text stringlengths 256 16.4k |
|---|
Let's say that we have an objective function $f(\mathbf x,\mathbf y)$ which has the parameters $\mathbf x=[x_1\ldots x_n]$ and $\mathbf y=[y_1\ldots y_n]$. Here, $\mathbf y$ is a blackbox variable which is calculated from a simulation of a network $\mathcal N$ by taking $\mathbf x$ as input.
$f$ is an objective functio... |
Definition:Pointwise Addition of Mappings Definition
Let $G^S$ be the set of all mappings from $S$ to $G$.
Then pointwise addition on $G^S$ is the binary operation $\circ: G^S \times G^S \to G^S$ (the $\circ$ is the same as for $G$) defined by: $\forall f,g \in G^S: \forall s \in S: \left({f \circ g}\right) \left({s}\r... |
Quasi In Situ Growth Observation and Precipitation Kinetics Assessment of the β-Mn Phase in Fe-30Mn-9Al-1C Steel 15 Downloads Abstract
This paper investigated the microstructure evolution of cold-rolled Fe-30Mn-9Al-1C steel at various heat treatment temperatures and found that the β-Mn phase could rapidly precipitate a... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
(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... |
TL;DR: Unless you assume people are unreasonably bad at judging car color, or that blue cars are unreasonably rare, the large number of people in your example means the probability that the car is blue is basically 100%.
Matthew Drury already gave the right answer but I'd just like to add to that with some numerical ex... |
I) OP wrote (v2):
I know that $\mathcal{L}$ is a
functional not a function.
Actually for local theories the Lagrangian density $$ \mathcal{L}(\phi(x), \partial\phi(x), \partial^2\phi(x), \ldots, ;x) $$is a
function of $\phi(x)$, $\partial\phi(x)$, $\partial^2\phi(x)$, $\ldots$, and $x$. In contrast, the action $S[\phi]... |
And I think people said that reading first chapter of Do Carmo mostly fixed the problems in that regard. The only person I asked about the second pset said that his main difficulty was in solving the ODEs
Yeah here there's the double whammy in grad school that every grad student has to take the full year of algebra/ana... |
Given the function
$g(n,m)=\min\Big\{f(a,b)+f(n-a,c)+f(n,m-bc)\Big|\\a,b,c\ \ \text{with} \left\{\begin{matrix} a,\ b,\ n-a,\ c,\ m-bc \geq 0 \\ b\leq a! \\ c\leq (n-a)! \\ \end{matrix}\right. \Big\} $
Assuming that $n,m\geq 0,\ ((\lceil n/2\rceil)!)^2\leq m\leq n!,\ f(n,m)=\Omega (n)$,
is it true that $g(n,m) \geq 2f(... |
I found another mistake in Romer's "proof", but I also got some (wrong-headed) pushback on the econ job rumors forum about my take on Paul Romer's mathiness. Here's the comment:
Yeah, [this post] is complete garbage. Mathematically, it's an issue of pointwise vs. uniform convergence, plain and simple. Economically, Rom... |
ISSN:
1531-3492
eISSN:
1553-524X
All Issues
Discrete & Continuous Dynamical Systems - B
March 2007 , Volume 7 , Issue 2
Select all articles
Export/Reference:
Abstract:
In this paper, we analyze theoretically an age structured population model with cannibalism. The model is nonlinear in that cannibalism decreases the bi... |
We have a DFA $A = (Q,\Sigma, \delta, q_0, F)$. States $p, q$ $\in Q$ are equivalent, $p \sim q$ if $ \forall w \in \Sigma ^ \ast$ $ \delta^*(p,w) \in F \iff \delta^*(q,w) \in F$
States $p,q$ are equivalent after $i$ steps, $p \sim ^i q$, if $ \forall w \in \Sigma ^ \ast$ such that $|w|\le i$ $ \delta^*(p,w) \in F \iff... |
I'm trying to convert some English statements to first order logic statements and I'm trying to use Prolog to verify the translations. My question is: how do I convert a first order logic statement (having $\forall$ and $\exists$ quantifiers) into Prolog rules?
For example, there's this English statement:
Every voter v... |
Alright, I have this group $\langle x_i, i\in\mathbb{Z}\mid x_i^2=x_{i-1}x_{i+1}\rangle$ and I'm trying to determine whether $x_ix_j=x_jx_i$ or not. I'm unsure there is enough information to decide this, to be honest.
Nah, I have a pretty garbage question. Let me spell it out.
I have a fiber bundle $p : E \to M$ where ... |
Alright, I have this group $\langle x_i, i\in\mathbb{Z}\mid x_i^2=x_{i-1}x_{i+1}\rangle$ and I'm trying to determine whether $x_ix_j=x_jx_i$ or not. I'm unsure there is enough information to decide this, to be honest.
Nah, I have a pretty garbage question. Let me spell it out.
I have a fiber bundle $p : E \to M$ where ... |
(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... |
I kind of have an elementary solution, it seems to be fine but I am not sure if everything is correct; please point out the mistake(s) I'm making, if any.
Define $$H_n:=\sum_{i=1}^n \frac{1}{i}$$Since $0<H_n<n$, if $\exists$ some $n$ for which $H_n$ is integral then $H_n=k$ where $0<k<n$. Then $$H_n=k=1+\frac{1}{2}+\fr... |
I need to calculate the number of ways of distributing $n$ balls among $k$ boxes, each box may contain no ball, but if it contains any, then it must contain $\geq L$ & $\leq M$ balls.
This effectively solves:
$x_1+x_2+x_3+\dotsb+x_k = n; \quad x_i\in [0,L,L+1,L+2,\dotsc,M-1,M]$.
Is there a known solution to this? Googl... |
This is my first question, please forgive me if I mistake something, since I don't think I will be allowed to edit the question later.
So, let me explain the kind of matrices I'm talking about. Think of a $n\times n$ square matrix, and think of a sequence of $n^2$ consecutive squares starting at $k^2$ (the most natural... |
Suppose we have a real function $ f: \mathbb{R} \to \mathbb{R}$ that is two times differentiable and we draw its graph $\{(x,f(x)), x \in \mathbb{R} \} $. We know, for example, that when the first derivative is not continuous at a point we then have an "corner" in the graph. How about a discontinuity of $f''(x)$ at a p... |
Let $E$ be a non-empty subset of an ordered space. Suppose that a is a lower bound of $E$ and $\beta$ is a upper bound of $E$. Show that $ \alpha \leq \beta $.
Proof: (1) If $\alpha$ is a lower bound of $E$ then $\forall x\in E\quad x\geq \alpha$ (2) If $\beta$ is a upper bound of $E$ then $\forall x\in E\quad x\leq \b... |
The problem I'm trying to solve is as follows:
Let $X$ be a space and let $A$ be a $\sigma$-algebra on $X$ that contains infinitely many elements. An infinite partition is a countably infinite sequence on non-empty and pairwise disjoint sets $C_1, C_2, ...$, all in $A$, such that their union is $X$. Show that such a pa... |
This is the question i would like to discuss, properly stated.
Given a model $M$ for a collection of set theory axioms (ZFC, for example), list all basic modal formulas $\phi$ such that $M\Vdash \phi$ and $\nVdash \phi$ (that is, $\phi$ is valid on the basic modal frame $M$, and $\phi$ is not a formula valid in the cla... |
I read the following statement in my modal logic book.
Propositional calculus system $L$ is consistent if and only if for every proposition symbol $p$ in $L$, $\not\vdash p$
I wonder how to prove this statement. And is this also true in FOL?
To make sure, I write some definitions here.
The propositional calculus system... |
Is there a function in Mathematica that can be used to find the perturbation solution of an equation like $x^2 − 1 = \epsilon \,x$, $x − 2 = \epsilon \cosh(x)$ or $x^2 − 1 = \epsilon\, e^x$?
Decide up to which power you would like to expand:
pow = 4;
Let's do one of the equations you mentioned as an example (bring all ... |
Seminar
Parent Program: Location: Space Science Lab, Room 105
In this work, we study the volume ratio of the projective tensor products $\ell^n_p\otimes_{\pi}\ell_q^n\otimes_{\pi}\ell_r^n$ with $1\leq p\leq q \leq r \leq \infty$. The asymptotic formulas we obtain are sharp in almost all cases. As a consequence of our e... |
What does it mean to say \(P(event) = something \)
This blog post is an attempt to explain the following tutorial to a more general audience. I gave that tutorial to explain some of my favorite ideas in the Shafer and Vovk book Probability and Finance, It’s only a Game!
Horse Gambling Games
Way before Probability Theor... |
Im working out this proof needed for the caratheodory - koebe theory.
The idea is quite simply to understand but there is an argument using sqeunces which im questioning about.
The statement is the following:
Let $D \subset \mathbb{C}$ a domain with $0 \in D$. $f,g$ holomorphic in $D$ with $f,g$ not constant. $g$ is in... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
Call the strategies of rock, paper, and scissors A, B, and C: C beats B beats A beats C.Label the possible positions in this game with $2(n-1)$ dollars in the pot as either: $T_{n-1}$ if the previous result was a tie; $G_{n-1}$ if player I has a winning streak of 1 using strategy A (where A could be any of rock, paper ... |
Developing flow From Thermal-FluidsPedia
Line 7: Line 7:
Similar analysis and conclusions can be made with the Schmidt number, Sc, relative to mass transfer problems concerning the entrance effects due to mass diffusion. If one needs to get detailed information concerning the hydrodynamic, thermal or concentration entr... |
Another method, not covered by the answers above, is
finite automaton transformation. As a simple example, let us show that the regular languages are closed under the shuffle operation, defined as follows:$$L_1 \mathop{S} L_2 = \{ x_1y_1 \ldots x_n y_n \in \Sigma^* : x_1 \ldots x_n \in L_1, y_1 \ldots y_n \in L_2 \}$$Y... |
And I think people said that reading first chapter of Do Carmo mostly fixed the problems in that regard. The only person I asked about the second pset said that his main difficulty was in solving the ODEs
Yeah here there's the double whammy in grad school that every grad student has to take the full year of algebra/ana... |
As I understand it, the definition of the hazard ratio is the ratio of two hazard rates. Often the exp(coef) from a Cox model is also used as an estimate of the hazard ratio. These methods give two different, although similar, results. Are there circumstances in which it's appropriate to use one method vs. the other?
I... |
Basically, what you're saying is that a homogeneous electric field $\vec{E}(\vec{r},t)=\cos \omega t \ \hat {z}$ in vacuum requires you to have a magnetic field that satisfies$$\nabla \times \mathbf{B} =\frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial t},$$giving you a non-homogeneous magnetic field, which would then r... |
Homework is due by 4:30 pm next
Wednesday, October 17th and can be handed in outside 329 Annenberg, or electronically by emailing keenan@cs.caltech.edu. Homework will be graded not only on the basis of correctness, but also on Remember that proofs are meant for human beings, not for machines. Legible handwriting, compl... |
An RLC circuit is a simple electric circuit with a resistor, inductor and capacitor in it -- with resistance
R, inductance Land capacitance C, respectively. It's one of the simplest circuits that displays non-trivial behavior.
You can derive an equation for the behavior by using Kirchhoff's laws (conservation of the st... |
I am working on the following problem:
Let $Y$ be the image of $\mathbb{P}^2$ in $\mathbb{P}^5$ by the Veronese embedding. Let $Z$ be a closed subvariety of $Y$ of dimension 1. Show that there exists a hypersurface $V$ of $ \mathbb{P}^5$ such that $V\cap Y = Z$
This is what I have done so far:
As $Z$ is a subvariety of... |
ISSN:
1547-5816
eISSN:
1553-166X
All Issues
Journal of Industrial & Management Optimization
October 2013 , Volume 9 , Issue 4
Select all articles
Export/Reference:
Abstract:
In this paper, we propose a primal-dual approach for solving the generalized fractional programming problem. The outer iteration of the algorithm ... |
Anyone knows if there is an algorithm for directly write the context-free grammar that generates a given regular expression?
I assume you want to get a grammar that generates the same language as the given regular expression.
You can achieve that by the following steps:
Translate the regular expression into an NFA. Tra... |
Search
Now showing items 1-10 of 52
Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
I was inspired by Dietrich Vollrath's latest blog post to work out the generalization of the macro ensemble version of the information equilibrium condition [1] to more than one factor of production. However, as it was my lunch break, I didn't have time to LaTeX up all the steps so I'm just going to post the starting p... |
Given that you already accept that the duality gap along the central path is $m/t$, then the inequality you're struggling with is really rather simple. Remember, the dual problem provides lower bounds for the optimal value of the primal. So $p^*$ is necessarily in between the objective values of any feasible primal poi... |
Search
Now showing items 1-10 of 23
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 ... |
Equivalence point means equal numbers of moles of acid and base have been added. If $x$ moles of the weak base $\ce{B}$ and the strong acid $\ce{HA}$ have been added, then the $\ce{H^+}$ ions will react away $\ce{OH^-}$ until all the weak base has associated into $\ce{BH^+}$ and $\ce{OH^-}$ (which of course has been re... |
Given two independent events $A$ and $B$, with given conditions:
$0 \lt P(A) , P(B) <1 $. Which one of the following options is/are false? $A$ and $B’$ are independent. $A’$ and $B’$ are independent. $P(A|B) = P(A|B’)$ For any event c, with $0 \lt P(c) \lt 1$, $P(AB|c)= P(A|c)\cdot P(B|c)$
Here is what I tried:
A and B... |
Consider a heat equation in one space dimension $$\frac{\partial u(t,x)}{\partial t} = \frac12\Theta(x)\frac{\partial^2u(t,x)}{\partial x^2} \tag{1}$$ where Heavyside function $$ \Theta(x) = \begin{cases} 0,\, x<0 \\ 1,\, x\ge 0 \end{cases} $$ with initial condition $$u(t=0,x) = x_+.$$
Obviously, $u(t,x)=0,\,\forall x<... |
There are many explanations to be found about shot noise in optics, but the answers I find are incompatible. There are three ways shot noise in optics is explained.
(Note that according to Wikipedia, in general, shot noise is a type of noise which can be modeled by a Poisson process.)
It is the noise purely arising for... |
First of all, the answer that applies here was already given by Raphael in the comments to the question: "
Given that we don't even know how to find one simple shortest path in linear time, I doubt it." In the following, thus, I will assume you are interested in knowing about the best available algorithms in the curren... |
Skills to Develop
When a substrate binds to one enzymatic subunit, the rest of the subunits are stimulated and become active. Ligands can either have non-cooperativity, positive cooperativity or negative cooperativity.
A significant portion of enzymes function such that their properties can be studied using the Michael... |
rmsprop¶
This module provides an implementation of rmsprop.
class
climin.rmsprop.
RmsProp(
wrt, fprime, step_rate, decay=0.9, momentum=0, step_adapt=False, step_rate_min=0, step_rate_max=inf, args=None)¶
RmsProp optimizer.
RmsProp [tieleman2012rmsprop] is an optimizer that utilizes the magnitude of recent gradients to ... |
Definition:Harmonic Numbers Contents Definition
The
harmonic numbers are denoted $H_n$ and are defined for positive integers $n$: $\displaystyle \forall n \in \Z, n \ge 0: H_n = \sum_{k \mathop = 1}^n \frac 1 k$
From the definition of vacuous summation it is clear that $H_0 = 0$.
Let $r \in \R_{>0}$.
For $n \in \N_{> 0... |
Steve Roth linked to Ben Casselman in a Tweet about the latest JOLTS data, and both brought attention to the fact that the ratio of unemployed to job openings appears to have flattened out; Steve also made the observation that it doesn't seem to go below 1.
I thought that the JOLTS data might make a good candidate for ... |
when solving the advection equation in 1D that is:
$$ \frac{\partial u}{\partial t} + c\frac{\partial u}{\partial x} = 0 $$ with $ u'(t,0) = 0$ and $u(t,L) = 0$ , $u(0,x) = u_{0} $
one numerical scheme is the FTCS (Forward time-centered space), but this numerical scheme is unstable.
$$\frac{u_{j}^{n+1}-u_{j}^{n}}{ h_{t... |
Inertia
In power systems engineering, "inertia" is a concept that typically refers to rotational inertia or rotational kinetic energy. For synchronous systems that run at some nominal frequency (i.e. 50Hz or 60Hz), inertia is the energy that is stored in the rotating masses of equipment electro-mechanically coupled to ... |
I read in a book, it is hard to formulate the theory of everything by unifying all the forces, because general relativity is a background independent theory while electromagnetism isn't. Why is this true?
I believe this to be a very important conceptual novelty of GR. Let me explain.
Electromagnetism depends on the bac... |
X
Search Filters
Format
Subjects
Library Location
Language
Publication Date
Click on a bar to filter by decade
Slide to change publication date range
1. Measurement of D⁎±, D± and Ds± meson production cross sections in pp collisions at s=7 TeV with the ATLAS detector
Nuclear Physics, Section B, ISSN 0550-3213, 06/2016,... |
(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... |
In a certain economy, time is discrete with periods $t=0,1,2,...$. The economy is populated by many households and identical firms. The utility of a household is:
$\displaystyle\sum^{\infty}_{t=0}\beta^t\Big(\log c_t - \gamma L_t^{\frac{1}{\gamma}}\Big)$
where $c_t$ is consumption and $L_t$ is labor in hours worked. Th... |
Let T be a second-order arithmetical theory, Λ a well-order, λ < Λ and X ⊆ ℕ. We use $[\lambda |X]_T^{\rm{\Lambda }}\varphi$ as a formalization of “φ is provable from T and an oracle for the set X, using ω-rules of nesting depth at most λ”.
For a set of formulas Γ, define predicative oracle reflection for T over Γ (Pre... |
I do not understand why: $$\cos(x)-i\sin(x) = \cos(-x)+i\sin(-x)$$
The last step i understand. (It is one of the solutions of a quadratic equation if it matters)
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 minute to ... |
When I typed this question in google I found this link: http://octomatics.org/ Just from the graphic point of view: this system seems to be easier (when he explains that you can overlap the line). He also talks about how base 8 is useful for computers. Is base 8 really the best,what makes one base better than the other... |
I studied algebraic topology from a mathematical point of view, so I can only try to explain the physical interpretation.
Beginning with the mathematics. The fundamental group associated with a pointed topological space is a set of equivalence classes of closed loops (under homotopy). But what does this mean? Let's sta... |
Some authors claim that an alignment between the Earth, the Sun, and the black hole in the center of the Milky Way will occur on 12/21/2012. We show why this is impossible, but also discuss why it wouldn't be a problem if it did. Claims
Some proponents claim that there will be an eclipse of the central black hole of ou... |
Inertia
In power systems engineering, "inertia" is a concept that typically refers to rotational inertia or rotational kinetic energy. For synchronous systems that run at some nominal frequency (i.e. 50Hz or 60Hz), inertia is the energy that is stored in the rotating masses of equipment electro-mechanically coupled to ... |
In my job as a data scientist, I am required to model the relationship between the price of a product and the sales or number of unit sold. I am trying to build a simplistic model, the assumptions of which are given below. I am not sure if all the assumptions will hold true simultaneously, or if there is a missing assu... |
I am facing a simple (at first glance) problem. I need to implement a numerical scheme for the solution of the first order wave propagation equation with chromatic dispersion included. My original problem is (for a forward propagating wave):
\begin{equation} \frac{1}{c} \frac{\partial u(x,t)}{\partial t} = -\frac{ \par... |
Practical Guide to Variational Inference
Update: since I wrote this blog post 5 years ago, it’s quite a ride along the variational inference path, both for me and the state of the art! There was no mention of VAEs or normalizing flows or autodiff variational inference because they had not been invented yet (though BBVI... |
A recent question discussed the now-classical dynamic programming algorithm for TSP, due independently to Bellman and Held-Karp. The algorithm is universally reported to run in $O(2^n n^2)$ time. However, as one of my students recently pointed out, this running time may require an unreasonably powerful model of computa... |
For a homework , I struggled to solve the following question but couldn't go further:
endowment of person 1 = (30,0)endowment of person 2 = (0,20)
utility functions are such that:\begin{eqnarray*} U (a_1,b_1) & = & \min(a_1,b_1) \\\\ U (a_2,b_2) & = & \min(4a_2,b_2).\end{eqnarray*}
What I am doing is setting a1 equal t... |
Golden Meantone Golden Meantone is based on making the relation between the whole tone and diatonic semitone intervals be the Golden Ratio
[math]\varphi = \frac 1 2 (\sqrt{5}+1) \approx 1.61803\,39887\ldots\,[/math]
This makes the Golden fifth exactly
[math](8 - \varphi) / 11[/math]
octave, or
[math](9600 - 1200 \varph... |
If there were an algorithm that factored in polynomial time by means of examining each possible factor of a complex number efficiently, could one not also use this algorithm to solve unbounded knapsack problems since two factors can be viewed as one value, say within the set for the knapsack problem, and the other bein... |
Primes are positive integers that do not have any proper divisor except 1. Primes can be regarded as the building blocks of all integers with respect to multiplication.
Theorem \(\PageIndex{1}\): Fundamental Theorem of Arithmetic
Given any integer \(n\geq 2\), there exist primes \(p_1 \leq p_2 \leq \cdots \leq p_s\) su... |
Let $x$ denote the solution of $Ax=b$ and let $\hat{x}$ denote the computed solution. We cannot hope to do better than $$\hat{x} = \text{fl}(x),$$ i.e., the floating point representation of $x$. In this, the most favorable case, we have $\hat{x}_j = x_j(1+\delta_j)$ where $|\delta_j| \leq u$ and $u$ is the unit roundof... |
Search
Now showing items 1-9 of 9
Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
Fishburn-Shepp inequality $xyz$ inequality
An inequality for linear extensions of a finite partially ordered set $(X,\prec)$. Elements $x,y\in X$ are incomparable if $x\neq y$ and neither $x\prec y$ nor $y\prec x$. Denote by $<_0$ a general linear order extension of $\prec$ on $X$, let $N$ be the number of linear exten... |
In last night's post, I looked at the ratio of the level of unemployment $U$ to job vacancies $V$ in terms of the "naive dynamic equilibrium" model. There was a slight change from the original version describing the unemployment rate $u$ where instead of taking the dynamic equilibrium to be:
\frac{du}{dt} \approx \; \t... |
1) Given \(\vecs r(t)=(3t^2−2)\,\hat{\mathbf{i}}+(2t−\sin t)\,\hat{\mathbf{j}}\),
a. find the velocity of a particle moving along this curve.
b. find the acceleration of a particle moving along this curve.
Answer: a. \(\vecs v(t)=6t\,\hat{\mathbf{i}}+(2−\cos t)\,\hat{\mathbf{i}}\) b. \(\vecs a(t)=6\,\hat{\mathbf{i}}+\s... |
This question already has an answer here:
Let $f : X \longrightarrow Y$ be continuous, and let $A \subseteq X$. Show that $f(\overline A) \subseteq \overline{f(A)}$.
My attempt
Let $y \in f(\overline A)$. Then there exists $x \in \overline A$ such that $f(x) = y$. Now let us take an open neighbourhood $V$ of $y$ in $Y$... |
(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... |
Well done Shaun from Nottingham and Maria from Seville.
In this diagram $OX$ makes an angle $\theta$ with the vertical, which means that the $2$ and $3$ weights both make an angle $\theta$ with the horizontal.
If we take the length $OX$ as the unit and then think about a vertical line through $O$ and the horizontal spa... |
Numeric
Symbolic
fast usually slower approximate exact well suited for simulations/DE/root finding well suited for algebraic/geometric problems sensible to unstability always stable not certified certified bertini/PHCpack... CoCoA/Singular/Macaulay/Magma... not good for exact problems hopeless for certain problems
Let ... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
In Section 4.2.2 of the book "Principles of Model Checking", there is a definition (Definition 4.16; Page 165) of "Product of Transition System and NFA". You are right about the states (i.e., $S \times Q$) of the product but make mistakes about its transition relation. Below I focus on the transition relation.Definitio... |
Search
Now showing items 1-10 of 26
Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
Could anyone comment on the following ODE problem? Thank you.
Given a 2-d system in polar coordinates: $$\dot{r}=r+r^{5}-r^{3}(1+\sin^{2}\theta)$$ $$\dot{\theta}=1$$
Prove that there are at least two nonconstant periodic solutions to this system.
It's easy to prove that there is a noncostant periodic solution using Poi... |
According to Bennett McCallum [1], the quantity theory of money (QTM) is the macroeconomic observation that the economy obeys long run neutrality of money (it's not just
MV = PY). This Implies supply and demand functions will be homogeneous of degree zero, i.e. ratios of $D$ to $S$ such that if $D \rightarrow \alpha D$... |
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... |
Trudy Mat. Inst. Steklov., 1976, Volume 142, Pages 254–266 (Mi tm2576) This article is cited in scientific papers (total in 3 4 papers) The Hamiltonian system connected with the equation $u_{\xi_\eta}+\sin u=0$ L. A. Takhtadzhyan , L. D. Faddeev Full text: PDF file (1081 kB) English version: Proceedings of the Steklov ... |
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. ... |
CS-92-56 Title Applying Database Dependency Theory to Software Engineering Authors D. Raymond and F.W. Tompa Abstract We describe the use of database dependency theory for investigating software designs. Dependency theory cap- tures some of the essential constraints implicit in a sys- tem, and focuses attention on its ... |
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... |
$$x = c_1\cos (t) + c_2\sin (t) $$ is a two-parameter family of solutions of the second-order DE $$x'' + x = 0. $$
Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions:
$$x\left(\frac{\pi}{6}\right) = \frac{1}{2} $$
and
$$x'\left(\frac{\pi}{6}\right) = 0 $$
I... |
Definition:Differential/Functional Definition
Let $J \sqbrk y$ be a differentiable functional.
Let $h$ be an increment of the independent variable $y$.
Then the term linear with respect to $h$ is called the differential of the functional $J$, and is denoted by $\delta J \sqbrk {y; h}$. Notes For a differentiable functi... |
Suppose I made a tag and it is used by many people everyday, so will it increase my reputation? And also, suppose no one uses it even once for a long time, i.e. 6 months, then?
Maybe it could be called book-errata? I cannot give many examples of discussions from math.SE offhand but at least one example from here Find l... |
This is something of a partial idea, a work in progress. Let's say there is some factor of production $M$ allocated across $p$ different firms. The $p$-volume bounded by this budget constraint is:
V = \frac{M^{p}}{p!}
$$
p-volume bounded by budget constraint M
Let's say total output $N$ is proportional to the volume $V... |
Suppose we have $75$ boxes that are labeled from $1$ to $75$ and that in each box there is at least one ball, but there are not more than $125$ balls total. I'm trying to find the largest number $n \in \left\{1,\, \ldots,\, 75 \right\}$ such that this statement is true: There is a collection of neighbouring boxes that ... |
I am trying to plot a function $ {\bf x}(t) = a(t)\hat{v} + {\bf b}(t) $$ {\bf x}(t) = r(t)\hat{v} + {\bf b}(t) $, with unit vector $ \hat{v} $ and vector $ {\bf b}(t) $ given in spherical coordinates. For simplicity, assume that $ \hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta) $, and $ {\bf b}(t) = [t,... |
Consider a tensor $T\in\mathbb{R}^{N\times N\times N\times M}$ and two vectors $x,y\in\mathbb{R}^N$. I want to compute the $N\times M$ vector defined by $X_{ij}=\operatorname{tr}(x^\top T_{:,:,i,j}y)=\operatorname{tr}_{12}(yx^\top T)$ efficiently.
I tried this in two different ways:
TCtable[x_, T_, y_] := ParallelTable... |
I'm a bit confuse with all theses notions. Let $E$ a normed vector space of infinite dimension (also Banach, but it's probably not important).
The theorem of Eberlin Smulian theorem says that : all bounded sequence that has a subsequence that converge weakly $\iff$ it's reflexive.
(In fact it just says implication, but... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.