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I'm trying to understand the equivalence in expressive power of formal grammars whose rules take the form:
$$ \alpha \rightarrow \beta $$ where $ |\alpha| \leq |\beta| $ (called a
monotonic grammar), and grammars whose rules take the form:
$$ \alpha B \gamma \rightarrow \alpha C \gamma $$
where $\alpha $ and $\gamma$ a... |
I know that stable non-circular orbits in euclidean space exist only in 3 spatial dimensions but what about if the spatial dimensions are hyperbolic instead? Are there any stable non-circular orbits in 2 or 3 dimensional hyperbolic space?
The gravitational field for any space of dimension > 1 scales inversely with the ... |
Is it possible to "construct" the Hamiltonian of a system if its ground state wave function (or functional) is known? I understand one should not expect this to be generically true since the Hamiltonian contains more information (the full spectrum) than a single state vector. But are there any special cases where it's ... |
The two famous theorems of Jingrun Chen, both with similar proofs, state (respectively) that all sufficiently large even numbers are the sum of a prime and an element of $P_2$, and that there are infinitely many numbers $n$ such that $\{n, n+2\}$ consists of a prime and an element of $P_2$. Here $P_2$ is the set of num... |
I will use the below mentioned form of Reynolds Transport theorem(usually derived in Fluid Mechanics context) to give a relation between a Control mass system(no mass in or out) and Control Volume(randomly chosen time varying region of interest). It gives the relation between a chosen region of interest called control ... |
This question is a sequel of sorts to my earlier (resolved) question about a recent paper. In the paper, the authors performed molecular dynamics (MD) simulations of parallel-plate supercapacitors, in which liquid resides between the parallel-plate electrodes. The system has a "slab" geometry, so the authors are only i... |
You are asking to compute the double quotient $B\backslash G /B.$ This is the same as computing $G\backslash (G/B \times G/B)$. A point in $G/B$ is a full flag on $k^n$. So youare trying to compute the set of pairs $(F_1,F_2)$ of flags, modulo the simultaneous actionof $G$.
Another way to think about $G/B$ is that it i... |
I'm trying to compute ideal class groups of various number fields, and now I'm a little familiar to a class group of a quadratic number field. However, I can't find any non-cyclic example of a class group of a cubic number field. In Marcus' "Number Fields" book, there are some exercises that deal with $\mathbb{Q}(\sqrt... |
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math-ph
Change to browse by: References & Citations Bookmark(what is this?) Mathematical Physics Title: On the classification of multidimensionally consistent 3D maps
(Submitted on 10 Sep 2015 (v1), last revised 24 Feb 2016 (this version, v2))
Abstract: We classify multidimensionally consistent ... |
It isn't true that every DFA for this language is non-planar:Here is a language that is truly non-planar:$$\left\{ x \in \{\sigma_1,\ldots,\sigma_6\}^* \middle| \sum_{i=1}^6 i\#_{\sigma_i}(x) \equiv 0 \pmod 7 \right\}.$$Take any planar FSA for this language. If we remove all unreachable states, we still get a planar gr... |
Take the following transfer function of a 3rd order system:
$$H(s)=\dfrac{2.302~s+0.3548}{s^3+0.739~s^2+3.223~s+0.3548}$$
with poles:
Pole Damping Frequency Time Constant (rad/seconds) (seconds) -1.13e-01 1.00e+00 1.13e-01 8.89e+00 -3.13e-01 + 1.75e+00i 1.76e-01 1.78e+00 3.19e+00 -3.13e-01 - 1.75e+00i 1.76e-01 1.78e+00... |
Suppose that the household faces the following problem:
$\underset{ c_t , k_{t+1}, n_t } \max \mathbb{E}_0 \sum_{t=0}^{\infty} \beta^t \ln c_t + \ln (1 - n_t)$
subjected to
$ k_{t+1} = A_t k_t ^{\alpha} n_t ^{1- \alpha} - c_t $
Usually, in my macroeconomic course, we would formulate the Bellman equation as the followin... |
15.2. Deep Convolutional Generative Adversarial Networks¶
In Section 15.1, we introduced the basic ideas behind how GANs work. We showed that they can draw samples from some simple, easy-to-sample distribution, like a uniform or normal distribution, and transform them into samples that appear to match the distribution ... |
Difference between revisions of "Hand Dynamics and Control"
(→Chapter Summary)
Line 9: Line 9:
== Chapter Summary ==
== Chapter Summary ==
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +... |
Let $k$ be a field. What is an explicit power series $f \in k[[t]]$ that is transcendental over $k[t]$?
I am looking for elementary example (so there should be a proof of transcendence that does not use any big machinery).
MathOverflow is a question and answer site for professional mathematicians. It only takes a minut... |
Introduction¶
While the current hype about Deep Learning and Neural Networks is understandable given the vast number of cases where ANNs clearly outperformed every other algorithm, a lot of people think (myself included) that Neural Networks won't be the ONE Machine Learning algorithm that will solve every problem one ... |
It is caused by the wettability of the surface of the nanoparticles. For naked particles this will be determined by the properties of gold but, as Daniel mentioned, it is likely that there is a capping agent, in which case the wettability will be governed by the properties of the capping agent. From this point on I wil... |
Preliminary remarks.
As Danu writes in his comment, the physics of the other four generators has to do with spacetime translations, one for each spatial direction, and one for time. But how do we see this explicitly in the math behind the somewhat odd-looking presentation of the Poincare group and its Lie algebra that ... |
I was wondering how Alcubierre derived the metric for the warp drive? Sources have said it's based on Einstein's field equations, but how did he go from this to the metric?
Alcubierre started with the metric and used the Einstein equation to calculate what stress energy tensor was required.
The Einstein equation tells ... |
I was not quite sure what the right SE for this was, so I posted this also here on DSP. Please tell me which one to remove :)
Problem statement
I have a few hundred unrelated time series, say $P_i(t)$, with $i=1,2,...,N$. The sample times are all unequally spaced.
It is known that during certain (unknown) intervals, th... |
I have a table with 4 columns and 4 rows, in the last row of which I'm using
multicolumn to have cells 2 columns wide. However, since one is taller than the other, for some reason they are automatically aligned to the middle (vertically speaking) of the cell, not the top. I have tried
p instead of
l in the column desig... |
I'm trying to write the following equation:
\rho = \max \left\{ \frac{|\mathbf{w} \cdot \mathbf{x^{(i)}} + b|}{\|\mathbf{w}\|} \right\}
but the PDF output renders the math operator
\max in italic instead of upright. I've tried the same with
\log and
\cos, and they behave just the same. What am I doing wrong here?
Docum... |
$ds^2= r^2 (d\theta^2 + \sin^2{\theta}d\phi^2)$
The following is the tetrad basis
$e^{\theta}=r d{\theta} \,\,\,\,\,\,\,\,\,\, e^{\phi}=r \sin{\theta} d{\phi}$
Hence, $de^{\theta}=0 \,\,\,\,\,\, de^{\phi}=r\cos{\theta} d{\theta} \wedge d\phi = \frac{\cot{\theta}}{r} e^{\theta}\wedge e^{\phi}$
Setting the torsion tensor... |
I'm playing around with dynamic programming and need to calculate a multidimensional integral $E[V(W)]$ where we assume $W$ has a log normal distribution. I was looking at the following example in this pdf, section 9.4.3 on page 83.
To give some background (I summarize from the section): The example is from economics a... |
I started digging into the history of mode detection after watching Aysylu Greenberg’s Strange Loop talk on benchmarking. She pointed out that the usual benchmarking statistics fail to capture that our timings may actually be samples from multiple distributions, commonly caused by the fact that our systems are comprise... |
IWOTA 2019
International Workshop on
Operator Theory and its Applications
We discuss how ideas from knot theory and categorical Lie theory can be used to understand the representation theory of Hecke algebras of complex reflection groups. The talk will focus mostly on the combinatorics and diagrammatics underlying thes... |
Dynamics of { $\lambda tanh(e^z): \lambda \in R$\ ${ 0 }$ }
1.
Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati - 781039, India, India
$\mathcal{M} = { f_{\lambda}(z) = \lambda f(z) : f(z) = \tanh(e^{z}) \mbox{for} z \in \mathbb{C} \mbox{and} \lambda \in \mathbb{R} \setminus \{ 0 \} }$
is st... |
Let $k$ be a positive integer and let $\Gamma$ be a finite index subgroup of the modular group $\SL(2,\Z)$.
A (classical)
modular form $f$ of weight $k$ on $\Gamma$, is a holomorphic function defined on the upper half plane $\mathcal{H}$, which satisfies the transformation property\[f(\gamma z) = (cz+d)^k f(z)\] for al... |
@Secret et al hows this for a video game? OE Cake! fluid dynamics simulator! have been looking for something like this for yrs! just discovered it wanna try it out! anyone heard of it? anyone else wanna do some serious research on it? think it could be used to experiment with solitons=D
OE-Cake, OE-CAKE! or OE Cake is ... |
The $\Theta(n)$ difference-of-sums solution proposed by Tobi and Mario can in fact be generalized to any other data type for which we can define a (constant-time) binary operation $\oplus$ that is:
total, such that for any values $a$ and $b$, $a \oplus b$ is defined and of the same type (or at least of some appropriate... |
Content – Forms of energy
Sound is produced when a force causes an object or substance to vibrate.
Sound energy is transferred through the environment (matter) by wave motion caused by the vibrating object.
Sound energy is often measured by its pressure and intensity, in units called decibels.
Waves
A vibrating object ... |
IWOTA 2019
International Workshop on
Operator Theory and its Applications
We show that dual truncated Toeplitz operators on the orthogonal complement of a model space are equivalent after extension to certain paired operators, and we use this to study their kernels and their spectral properties.
Based on joint work wit... |
I'm currently reading the book
"Classical Theory of Gauge Fields" by Rubakov, therefore I will use his convention in this question. In the following we assume that: $\phi$ comprises columns consisting of complex scalar fields. $G$ is a simple compact Lie Group. The representations $\rho:G\rightarrow \mathrm{Gl}(V)$ are... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
I am feeling a little nostalgic. So I rebuilt one of the first circuits I put together when I started messing around with circuits in eighth grade. It’s a very simple beginner project, and might appeal to your child – real or inner!
Another reason I wanted to put this up is because most “blinky” circuits I see now are ... |
In practice, the runtime of numerically solving an IVP $$ \dot{x}(t) = f(t, x(t)) \quad \text{ for } t \in [t_0, t_1] $$ $$ x(t_0) = x_0 $$ is often dominated by the duration of evaluating the right-hand side (RHS) $f$. Let us therefore assume that all other operations are instant (i.e. without computational cost). If ... |
10.5. Mini-batch Stochastic Gradient Descent¶
In each iteration, the gradient descent uses the entire training data set to compute the gradient, so it is sometimes referred to as batch gradient descent. Stochastic gradient descent (SGD) only randomly select one example in each iteration to compute the gradient. Just li... |
In my AP Chem class we are working on testing Hess's Law and conducted three reactions. Then enthalpy changes of the 1) $\ce{NaOH + HCl}$ and 2) $\ce{NaOH + NH4Cl}$ to predict the enthalpy change of 3) $\ce{HCl + NH3}$.
I used the equation $q = C_pm\Delta T$. We determined the $q$-values using a method given to us by o... |
This is College Physics Answers with Shaun Dychko. We have <i>β</i>-decay of this nuclide <i>X</i> with atomic number <i>Z<i/>, mass number <i>A</i> and number of neutrons <i>N</i>. <i>β</i>-decay means that a neutron turns into a proton and so there is a additional proton here in this daughter nuclide and in order to ... |
use parseval's identity to evaluate the integral
\begin{equation} \int_{-\pi}^{\pi}(\sin x)^4dx\end{equation}
I'm familiar with Parseval's identity which states that for each piecewise continuous complex function $f$ we have the equality \begin{equation} \int_{-\pi}^{\pi}\left|f(x) \right|^{2}dx=\frac{|a_{0}|^{2}}{2}+\... |
UPDATE (18/04/18): The old answer still proved to be useful on my model. The trick is to model the partition function and the distribution separately, thus exploiting the power of softmax.
Consider your observation vector $y$ to contain $m$ labels. $y_{im}=\delta_{im}$ (1 if sample i contains label m, 0 otherwise). So ... |
If an automorphism fails (C), then obviously it satisfies (B). An (A)+(B) example easily extends from rank 1 to ranks 2: take a root of unity $\zeta$ in $\mathbb Z_p^\times$ that is not $\pm1$ (requiring $p\geqslant 5$). If the generators of the free group are $x$ and $y$, then there is an automorphism of the $p$-adic ... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
When hydrogen peroxide is mixed with potassium permanganate, oxygen gas and water vapour are formed, according to the reaction (source):
$$\ce{2MnO4- + 3H2O2 -> 2MnO2 + 2H2O + 3O2 + 2OH-}$$
This reaction is spontaneous, and exothermic. It is an example of a redox reaction, with the following half reactions occurring (d... |
Stepping backwards during debugging as a motivation for non-determinism
The notion of a non-deterministic machine suggests itself when you wish to step backward (in time) through a program while debugging. In a typical computer, each step modifies only a finite amount of memory. If you always save this information for ... |
One more assumption must be made regarding the $^{222}Rn$ concentration at time zero (week ago). If you assume radioactive equilibrium between $^{222}Rn$ and the parent $^{238}U$ you can proceed like you did. But instead of taking one wall, you should take into account all the walls made of the $^{238}U$ contaminated m... |
Question:
Two identical, non-interacting spin-$1/2$ particles are in a 1D Harmonic Oscillator Potential. Their Hamiltonian is given by
$$H=\frac{p_{1x}^2}{2m}+\frac{1}{2}m\omega^2 x_1^2+\frac{p^2_{2x}}{2m}+\frac{1}{2}m\omega^2x_2^2 $$
What is the ground state wave function for the two particles in the singlet and tripl... |
This is an interesting question that I have asked myself. Below is my take.
Let us consider an economy $(\Omega,\mathcal{F},P)$ equipped with a filtration $(\mathcal{F})_{t \geq 0}$ consisting on a traded asset $S_t$ and a
numéraire $N_t$ specified by the following stochastic differential equations:$$\begin{align}\text... |
Given the two jump-diffusions: \begin{equation} \begin{aligned} dX_{1,t} &= a_1 dt + b_1 dW_t + c_1 dN_t(\lambda) \\ dX_{2,t} &= a_2 dt + b_2 dW'_t + c_2 dN_t(\lambda) \\ corr(dW,dW') &= \rho \\ dN & \mbox{: Poisson process, of intensity } \lambda \end{aligned} \end{equation} which SDE $$df_t = ? $$ satisfies the funct... |
Which is the best way to put function plots into a LaTeX document?
To extend the answer from Mica,
pgfplots can do calculations in TeX:
\documentclass{standalone}\usepackage{pgfplots}\begin{document}\begin{tikzpicture} \begin{axis}[ xlabel=$x$, ylabel={$f(x) = x^2 - x +4$} ] \addplot {x^2 - x +4}; \end{axis}\end{tikzpi... |
Since I spend a lot of time on solving sparse linear equation systems then I am also a user of sparse matrix reordering methods. My claim to fame is that I have implemented approximate minimum degree myself and it is used in MOSEK.
Below I summarize some interesting link to graph partitioning software:
It is very commo... |
Here are the bond angles for each molecule (data from wikipedia):
\begin{array}{|c|c|}\hline\mathrm{Molecule} & \mathrm{Bond \space Angle \space (^\circ)} \\ \hline\ce{H2S} & 92.1 \\ \hline\ce{H2O} & 104.5 \\ \hline\ce{NH3} & 107.8 \\ \hline\ce{SO2} & 119 \\ \hline\end{array}
So $L \propto \frac{1}{BA}$ where $L$ is th... |
My question is in the title, but here is a more detailed formulation:
Let Top be the category of all topological spaces and continuous maps, and let CGTop be the subcategory of compactly generated spaces, as defined in Strickland's notes. We have a functor $k: Top \rightarrow CGTop$ that replaces the topology on a spac... |
This question already has an answer here:
Show that the language L = {ww^Rw: w in {a,b}*} is not a context-free language.
Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. It only takes a minute to sign up.Sign up to join this community
This q... |
Knapsack Problems¶
This module implements a number of solutions to various knapsack problems, otherwise known as linear integer programming problems. Solutions to the following knapsack problems are implemented:
Solving the subset sum problem for super-increasing sequences. General case using Linear Programming
AUTHORS... |
If two time series follow a GARCH process, and a third is a linear combination of them, is the third also GARCH process?
I think there are a lot of different ways to specify this problem. For simplicity, consider independent Garch processes $$ r_{1,t} \sim N\left(0,\sigma_{1,t}^{2}\right) $$ $$ \sigma_{1,t}^{2} = \beta... |
I googled it and I couldn't found it. And I am really sure this is a question that a lot of people ask, but I really googled it and couldn't find it.
Is it possible to use an "invisble equal sign" in the align environment? Some times I would like align to align equations different, instead of under the equation mark. I... |
Consider the following example:
\documentclass{article}\usepackage[utf8]{inputenc}\usepackage{amsmath, amsthm, amssymb, mathtools, thmtools, unicode-math}\begin{document} \begin{equation*} \begin{split} |\mu|(B):=\sup\left\{&\sum_{i=1}^k|\mu(B_i)|:k\in\mathbb N\text{ and}\right.\\ &\left.B_1,\ldots,B_k\in\mathcal E\tex... |
Seeing that in the Chomsky Hierarchy Type 3 languages can be recognised by a DFA (which has no stacks), Type 2 by a DFA with one stack (i.e. a push-down automaton) and Type 0 by a DFA with two stacks (i.e. with one queue, i.e. with a tape, i.e. by a Turing Machine), how do Type 1 languages fit in...
Considering this ps... |
Formal approach of the problem
We’ve seen before that the classical estimation technique used to estimate the parameters of a parametric model was to use the maximum likelihood approach. More specifically, \widehat{\mathbf{\beta}}=\text{argmax}\lbrace \log\mathcal{L}(\mathbf{\beta}|\mathbf{x},\mathbf{y})\rbraceThe obje... |
Let's assume that we are simply trying to maximize the expected value of our roll. (As discussed this might not be a realistic representation of actual gameplay, but we can work it out anyway.) Then the rolls on any of the dice don't affect our decisions to reroll for other dice - that is, any one die's rolls and strat... |
We have the matrix Laplacian matrix $G=A^TA$ which has a set of eigenvalues $\lambda_0\leq\lambda_1\leq\ldots\leq \lambda_n$ for $G\in\mathbb{R}^{n\times n}$ where we always know $\lambda_0 = 0$. Thus the Laplacian matrix is always symmetric positive semi-definite. Because the matrix $G$ is not symmetric positive defin... |
In the solution to Making more easy the itemized of item with tabulation system, I am counting up the number of spaces in order to determine the type of leading character to insert. However, if the I replace the leading spaces with a tab character, the solution does not work.
If I could detect the tab character in the
... |
Introduction to Quasisymmetric Functions¶
In this document we briefly explain the quasisymmetric function bases andrelated functionality in Sage. We assume the reader is familiar with thepackage
SymmetricFunctions.
Quasisymmetric functions, denoted \(QSym\), form a subring of the power series ring in countably many var... |
I want to optimize the vertex positions in a mesh, with a given cost function on the associated triangles. The paper gives a cost function, which evaluates to an real number by using a sum over the triangles in the mesh, which connect the vertices to a valid simplical complex. They suggest to use a L-BFGS solver and i ... |
A) \[\frac{599}{311}\]
B) \[\frac{680}{216}\]
C) \[\frac{642}{133}\]
D) \[\frac{501}{301}\]View Solution
A) \[\frac{24}{5}\]
B) \[-\frac{24}{5}\]
C) \[25\]
D) \[-25\]View Solution
A) \[\frac{2}{5}\]
B) \[\frac{8}{17}\]
C) \[-\frac{2}{3}\]
D) \[-\frac{4}{3}\]View Solution
A) \[-\frac{13}{2}\]
B) \[-\frac{15}{2}\]
C) \[\... |
What you have done is correct! Note that whenever you have inverse trigonometric expressions you can express your answer in more than one way! Your answer can be expressed in a different way (without the trigonometric and inverse trigonometric functions) as shown below.
We will prove that $$\sec \left( \arctan \left( \... |
Answer
$\frac{2i}{-1 - i\sqrt{3}}$ = $\frac{-\sqrt{3}}{2} - \frac{i}{2}$
Work Step by Step
$\frac{2i}{-1 - i\sqrt{3}}$ = $\frac{2cis90^\circ}{2cis240^\circ}$ = $cis(90-240)^\circ$ = $cis(-150)^\circ$ = $\frac{-\sqrt{3}}{2} - \frac{i}{2}$
You can help us out by revising, improving and updating this answer.Update this an... |
Let $a \in \Bbb{R}$. Let $\Bbb{Z}$ act on $S^1$ via $(n,z) \mapsto ze^{2 \pi i \cdot an}$. Claim: The is action is not free if and only if $a \Bbb{Q}$. Here's an attempt at the forward direction: If the action is not free, there is some nonzero $n$ and $z \in S^1$ such that $ze^{2 \pi i \cdot an} = 1$. Note $z = e^{2 \... |
Let $X$ be a noetherian scheme over $\mathbb{C}$, and let $E$ be a locally free sheaf of finite rank over $X$. Then we have the projective bundle $f: \mathbb{P}(E)\rightarrow X$.
Now $f$ is a flat morphism and we have $f_{*}\mathcal{O}_{\mathbb{P}(E)}=\mathcal{O}_X$ and $R^if_{*}\mathcal{O}_{\mathbb{P}(E)}=0$ for $i\ge... |
It might be better to write them in a bit plainer English: the first is
"Every
ordinal is in bijection with some initial ordinal,"
while the second is
"Every
set is in bijection with some initial ordinal."
Since there are lots of sets which aren't ordinals, in principle there's no reason for the first statement to impl... |
Kyle Kanos's answer looks to be very full, but I thought I'd add my own experience. The split-step Fourier method (SSFM) is extremely easy to get running and fiddle with; you can prototype it in a few lines of Mathematica and it is, extremely stable numerically. It involves imparting only unitary operators on your data... |
256 0
[tex]\int_0^\sqrt{6}}e^{-x^2}\frac{x^2}{2}[/tex]
should i use a u-substitution or integration by parts?
should i use a u-substitution or integration by parts?
RadiationX said:[tex]\int_0^\sqrt{6}}e^{-x^2}\frac{x^2}{2}[/tex] should i use a u-substitution or integration by parts? An answer in terms of erf is no wor... |
Prove that $$\sum_{n=1}^\infty\frac1{n^6}=\frac{\pi^6}{945}$$ by the Fourier series of $x^2$.
By Parseval's identity, I can only show $\sum_{n=1}^\infty\frac1{n^4}=\frac{\pi^4}{90}$. Could you please give me some hints?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and p... |
I have the following equation:
Notice how the last two terms are not centered? If I use the code specified below, I would get that effect. Now, what I would like to have is the effect shown in the first term (centered the term "Bias"). You probably also see that since I kind of fail with paint, the first terms are not ... |
Fully Truncated Simplices Barry Monson University of New Brunswick Leah Berman U. Alaska- Fairbanks Deborah Oliveros UNAM - Quer\'{e}taro Gordon WilliamsPDF U. Alaska - Fairbanks Minisymposium:POLYTOPES AND GRAPHS Content:If you truncate an equilateral triangle $\{3\}$ to its
edge midpoints you get another, smaller $\{... |
Let $M$ be a Riemannian manifold. Assume $\gamma$ is a path in $M$ , such that it's image is a totally geodesic submanifold of $M$.
I am trying to prove (the seemingly trivial result) that $\gamma$ must be a reparametrization of a geodesic in $M$.
I came up with two possible explanations (described below). I would like... |
The speed of sound is given by:
$$v = \sqrt{\gamma\frac{P}{\rho}} \tag{1} $$
where $P$ is the pressure and $\rho$ is the density of the gas. $\gamma$ is a constant called the adiabatic index.
The equation should make intuitive sense. The density is a measure of how heavy the gas is, and heavy things oscillate slower. T... |
First, existence: there is a primitive root modulo $n$ if and only if $n$ is $1$ or $2$ or $4$ or $p^\alpha$ or $2p^\alpha$, where $p$ is prime, $p\ne2$, and $\alpha\ge1$.
Second, a systematic way of finding all primitive roots modulo $n$. Begin by finding one primitive root, say $g$. Then all the units modulo $n$ are ... |
We can see the value \(y_2=3\) is incorrect: \(|x_2-a_2|=|2-2|=0\). The underlying reason is of course: we are not minimizing the second term \(|y_2-a_2|\).
A correct formulation will need extra binary variables (or something related such as a SOS1 construct):\[\begin{align}\min\>&z\\&-z\le y_1-y_2 \le z\\& y_i \ge x_i... |
Is there an example of an eigenfunction of a linear time invariant (LTI) system that is
not a complex exponential? Justin Romberg's Eigenfunctions of LTI Systems says such eigenfuctions do exist, but I am not able to find one.
All eigenfunctions of an LTI system can be described in terms of complex exponentials, and co... |
(HP65) Factorial and Gamma Function
10-21-2017, 08:32 AM (This post was last modified: 10-26-2017 05:10 AM by Gamo.)
Post: #1
(HP65) Factorial and Gamma Function
Just noticed that HP 65 cannot calculate decimal Factorial and HP67 app for Android also cannot do it.
Here is a handy program using Stirling's approximation ... |
In a paper by Joos and Zeh, Z Phys B 59 (1985) 223, they say:This 'coming into being of classical properties' appears related to what Heisenberg may have meant by his famous remark [7]: 'Die "Bahn" entsteht erst dadurch, dass wir sie beobachten.'Google Translate says this means something ...
@EmilioPisanty Tough call. ... |
The following two facts concerning totally disconnected spaces should (separately) help you demonstrate that your space is totally disconnected.
Fact 1: Every T$_1$-space with a basis consisting of clopen sets ( i.e., every zero-dimensional space) is totally disconnected.
proof. Suppose that $A \subseteq X$ contains at... |
Low-energy limit of SMEFT applied to tau to pi pi nu_tau decays
Pre-published on: 2019 August 08
Published on: —
Abstract
We perform an effective field theory analysis of the $\tau^-\to \pi^- \pi^0 \nu_\tau$ decays, that includes the most general interactions between Standard Model fields up to dimension six, assuming ... |
In a paper by Joos and Zeh, Z Phys B 59 (1985) 223, they say:This 'coming into being of classical properties' appears related to what Heisenberg may have meant by his famous remark [7]: 'Die "Bahn" entsteht erst dadurch, dass wir sie beobachten.'Google Translate says this means something ...
@EmilioPisanty Tough call. ... |
First note, that hybridisation is a mathematical concept which can be applied to interpret a bonding situation. It has no physical meaning whatsoever. Instead it helps us to understand the direction of bonds better.
Second note, that the second period usually behaves quite differently from the remaining elements in a g... |
Answer
The solution set of the equation is $$\{90^\circ, 210^\circ,330^\circ\}$$
Work Step by Step
$$\sin3\theta=-1$$ over interval $[0^\circ,360^\circ)$ 1) Find corresponding interval for $3\theta$ The interval for $\theta$ is $[0^\circ,360^\circ)$, which can also be written as the inequality: $$0^\circ\le\theta\lt360... |
HI!We were given a lot of description this time :D and here they are:
Alice and Bob went a long way in crypto. They designed a super secure crypto system to encrypt their messages. We managed to steal the source and some other information. Find the FLAG! We also got this: Download Mirror File We also got this: Download... |
I have a general question in partial differential equations.
Can we say that when an even function is expressed as a Fourier series, the Fourier cosine series is also the Fourier series?
My thinking is that a Fourier series has the form,
$$f(x) = \frac{a_0}{2}+\sum^{\infty}_{n=1} a_n cos(nx) + \sum^\infty_{n=1}b_nsin(n... |
(
Update. Added a self-contained proof that under ZF+DC+BP there is no norm.)
Martín-Blas Pérez Pinilla is on the right track. You can't even put a norm on $C(\mathbb{R})$ without using the axiom of choice in an essential way. Dependent choice is not enough.
Claim. It is consistent with ZF+DC that there does not exist ... |
A) The current through NP is 0.5 A
B) The value of \[{{R}_{1}}=20\Omega \]
C) The value of \[R=14\Omega \]
D) The potential difference across R = 49 V
Correct Answer:
C
Potential difference across MP = p. d. across NO = p. d. across N.P (see figure.) \[\therefore \]\[{{I}_{NP}}\times 10=20\times 1\]or \[{{I}_{NP}}=2A\]... |
I happen to have revised our calculus syllabus for first year biology majors about one year ago (in a French university, for that matter). I benefited a lot from my wife's experience as a math-friendly biologist.
The main point of the course is to get students able to deal with
quantitative models. For example, my wife... |
The soft-photon theorem is the following statement due to Weinberg:
Consider an amplitude ${\cal M}$ involving some incoming and some outgoing particles. Now, consider the same amplitude with an additional soft-photon ($\omega_{\text{photon}} \to 0$) coupled to one of the particles. Call this amplitude ${\cal M}'$. The... |
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It's been a long time since my last exam on QM, so now I'm struggling with some basic concept that clearly I didn't understand very well.
1) The Sch. Eq for a free particle is ##-\frac {\hbar}{2m} \frac {\partial ^2 \psi}{\partial x^2} = E \psi## and the solutions are plane waves of the form ##\psi(x... |
For a given scalar field $\phi$, the stress energy tensor is \begin{equation} T_{\mu\nu}=\partial_{\mu}\phi\partial_{\nu}\phi - \frac{1}{2} g_{\mu\nu}(\partial_{\alpha}\phi\partial^{\alpha}\phi). \end{equation} How can I get a second order differential equation for $\phi$, assuming that the metric $g_{\mu\nu}$ satisfie... |
We have $X \sim \mathrm{Unif}[0,2]$ and $Y \sim \mathrm{Unif}[3,4]$. The random variables $X,Y$ are independent. We define a random variable $Z = X + Y$ and want to find the PDF of $Z$ using convolution. Here is my work so far:
The definition of convolution is:
$f_Z(z) = \int_{-\infty}^{\infty}f_X(x)f_Y(z-x)\mathrm{d} ... |
First off, ${\bf R}^2$ is not a field. Let me build up the idea you want. If $L/K$ is a field extension, then in particular $L$ is a vector space over $K$, and the degree of the extension $[L:K]$ is defined to be the dimension $\dim_KL$ of $L$ over $K$. So perhaps you want to ask
Question: What kinds of degree $2$ exte... |
Erratum to: On optimal designs for censored data 574 Downloads 1 Erratum to: Metrika DOI 10.1007/s00184-014-0500-1
In the original publication, Theorem 3.5 was incorrectly published as:
Theorem 3.5
Let \(\fancyscript{X} = \{x_{1}, x_{2}, x_{3}\}\) be the design region. For \(i, j \in \{1, 2, 3\}, i \ne j\), let \(d_{ij... |
statsmodels.tsa.statespace.structural.UnobservedComponents¶ class
statsmodels.tsa.statespace.structural.
UnobservedComponents(
endog, level=False, trend=False, seasonal=None, freq_seasonal=None, cycle=False, autoregressive=None, exog=None, irregular=False, stochastic_level=False, stochastic_trend=False, stochastic_seas... |
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