is placed on a chess board. The knight chooses from its 8 possible moves uniformly at random. When it steps off the board it doesn’t move anymore. What is the probability that the knight is still on the board after \( n \) steps?
We could calculate this direct... |
Learning Objectives
Describe the general characteristics of friction List the various types of friction Calculate the magnitude of static and kinetic friction, and use these in problems involving Newton’s laws of motion
When a body is in motion, it has resistance because the body interacts with its surroundings. This r... |
For the electromagnetism, the charge density is defined as the total amount of charge carried for a particular length, area, or the volume. The symbol Pho (ρ) is used to denote the electric charge and subscript (v) is added to indicate the volume charge density.
Here, is given the volume charge density formula for your... |
The normal contact impulse $J$ between the rod and plane has two effects : it changes the velocity of the CM of the rod, and it makes the rod rotate about its CM.
The impulsive force is related to the change in momentum of the CM of the rod, and the impulsive torque to the change in angular momentum of the rod, as foll... |
Note that it suffices to prove that every partition of $V$ into finite sets, $U_i$, with $|U_i|\geq k$ you can choose $v_i$ as described. The result would then hold for arbitrary partitions: if $U_i$ with $i\in I$ is a partition such that $|U_i|\geq k$ for all $i$, pick any subpartition of finite sets, $W_i$ indexed by... |
I'm a high school student who never studied any relativity before, but I'm just wondering what was THE question that Einstein asked himself before going into this field. I knew he has done lots of work such as Brownian motion, photoelectric effect,etc. What was the question that baffled and therefore motivated him to w... |
Harmonic Wave Equation
For the rest of the course we will focus on infinite repeating waves of a specific type:
harmonic waves. Mechanical harmonic waves can be expressed mathematically as \[y(x,t) - y_0 = A \sin{\left( 2 \pi \dfrac{t}{T} \pm 2 \pi \dfrac{x}{\lambda} + \phi \right)}\]The displacement of a piece of the ... |
I am trying to solve the following:
The nonnegative, integer-valued, random variable X has generating function $g_{X(t)}=log(\frac{1}{1-qt})$. Determine $P(X = k)$ for $k = 0, 1, 2, . . .$, $E[X]$, and $Var[X]$.
I know the probability generating function is of the form $g_{X(t)}=E[t^{x}]=\sum_{n=1}^{\infty}t^{n}*P(X=n)... |
Let $f :[a , \infty)\to \mathbb{R}$ a positive and Monotonic function such that $\int_a^\infty f$ converge
prove: $\lim_{x\to\infty}f(x)=0$
That's an easy calculation… assume $$\lim_{x\to\infty}f(x)\not=0$$ then because f is monotone and positive there exists an $\varepsilon > 0$ s.t. $f>\varepsilon$ so $$\int_a^\infty... |
From the theory of conics circumscribing a quadrilateral we know that only one (degenerate or non degenerate) equilateral hyperbola passes through the four vertices of a quadrilateral (convex, concave or crossed), except when the two pairs of lines of opposite sides of the quadrilateral are perpendicular. In this excep... |
Consider the following situation.
$1m^3$ of water is in the surface of the ocean. If we get that volume of water, and transport it $11km$ down into the ocean, what is going to be the new density of the water?
After a friend of mine asked this question to me, I considered the compressibility equation, that relates press... |
This question already has an answer here:
Why does the concatenation of $\emptyset$ with any language give $\emptyset$. I would like to know the intuitive explanation for it.
Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. It only takes a mi... |
I've recently learned that the cotangent satisfies the following functional equation:
$$\dfrac1{f(z)}=f(z)-2f(2z)$$
(true for $f(z)\neq 0$).
Can we solve this equation for real or complex functions $f?$ Can we give additional conditions such that $\cot$ is the only real or complex function satisfying these conditions a... |
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You have a good intuition on the possible answer because it does involve oscillations, but you need to visualize the string differently. The origin of the conundrum is not quantum, but relativistic. Here's why:
Consider an inertial frame O and set up a string spanning the entire $x$ axis, stretching from $x \rightarrow... |
Functiones et Approximatio Commentarii Mathematici Funct. Approx. Comment. Math. Volume 37, Number 2 (2007), 461-471. Hypothesis H and the prime number theorem for automorphic representations Abstract
For any unitary cuspidal representations $\pi_n$ of $GL_n(\mathbb{Q}_\mathbb{A})$, $n=2,3,4$, respectively, consider tw... |
I have found a new proof of the Barwise extension theorem, that wonderful yet quirky result of classical admissible set theory, which says that every countable model of set theory can be extended to a model of $\text{ZFC}+V=L$.
Barwise Extension Theorem. (Barwise 1971) $\newcommand\ZF{\text{ZF}}\newcommand\ZFC{\text{ZF... |
Here is a well-known interview/code golf question: a knight is placed on a chess board. The knight chooses from its 8 possible moves uniformly at random. When it steps off the board it doesn’t move anymore. What is the probability that the knight is still on the board after \( n \) steps?
We could calculate this direct... |
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science > Hokkaido University Preprint Series in Mathematics > Chambers of Arrangements of Hyperplanes and Arrow's Impossibility Theorem
Title: Chambers of Arrangements of Hyperplanes and Arrow's Impossibility Theo... |
Difference between revisions of "User:Nikita2"
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I am Nikita Evseev
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I am Nikita Evseev Novosibirsk, Russia.
My research interests are in [[Mathematical_analysis | Analysis]] and [[Sobolev space|Sobolev spaces]].
My research interests ... |
OpenCV 3.4.3
Open Source Computer Vision
Structured forests for fast edge detection EdgeBoxes Filters Superpixels Image segmentation Fast line detector Fourier descriptors
void cv::ximgproc::anisotropicDiffusion (InputArray src, OutputArray dst, float alpha, float K, int niters) Performs anisotropic diffusian on an ima... |
Let's discuss all of the "ingredients" separately, and then add them:
The base odds for rolling any given number on a d6 are \$\frac{1}{6}\$. The base odds for rolling a 5 or 6 on a d6 are \$\frac{1}{3} = 0.33\$ (2 out of 6 making \$\frac{2}{6} = \frac{1}{3}\$). Similarly, the odds for rolling 1-4 on a d6 are \$\frac{2... |
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