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From: https://stats.stackexchange.com/a/236297/22199, I quote
A mixture distribution combines different component distributions with weights that typically sum to one (or can be renormalized). A gaussian-mixture is the special case where the components are Gaussians.
Does this mean the following is a regression equatio... |
Regarding question 2: FQHEs are examples of topological phases of matter, whose effective field theories are topological quantum field theories, whose quasi-particle excitations are (essentially) described by modular tensor categories (MTCs). Since what we're usually interested in for constructing models of topological... |
This question already has an answer here:
Density of irrationals 5 answers
Proof that for $a,b \in \mathbb{R}$ there is an irrational number $r$ so that $a < r < b$. Basically, proof, that between any two irrationals, there is another irrational r.
I'm sure there are already many ways out there how to do it, however I ... |
Integer Addition is Commutative
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Theorem $\forall x, y \in \Z: x + y = y + x$
$\blacksquare$
Let $x = \eqclass {a, b} {}$ and $y = \eqclass {c, d} {}$ for some $x, y \in \Z$.
Then:
\(\displaystyle x + y\) \(=\) \(\displaystyle \eqclass {a, b} {} + \eqclass {c, d} {}\) Definition of Inte... |
Consider an undirected network $G = (V,E)$ in which edge $e$ $\in$ $E$ fails after (deterministic) time $t(e) > 0$. Network failure occurs at the first instant in which $G$ is no longer connected. Let $m = |E|$ and assume the values $\{t(e): e \in E\}$ are distinct.
You wish to determine the instant $\tau$ at which the... |
You must guard against division by zero. When you "cancel out $t^2$", you are dividing both sides of your equation by $t^2$. Consequently, the correct form of inference is
$$\begin{align*} 2t^2+t^3 &= t^4 & & \\ 2 + t &= t^2 \qquad \text{ or } \qquad t^2 = 0.\end{align*}$$
The resulting left choice has the solution set... |
I'm playing a bit with category theory, and I've noticed that it is actually not rare when an object $C$ of a category $\mathcal{C}$ is isomorphic to its square $C \times C$.
An object $C$ of a category $\mathcal{C}$ is therefore called idempotent whenever it is isomorphic to its (categorical) product. Trivial examples... |
Is $$ f(n,x,y)=\sum^{n-1}_{k=1}{n\choose k}x^{n-k}y^k,\qquad\qquad\forall~n>0~\text{and}~x,y\in\mathbb{Z}$$ always divisible by $2$?
(Hint) An odd number raised to any power is odd, and an even number raised to any power is even. In particular, $$ (x + y)^n \equiv (x + y) \pmod 2 $$ Using this along with the binomial f... |
Here's a question on a passage from this paper I'm reading. Here's the quote:
Given the vector of portfolio weights $w$, and the estimate of the conditional variance, $\Sigma_{t,k}$, the predicted portfolio variance is $\hat{\sigma}_{p,t,k} = w'\Sigma_{t,k}w$. The VaR at the $1\%$ and $5\%$ level is computed for each p... |
When I write
\[\left \lVert \overrightarrow{\nabla} \right \rVert\]
I get way too much extra space under the baseline:
Why is this happening, and how can I fix it?
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. It only takes a minute to sign u... |
Damping in Structural Dynamics: Theory and Sources
If you strike a bowl made of glass or metal, you hear a tone with an intensity that decays with time. In a world without damping, the tone would linger forever. In reality, there are several physical processes through which the kinetic and elastic energy in the bowl di... |
SemiCircleContour¶ class
SemiCircleContour(
integral_lower_bound=None, circle_eccentricity=None, logarithmic_bunching=None, circle_points=None, fermi_line_points=None, fermi_function_poles=None)¶
An equilibrium contour using the semi-circle contour points and weights defined in [gBMO+02].
Parameters: integral_lower_bou... |
Studying relation properties. My definition of a transitive relation is as follows:
A relation is transitive if and only if $\forall a,b,c \in A [aRb \land bRc \implies aRc]$
My question is: if $aRb \land bRc$ never occurs in the first place, is the relation considered transitive?
I ask this because when I read $\foral... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
If $\lambda_1,\dots,\lambda_n$ are distinct positive real numbers, then $$\sum_{i=1}^n \prod_{j\neq i} {\lambda_j\over \lambda_j-\lambda_i}=1.$$This identity follows from a probability calculation that you can find at the top of page 311 in the 10th edition of
Introduction to Probability Models by Sheldon Ross.
Is ther... |
Gradient Boosting Seen as Gradient DescentMathematics · tldr
The short version of this whole thing is that we can see the gradient boosting algorithm as just gradient descent on black-box models. Typically gradient descent involves parameters and a closed form solution to the gradient of your learner as a way to update... |
OpenCV 3.4.3
Open Source Computer Vision
class cv::line_descriptor::BinaryDescriptor Class implements both functionalities for detection of lines and computation of their binary descriptor. More... class cv::line_descriptor::BinaryDescriptorMatcher furnishes all functionalities for querying a dataset provided by user o... |
As soon as you will get into pretty complex derivatives, for example, you will need to generate correlated assets for pricing purposes. Example of such derivatives can be: Basket options Rainbox options Moutain ranges (created by Société Générale) The most complex amongst these derivatives cannot be priced using closed... |
I'm making some graphs and I have to label the axes. I want to be extra careful and put the units in even though the meaning of $\text{pH}$ is well known. But I have a problem (though a simple one): $\text{pH}$ is a minus logarithm (base 10) of concentration of hydrogen ions (or rather their activity). What is the unit... |
For the purpose of keeping essentials and being consistent with my source material, I took the freedomto replace the OP's original equation by the following:$$\frac{dc}{dt}=K\Delta c \quad \rightarrow \quad\frac{\partial T}{\partial t} = \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2}$$This means ... |
Discussion on Bangladesh Mathematical Olympiad (BdMO) National
Moon Site Admin Posts: 751 Joined: Tue Nov 02, 2010 7:52 pm Location: Dhaka, Bangladesh Contact:
Problem: In triangle $ABC$, medians $AD$ and $CF$ intersect at point $G$. $P$ is an arbitrary point on $AC$. $PQ$ & $PR$ are parallel to $AD$ & $CF$ respectivel... |
This answer uses a simplified method, which avoids the complications of having to deal with internal forces between the link and cylinders.
The motion of the two cylinders is identical, so they can be treated as one cylinder of mass $2M$. The link is then a point mass $m$ located at distance $r_0$ from the centre O. We... |
In Jackson's text he says that Faraday law is actually:$$\oint_{\partial \Sigma} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell} = -k\iint_{\Sigma} \frac{\partial \mathbf B}{\partial t} \cdot \mathrm{d}\mathbf{S}$$where $k$ is a constant to be determined.
(page 210, third ed.).He claims that $k$ is not an independent empi... |
I know that this question has been submitted several times (especially see How are anyons possible?), even as a byproduct of other questions, since I did not find any completely satisfactory answers, here I submit another version of the question, stated into a very precise form using only
very elementary general assump... |
The set of lambda calculus expressions $Expr$ is generated by the grammar $$ Expr \ni e ::= x \mid \lambda x\ldotp e \mid e_1 e_2 $$
We can define an interpreter without explicit substitution by using
environments and closures:$$ \begin{align*} Env &= Var \rightharpoonup Cl &\text{($\rightharpoonup$ is partial function... |
June 15th, 2015, 12:48 AM
# 1
Senior Member
Joined: Apr 2008
Posts: 194
Thanks: 3
Is this word problem solvable with a lack of information?
Two gears engage with each other. Gear 1 has 6 teeth. Gear 2 has 8 teeth. As Gear 1 turns, it causes Gear 2 to turn at a different rate. Gear 1 is rotated until the two gears are b... |
I've formulated two conjectures that seems to imply a strong result when are combined with well known equivalences of the Riemann hypothesis, and I would like to know how get a disproof of such statements.
Let $S(n)=\sum_{k=1}^n\text{n mod k}$
the sum of remainder function, then it is know that for each $n>1$$$\sigma(n... |
For this univariate linear regression model $$y_i = \beta_0 + \beta_1x_i+\epsilon_i$$ given data set $D=\{(x_1,y_1),...,(x_n,y_n)\}$, the coefficient estimates are $$\hat\beta_1=\frac{\sum_ix_iy_i-n\bar x\bar y}{n\bar x^2-\sum_ix_i^2}$$ $$\hat\beta_0=\bar y - \hat\beta_1\bar x$$ Here is my question, according to the bo... |
It is maybe simpler to consider all the generators as representations of $SL(2,C)$, so, using spinor indices, you will have : $M^{\alpha \dot \alpha \beta \dot \beta}, P^{\beta \dot \beta}, Q_\alpha, \bar Q^\dot\beta$
Indices are raised and lowered with the Levi-Civita symbols $\epsilon_{\alpha \beta}, \epsilon^{\alpha... |
joriki
I don't know why people complain about copy-pasted homework. I wish people would copy-paste their homework. What gets me is when they paraphrase it incorrectly or copy it sloppily by hand and a lot more work is spent on fixing the problem statement and figuring out which errors were in the original and which are... |
Let $S=K[X_1,\dots,X_{n-1}]$. Now consider the polynomial extension $S\subset S[X]$. The question becomes
Why a maximal ideal of $S[X]$ lies over a maximal ideal of $S$?
This holds in the more general frame of finitely generated algebras over a field, and a proof can be found here. (However, one can not extend the prop... |
I received this question during an onsite interview for a quant job and I'm still scratching my head on how to solve this problem. Any help would be appreciated.
Mr Quant thinks that there is a linear relationship between past and future intraday returns. So he would like to test this idea. For convenience, he decided ... |
Fernholz and Karatzas have published various papers about so called stochastic portfolio theory. Basically they say that the return to be expected from a portfolio on the long run is rather the growth rate $$ \gamma = \mu - \frac12 \sigma^2 $$ than $\mu$, where $\mu$ is the drift coefficient of the price process $S_t$ ... |
Overview
This solution is a simpler altervative to that of gIS. It makes use only of the standard functions of Mathematica non-commutative multiplication (NCM) and replacement. Due to the uncommon features of the NCM, some care must be taken with linear combinations
In the first part we study the expression $\frac{1}{1... |
Every node is equivalent to every other node.
To see this, draw the graph of this Markov chain:
Each of these four figures is a graph of the chain--all are equally good representations of it. The nodes are consistently represented by color and the transitions by edge style: the solid edges are, say, the $\alpha$ transi... |
Answer
5.4 percent
Work Step by Step
We use the margin of error equation to find: $$=100\times \frac{1}{\sqrt{n}}\\ = 100 \times \frac{1}{\sqrt{340}} \\ =5.4\text{%}$$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have
24 hours to send in a draft... |
I asked this question before about whether I can take a component of angular velocity along another axis and say that the body spins about that axis with that component.
Now I have another doubt:
Consider a rigid body having an inertia $I_0$ and angular velocity $\omega_0$ about some axis. So according to the answer to... |
Do you like data? Data about rocks? Open, accessible data that you can use for any purpose without asking? Read on.
The server I run the wiki on — legacy Amazon AWS infrastructure — crashed, and my backup strategy turned out to be <cough> flawed. It's now running on state-of-the-art Amazon servers. So my earlier effort... |
Generalizing the entanglement entropy of singular regions in conformal field theories Abstract
We study the structure of divergences and universal terms of the entanglement and Rényi entropies for singular regions. First, we show that for (3 + 1)-dimensional free conformal field theories (CFTs), entangling regions eman... |
Quantum Fidelity between two density operators, $\hat{\rho}$ and $\hat{\sigma}$, is given by $F(\hat{\rho},\hat{\sigma})=\left(Tr\sqrt{\sqrt{\hat{\rho}}\hat{\sigma}\sqrt{\hat{\rho}}}\right)^2$, where $Tr$ represents the trace.
If both the density operators represent pure states: $\hat{\rho}=|\psi\rangle\langle\psi|$ an... |
№ 9
All Issues Volume 58, № 12, 2006 Order reduction for a system of stochastic differential equations with a small parameter in the coefficient of the leading derivative. Estimate for the rate of convergence
Ukr. Mat. Zh. - 2006. - 58, № 12. - pp. 1587–1601
In the metric $\rho(X, Y) = (\sup\limits_{0 \leq t \leq T} M|... |
Addition of Cross-Relation Equivalence Classes on Natural Numbers is Well-Defined Theorem
Let $\struct {\N, +}$ be the semigroup of natural numbers under addition.
Let $\struct {\N \times \N, \oplus}$ be the (external) direct product of $\struct {\N, +}$ with itself, where $\oplus$ is the operation on $\N \times \N$ in... |
Abstract
In this paper, we study optimization of the first eigenvalue of $$-\nabla \cdot (\rho (x) \nabla u) = \lambda u$$-∇·(ρ(x)∇u)=λu in a bounded domain $$\Omega \subset {\mathbb {R}}^n$$Ω⊂
Rn under several constraints for the function $$\rho $$ρ. We consider this problem in various boundary conditions and various ... |
Arithmetic, algebra, number theory, sequence and series, analysis, ...
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f:R->R is a function satisfying the following properties:
(i) f(-x) = - f(x) (ii) f(x+1) = f(x) + 1 (iii) f(1/x) = f(x)/(x^2) for x not equal to 0. Determine whether or not f(x) = x for all real values of x. NOTE: R ... |
I can shed some light on the question, but am not sure I can answer it as I am not sure it is really even well defined.
(1) The Weak Axiom of Revealed Preference is a decision theoretic concept regarding the choices of a single agent. So I do not understand how having $N$ agents is relevant to the problem.
(2) Generall... |
Performing algebraic operations on functions combines them into a new function, but we can also create functions by composing functions. When we wanted to compute a heating cost from a day of the year, we created a new function that takes a day as input and yields a cost as output. The process of combining functions so... |
I wouldn't call this novel but... I'm going to give an example on how to do this for a specific filter with a specific discretization.
A 1st order butterworth low-pass filter is given by:
$H(s) = \frac{Y(s)}{X(s)} =\frac{\omega_c}{s + \omega_c}$
Where $\omega_c$ is the cut-off frequency of the filter.
The backward diff... |
This is a linear recursion relationship. The methods for calculating formulas for the $n$ term are well known. In particular, we can form a vector for $k$ adjacent elements of the sequence: $$U_i = \begin{bmatrix}u_{i+k}\\u_{i+k-1}\\\vdots\\u_i\end{bmatrix}$$
Then we find that $$U_{i+1} = AU_i$$ where $$A = \begin{bmat... |
There are three bodies $a,b,c$ which are discs of diameter $2m,4m,$ and $6m$ respectively.
Their emitted wavelengths are $300nm,400nm$ and $500nm$ respectively.
Which emission power is maximum ?
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes... |
Please assume that this graph is a highly magnified section of the derivative of some function, say $F(x)$. Let's denote the derivative by $f(x)$.Let's denote the width of a sample by $h$ where $$h\rightarrow0$$Now, for finding the area under the curve between the bounds $a ~\& ~b $ we can a...
@Ultradark You can try d... |
Hello, I've never ventured into char before but cfr suggested that I ask in here about a better name for the quiz package that I am getting ready to submit to ctan (tex.stackexchange.com/questions/393309/…). Is something like latex2quiz too audacious?
Also, is anyone able to answer my questions about submitting to ctan... |
Terms sourced from: http://iupac.org/publications/pac/68/12/2223/
"Glossary of terms used in photochemistry (IUPAC Recommendations 1996)", Verhoeven, J.W.,
Pure and Applied Chemistry 1996, 68(12), 2223
absorbance \(A\)absorptance \(\alpha\)absorption absorption coefficient absorption cross-section \(\sigma\)absorptivit... |
Welcome back! I took a few-weeks’ blogging hiatus to focus on end-of-term craziness, but I am now resuming a regular(ish) weekly schedule throughout the summer. Let’s get back to Wythoff’s game!
Here’s a brief recap: In trying to solve for optimal play in Wythoff’s game, we saw how to algorithmically find the blue “los... |
You are right, this is true if and only if $n = 2$. To prove this (the only if part), observe that if $a_1, a_2, a_3$ are in arithmetic progression, then $a_2 = \dfrac{a_1 + a_3} 2$.
Now, let the coefficient matrix be$$A = \begin{bmatrix}a_1&a_2&a_3\\b_1&b_2&b_3\\c_1&c_2&c_3\end{bmatrix}$$where in each row, the entries... |
I'm not entirely sure what you mean in your set-up. Typically, what one wants to do is maximize utility given some turnover constraint. I believe what you're talking about is optimizing several portfolios and minimizing the turnover across all of them. Hence, if you understand the simple case, then it should be easy to... |
Recall that the base of an exponential function must be a positive real number other than 1. Why do we limit the base
b to positive values? To ensure that the outputs will be real numbers. Observe what happens if the base is not positive: Let b= –9 and [latex]x=\frac{1}{2}[/latex]. Then [latex]f\left(x\right)=f\left(\f... |
List of variables
The environmental variables used throughout the website are listed below. The definitions include mathematical formulations that are likely to scare users that don’t possess a high scientific education. If you don’t understand the equations, don’t panic! Just skip them. You should be able, anyway, to ... |
The deeper problem with this supposition is that it assumes a conceptual identity between the notions of Hamiltonian and energy, and this is an identity that is not correct. That is, discernment needs to be applied to separate the two of these things.
Conceptually, energy is a physical quantity that is, in a sense, "na... |
The Piecewise Constant Pairwise Interaction Point Process Model
Creates an instance of a pairwise interaction point process model with piecewise constant potential function. The model can then be fitted to point pattern data.
Usage
PairPiece(r)
Arguments r
vector of jump points for the potential function
Details
A pair... |
I've determined a number of probabilities pertaining to three subsets of the "magic simplex" of quantum states described in https://arxiv.org/abs/1212.5046, and certainly would like to have a pictorial representation of their interrelations--presumably, in the form of a Venn diagram (cf. Fig. 3 in cited paper).
One set... |
Harmonic Notch Filter
My basement is covered with power lines and florescent lights which makes collecting ECG and EEG data rather difficult due to the 60 cycle hum. I found the following notch filter to work very well at eliminating the background signal without effecting the highly amplified signals I was looking for... |
Relation/Examples/Ordering on Arbitrary Sets of Integers/Not Many-to-One
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Example of Relation which is not Many-to-One
Consider the following diagram, where:
$A$ runs along the top $B$ runs down the left hand side a relation $\mathcal R$ between $A$ and $B$ is indicated by marking with ... |
SINGH R P
Articles written in Pramana – Journal of Physics
Volume 87 Issue 1 July 2016 Article ID 0007 Regular
Lifetimes of excited states in the yrast band of the gamma-soft nuclei $^{131}$Ce and 133Pr have been measured using the recoil distance Doppler shift and Doppler shift attenuation methods. The yrast bands in ... |
Writing Mathematics for MathJax¶ Putting mathematics in a web page¶
To put mathematics in your web page, you can use TeX and LaTeX notation, MathML notation, AsciiMath notation, or a combination of all three within the same page; the MathJax configuration tells MathJax which you want to use, and how you plan to indicat... |
Measurable function
Set
context $ \langle X,\Sigma_X\rangle\in \mathrm{MeasurableSpace}(X) $ context $ \langle Y,\Sigma_Y\rangle\in \mathrm{MeasurableSpace}(Y) $
postulate $ f\in \mathrm{Measurable}(X,Y) $
context $ f:X\to Y $ $y\in \Sigma_Y$
postulate $ f^{-1}(y)\in\Sigma_X $ Discussion
This is very similar to the def... |
The Earth is moderately conductive, so your second schematic is identical to the first. The only difference is that the Earth has quite a higher resistance than a wire, but if we are only wondering about the state of this circuit in equilibrium, that is insignificant.
An insightful question to ask is this: what happens... |
JOSHI P
Articles written in Pramana – Journal of Physics
Volume 87 Issue 1 July 2016 Article ID 0007 Regular
Lifetimes of excited states in the yrast band of the gamma-soft nuclei $^{131}$Ce and 133Pr have been measured using the recoil distance Doppler shift and Doppler shift attenuation methods. The yrast bands in $^... |
Given a 4-vector, we can always define a 2x2 hermitian matrix:
$$X=x^\mu \sigma_\mu=\left(\matrix{x^0+x^3&x^1-ix^2\\x^1+ix^2&x^0-x^3} \right)$$
Where $\sigma_i$ are just the Pauli matrices. In this base, we can define the Lorentz transformations as $\Lambda(L)$, where $X'=LXL^\dagger$. This representation forms the bas... |
When there is no linear term in the equation, another method of solving a quadratic equation is by using the
square root property, in which we isolate the [latex]{x}^{2}[/latex] term and take the square root of the number on the other side of the equals sign. Keep in mind that sometimes we may have to manipulate the eq... |
The important things to take from the question:
elementary particles could have an intrinsic/quantized rest mass
Any rest mass that is not a whole number multiple of this constant has to be attained from interacting with the Higgs Field
Answer
You have just described exactly how things are (to current physics knowledge... |
Proof theory Framework
We can use logic to reason about logical derivations. The object language contains formulae $foo$, $bar$, etc. and we use
$foo\vdash bar$,
which one might reads as
“if $foo$ is provable, then $bar$ also provable.”
In the proof theoretic logic, we use a variable which represents a collection of ob... |
Fermat Number, a class of numbers, is an integer of the form $ F_n=2^{2^n} +1 \ \ n \ge 0$ .
For example: Putting $ n := 0,1,2 \ldots$ in $ F_n=2^{2^n}$ we get $ F_0=3$ , $ F_1=5$ , $ F_2=17$ , $ F_3=257$ etc.
Fermat observed that all the integers $ F_0, F_1, F_2, F_3, \ldots$ were prime numbers and announced that $ F_... |
SCM Repository View of /branches/vis12/test/unicode-cheatsheet.diderot
Revision
File size: 782 byte(s) 1927- ( download) ( annotate) Sat Jun 23 18:09:16 2012 UTC(7 years, 3 months ago) by jhr
File size: 782 byte(s)
converting to use "image" instead of "load" for image nrrd loading /* useful unicode characters for Dider... |
Just to make things clear - this property is not
fundamental but important. It is the fundamental difference when it comes to using DCT instead of DFT for spectrum calculation. Why do we do Cepstral Mean Normalisation
In speaker recognition we want to remove any channel effects (impulse response of vocal tract, audio p... |
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One of the main lessons of category theory is that whenever you think about some kind of mathematical gadget, you should also think about maps
between gadgets of this kind. For example, when you think about sets you should also thin... |
[This is the 6th post in the current series about Wythoff’s game: see posts #1, #2, #3, #4, and #5.
Caveat lector: this post is a bit more difficult than usual. Let me know what you think in the comments!]
Our only remaining task from last week was to prove the mysterious Covering Theorem: we must show that there is ex... |
In the formulation, presumably on the right side what is intended are 3-dimensional non-degenerate quadratic spaces (up to isomorphism), with discriminant 1 (same as $4^3$ mod squares as John Ma notes). But to make this work also in characteristic 2, it is better to proceed with a different point of view: that of confo... |
Definition:Rotation (Geometry)/Plane
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Definition $\map {r_\alpha} O = O$
That is, $O$ maps to itself.
Let $P \in \Gamma$ such that $P \ne O$.
Let $OP$ be joined by a straight line.
Let a straight line $OP'$ be constructed such that:
$(1): \quad OP' = OP$ $(2): \angle POP' = \alpha$ such... |
I want to know the expectation and the variance of the Gamma PnL for different hedging frequencies.
Let's say the return of the underlying follow a normal process: $dr= \sigma*dW$, the market trades 24hours and there is no transaction cost. I consider I have a constant dollar $\Gamma$ position (-r% or +r%, r $\in$ $\ma... |
Every geometry textbook has formulas for the circumference (\(C = 2 \pi r\)) and area (\(A = \pi r^2\)) of a circle. But where do these come from? How can we prove them?
Well, the first is more a definition than a theorem: the number \(\pi\) is usually
defined as the ratio of a circle’s circumference to its diameter: \... |
Let's say we have the following circuit:
Generator in the circuit has sinusoidal waveform $u_g(t)=\sin\omega t$. Other known values: $ L=0.25H\\ R=1\Omega \\ C=0.5F \\ \omega=1 \frac{rad}{s} \\ k=1$
Before the P2 switch is closed, we had steady state in the circuit, at the same time, switch P1 was in the position 1. At... |
This Domain is Ideal for a Baby products Related Store
Do yo want to get more traffic in your webstore? Want to Sell your products in high rate? If so you must know, in this virtual world everyone get interested in those products which are uploaded or listed with proper specificaion or with attractive images. We will e... |
Consider the following first order linear difference equation for $y$:
$$y_{t+1} = \alpha * y_{t} + \beta * x_{t-n+1} ~~\forall t \ge n$$
For initial conditions, one could assume that $x_{i} \in \mathbb{R} ~~\forall t = 1, \ldots n$. (except that they cannot all be zero).
The other constraint is that $$y_{n} = \sum_{i=... |
So i have this sequence
$\dfrac{\pi}{3}-k,\dfrac{\pi}{3},\dfrac{\pi}{3}+k,\dfrac{2\pi}{3}-k,\dfrac{2\pi}{3},\dfrac{2\pi}{3}+k,\dfrac{3\pi}{3}-k,\dfrac{3\pi}{3},\dfrac{3\pi}{3}+k,...$
I want to make a formula for this sequence, here is what i made myself for $n>=1$
$ceiling(\dfrac{n}{3})*\dfrac{\pi}{3}+ [(floor(n) \mod ... |
Suppose we have a random vector $\mathbf{X} = (X_1,\ldots,X_n)$ or sample with pdf or pmf $f(\mathbf{x};\theta)$, where $\theta \in \Theta$ is an unknown parameter (or vector of parameters), whose specification completely determines $f(\mathbf{x};\theta)$.
As far as I understand, a
statistic is just a a random variable... |
We are given a directed weighted graph $\mathcal{G} = (V, A)$, with $A \subseteq V^2$. The weight function is $w_{\mathcal{G}} \colon \mathcal{G}.A \to \mathcal{P}(\mathfrak{R}_{>} \times \mathfrak{R}_{\geq} \times (\mathfrak{R}_> \cup \{ \infty \}) \times \mathfrak{R})$, where $\mathfrak{R}_{\ast} = \{ x \in \mathfrak... |
Let $\mathbf{w}(t)$ be the trajectory of a moving charge. Let the observation event be $(\mathbf{r},t)$.
The scalar potential is:
$$\varphi = \frac{q}{4\pi\epsilon_0}\int \frac{\delta\left(\mathbf{r'} - \mathbf{w}\left(t - \frac{|\mathbf{r} - \mathbf{r'}|}{c}\right)\right)}{|\mathbf{r'}-\mathbf{r}|} \mathrm d^3\mathbf{... |
In my lecture notes, the Boltzmann entropy form was motivated as a valid form for entropy partly because it was extensive. However this hinges on the assumption that the statistical weight for a macrostate of two systems combined is their product. Why is this valid- for large systems at least- and when might it break d... |
Terms sourced from: http://iupac.org/publications/pac/68/1/0149/
"A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)", Laidler, K.J.,
Pure and Applied Chemistry 1996, 68(1), 149
activated complex activation activation energy adiabatic adiabatic transition-state theor... |
Let us now take a closer look at the
hex-fractal we sliced last week. Chopping a level 0, 1, 2, and 3 Menger sponge through our slanted plane gives the following:
This suggests an iterative recipe to generate the hex-fractal. Any time we see a hexagon, chop it into six smaller hexagons and six triangles as illustrated ... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
The surreal numbers are sometimes introduced as a place where crazy expressions like $(\omega^2+5\omega-13)^{1/3-2/\omega}+\pi$ (to use the nLab's example) make sense. The problem is, there seem to be varying definitions of the exponential in the surreal numbers and since I can't find any recent reference that covers t... |
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Change to browse by: References & Citations Bookmark(what is this?) Astrophysics > Solar and Stellar Astrophysics Title: Impact of Cosmic-Ray Feedback on Accretion and Chemistry in Circumstellar Disks
(Submitted on 21 Aug 2019 (v1), last revised 10 Sep 2019 (this version, v2))
Abstra... |
Cryptology ePrint Archive: Report 2000/005 On Resilient Boolean Functions with Maximal Possible Nonlinearity Yuriy Tarannikov Abstract: It is proved that the maximal possible nonlinearity of $n$-variable
$m$-resilient Boolean function is $2^{n-1}-2^{m+1}$ for
${2n-7\over 3}\le m\le n-2$. This value can be achieved only... |
Math has a lot of symbols. Some might say too many symbols. So lets do some math with pictures.
Lets have a paper, which we will draw on. To start the paper is empty, we will say that is equivalent to \$\top\$ or \$\textit{true}\$.
If we write other things on the paper they will also be true.
For example
Indicates that... |
The outputs of the function [latex]f[/latex] are the inputs to [latex]{f}^{-1}[/latex], so the range of [latex]f[/latex] is also the domain of [latex]{f}^{-1}[/latex]. Likewise, because the inputs to [latex]f[/latex] are the outputs of [latex]{f}^{-1}[/latex], the domain of [latex]f[/latex] is the range of [latex]{f}^{... |
Complete graph
Set
definiendum $ \langle V,E,\psi\rangle \in \mathrm{it}(E,V) $
postulate $ \langle V,E,\psi\rangle $ … simple graph
postulate $ u\neq v\implies \exists !(e\in E).\ \psi(e)=\{u,v\} $ Discussion
In a complete (undirected) graph, every two distinct vertices are connected.
The axiom $\{u\}\notin\mathrm{im}... |
№ 9
All Issues Volume 54, № 9, 2002
Ukr. Mat. Zh. - 2002. - 54, № 9. - pp. 1155-1162
For entire transcendental functions of finite generalized order, we obtain limit relations between the growth characteristic indicated above and sequences of their best polynomial approximations in certain Banach spaces (Hardy spaces, ... |
At first an example which I know how to treat. Let's say we have the following integral
$\int dx \frac{1}{x^2+a^2}$
Now we do an analytic continuation of the constant $a$ to the complex numbers: $a \rightarrow ia$. This gives
$\int dx \frac{1}{x^2-a^2}$
which now has poles at $x = \pm a$. Let's say I want to evade thes... |
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Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
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