text:
## Arrange fractions from least to greatest

$$\frac{15}{4}\,\,\,\,\,\frac{17}{6}\,\,\,\,\,\frac{11}{2}\,\,\,\,\,\frac{7}{3}$$

How do you sort improper fractions from least to greatest? One method is to convert them into mixed numbers and then arrange them.

1. Change each improper fraction into a mixed number:

$$\frac{15}{4}\,=\,3\frac{3}{4}$$

$$\frac{17}{6}\,=\,2\frac{5}{6}$$

$$\frac{11}{2}\,=\,5\frac{1}{2}$$

$$\frac{7}{3}\,=\,2\frac{1}{3}$$

2. Arrange the mixed numbers:

$$2\frac{1}{3}\,<\,2\frac{5}{6}\,<\,3\frac{3}{4}\,<\,5\frac{1}{2}$$

3. Switch the mixed numbers back into impropers:

$$\frac{7}{3}\,\,\,\,\,\frac{17}{6}\,\,\,\,\,\frac{15}{4}\,\,\,\,\,\frac{11}{2}$$

In the above example, we converted each fraction into a mixed number in order to compare the numbers. In this next example, none of the fractions are improper, so we will have to find common denominators in order to compare the fractions.

Arrange these fractions from least to greatest.

$$\frac{3}{4}\,\,\,\,\,\frac{5}{6}\,\,\,\,\,\frac{1}{2}\,\,\,\,\,\frac{2}{3}$$

1. To solve this problem, first rename the four fractions with a common denominator. In this case, 12 is a common denominator.

$$\frac{3}{4}\,=\,\frac{9}{12}$$

$$\frac{5}{6}\,=\,\frac{10}{12}$$

$$\frac{1}{2}\,=\,\frac{6}{12}$$

$$\frac{2}{3}\,=\,\frac{8}{12}$$

2. Now arrange the fractions:

$$\frac{6}{12}\,<\,\frac{8}{12}\,<\,\frac{9}{12}\,<\,\frac{10}{12}$$

3. Switch the fractions back to their original form"

$$\frac{1}{2}\,<\,\frac{2}{3}\,<\,\frac{3}{4}\,<\,\frac{5}{6}$$

 Directions: Sort the fractions from least to greatest. Place the fractions in the center of each circle. Once the fractions are correctly sorted, a message will pop up letting you know that you are correct. Duane Habecker, Created with GeoGebra

# Self-Check

 Question 1 Sort from least to greatest: $$\frac{5}{12}\,\,\,\,\,\frac{5}{6}\,\,\,\,\,\frac{5}{21}$$ [show answer] $$\frac{5}{21}\,<\,\frac{5}{12}\,<\,\frac{5}{6}$$

 Question 2 Sort from least to greatest: $$\frac{98}{99}\,\,\,\,\,\frac{45}{46}\,\,\,\,\,\frac{5}{6}$$ [show answer] $$\frac{5}{6}\,<\,\frac{45}{46}\,<\,\frac{98}{99}$$

 Question 3 Sort from least to greatest: $$\frac{5}{7}\,\,\,\,\,\frac{2}{5}\,\,\,\,\,\frac{6}{12}$$ [show answer] $$\frac{2}{5}\,<\,\frac{6}{12}\,<\,\frac{5}{7}$$


text:
For the frequency distribution:
Question:

For the frequency distribution:

Find the standard distribution.

Solution:

Given frequency distribution table

Now we have to find the standard deviation

Let us make a table of the given data and append other columns after calculations

And we know standard deviation is

$\sigma=\sqrt{\frac{\sum f_{i} x_{i}^{2}}{n}-\left(\frac{\sum f_{i} x_{i}}{n}\right)^{2}}$

Substituting values from above table, we get

$\sigma=\sqrt{\frac{1393}{60}-\left(\frac{277}{60}\right)^{2}}$

$\sigma=\sqrt{23.23-(4.62)^{2}}$

$\sigma=\sqrt{23.23-21.34}$

$\Rightarrow \sigma=1.37$

Hence the standard deviation is $1.37 .$

format: plain


text:
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i don’t think i’ve made the obligatory “please don’t send me a follow request if we’ve never interacted or you have no posts or bio; no hard feelings (unless you like, spam it ig)” post yet, so: yea here it is. just want to be able to vet who i follow and who follows me. also i’ll probably follow you back too

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in reference to this sudden meta (monads.online/@RussellsBarbers): if you have problems with flowless, please do me a favour and block me, because you’re almost definitely (at least, 99%, if not 100%) a racist head-ass i wouldn’t care to spend any time around. thank’s

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one of these days i’m gonna go full sicko mode and just make my own OS and some ridiculous program(s) that do(es) the things i want

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i think they could be and are used for a lot of good. like obviously computers cannot fix everything, that’s technocrat bullshit; the vast majority of problems we face today are social in nature, mostly created by the interests of awful white people. but i think that the way that computers can multiply our labour like a lever so that we can have more free time to better ourselves and self-fulfil, would definitely be very good to have in an actually democratic, classless(?), communist/socialist society

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“stop doing math” meme but for australia

STOP DOIN’ ‘STRAYA

• WE WHITE PEOPLE ARE NOT MEANT TO BE HERE
• 121 YEARS OF INDEPENDENCE yet NO-REAL WORLD USE FOUND for British settler colonialism other than oppressing ABORIGINAL PEOPLES
• Wanted to oppress Aboriginal peoples anyway for a laugh? We had a country for that: It was called “THE UNITED STATES OF AMERICA”
• “Yeah nah mate, fair dinkum true blue, she’ll be right” — Statements dreamed up by the utterly White

LOOK at what ‘Strayans have done with the Aboriginal land they continue to occupy to this day, with all the lives & resources they took by force (This is ROOL ‘Straya, done by ROOL ‘Strayans):

“G’day mate, y’ever done a shoey?”

They have played us for absolute fools

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← this user is neurodivergent (aka cool and epic) ←

Urgent: Does anyone want to commission me for a poem? I’m a homeless, trans and physically disabled individual. I need to start making a living from my poetry in order to obtain housing.

I have run out of funds to secure a hotel and was obtain to get the $900 I needed to get this apartment I was looking at. Poems are$15, state your user in the notes of the transaction. Funds go to PayPal.me/jennalawson210
BOOST!!

have not seen this type of guy but 100% exists

reddit in bio

back in my day we didn't have fancy "graphics" or "mouse cursor." we just had to close our eyes and imagine hairy little guys for 16 hours straight

none

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got the randomly-generated squad name “the virginity of ropes”

who up dwarfing they fortress

After fleeing donestic violence, I have no friends or gifts to wake up to on Hanukkah and Christmas. Please share

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Please ignore my deadname as it appears. Thank you so much ♡

being informed that the ogvent has something really cool on its 404 page

dwarf fortress premium edition release in a few days 👀

okay i multiplied two 4×4 matrices successfully

probably only really need that, honestly, unless constructing the perspective matrix needs something else; any other multiplications involving matrices are probably going to be done on the GPU

okay so if i understand this right, the type of a matrix should be [cols]@Vector(rows, T)

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text:
Mandelstam-Tamm uncertainty relation

The Mandelstam-Tamm enerty-time uncertainty relation states that $\Delta E \Delta t_A \ge \frac{\hbar}{2} \,,$ where $$\Delta E$$ is the energy uncertainty of a quantum system, and $$\Delta t_A$$ is the time required for a significant change of the expectation value of an observable $$A$$.

Derivation

Consider a quantum system with a Hamiltonian $$H$$. Let $$| \psi \rangle$$ be the time-dependent state of the system, and let $$A$$ be some observable. The uncertainty in the system's energy and the uncertainty in $$A$$ are defined, respectively, as \begin{align} &\Delta E = \sqrt{\langle H^2 \rangle - \langle H \rangle^2} \,, \\ &\Delta A = \sqrt{\langle A^2 \rangle - \langle A \rangle^2} \,, \end{align} where $$\langle \cdot \rangle = \langle \psi | \cdot | \psi \rangle$$ denotes the expectation value. $$\Delta E$$ and $$\Delta A$$ satisfy the uncertainty relation $\Delta E \Delta A \ge \frac{\big| \langle HA - AH \rangle \big|}{2} \,.$ Since the rate of change of the expectation value of $$A$$ is $\frac{d \langle A \rangle}{d t} = \frac{i}{\hbar} \langle H A - A H \rangle \,,$ the uncertainty relation reads $\Delta E \Delta A \ge \frac{\hbar}{2} \left| \frac{d \langle A \rangle}{dt} \right| \,.$ Defining $\Delta t_A = \left| \frac{d \langle A \rangle}{dt} \right|^{-1} \Delta A \,,$ one arrives at the Mandelstam-Tamm uncertainty relation. It follows from the above definition that $$\Delta t_A$$ is the time required for $$\langle A \rangle$$ to change by an amount of the order of $$\Delta A$$.

Example

Consider a quantum particle of mass $$m$$ moving freely along a line, taken to be the $$x$$ axis. Let the particle's state $$| \psi \rangle$$ be represented by a free-particle Gaussian wave packet: $\langle x | \psi \rangle = \left( \frac{2 \operatorname{Re} \alpha_t}{\pi} \right)^{1/4} \exp \left( -\alpha_t (x - x_t)^2 + \frac{i}{\hbar} p_0 (x - x_t) + i \frac{p_0^2 t}{2 \hbar m} + \frac{i}{2} \arg \frac{\alpha_t}{\alpha_0} \right) \,,$ where $$t$$ is time, and $x_t = x_0 + \frac{p_0 t}{m} \,, \qquad \alpha_t = \frac{\alpha_0}{1 + i \frac{2 \hbar t}{m} \alpha_0} \,.$ Here, $$x_0$$ and $$p_0$$ are the initial mean position and momentum of the particle, respectively, and complex-valued parameter $$\alpha_0$$ (satisfying $$\operatorname{Re} \alpha_0 > 0$$) quantifies the wave packet spread and position-momentum correlation at $$t=0$$.

The uncertainty in energy of the particle is given by $\Delta E = \frac{(\Delta p)^2}{m} \sqrt{\frac{1}{2} + \left( \frac{p_0}{\Delta p} \right)^2} \,,$ where $\Delta p = \frac{\hbar |\alpha_0|}{\sqrt{\operatorname{Re} \alpha_0}}$ is the momentum uncertainty.

The uncertainty in position is $\Delta x = \frac{1}{2 \sqrt{ \operatorname{Re} \alpha_t} } \,,$ and the rate of change of the mean position, i.e. the mean velocity of the particle, is $\frac{d \langle x \rangle}{d t} = \frac{p_0}{m} \,.$ Thus, the characteristic time associated with the change of particle's position is $\Delta t_x = \left| \frac{d \langle x \rangle}{dt} \right|^{-1} \Delta x = \frac{m \Delta x}{|p_0|} \,.$

Hence, \begin{align} \Delta E \Delta t_x &= \frac{(\Delta p)^2}{m} \sqrt{\frac{1}{2} + \left( \frac{p_0}{\Delta p} \right)^2} \frac{m \Delta x}{|p_0|} \\ &= \Delta x \Delta p \frac{\Delta p}{|p_0|} \sqrt{\frac{1}{2} + \left( \frac{p_0}{\Delta p} \right)^2} \\ &\ge \Delta x \Delta p \end{align} \,. Finally, the Heisenberg uncertainty relation, $\Delta x \Delta p \ge \frac{\hbar}{2} \,,$ (that is easily verified from the formulas above) implies $\Delta E \Delta t_x \ge \frac{\hbar}{2} \,.$ This is the Mandelstam-Tamm uncertainty relation in the case of $$A = x$$.


text:
# Product of two independent r.v.s following Pareto distributions

Suppose $X$ and $Y$ are independent random variables with $X ~ \sim Pareto(\theta_x, c),\ Y \sim Pareto(\theta_y, c)$, where the p.d.f. of $Pareto(\theta, c)$ is

\begin{align} f(t) = \begin{cases} \frac{\theta c^\theta}{t^{\theta+1}} & t \geq c \\ 0 & \text{otherwise} \end{cases} \end{align}

and c.d.f. is

\begin{align} F(t) = \begin{cases} 1 - \frac{c^\theta}{t^\theta} & t \geq c \\ 0 & \text{otherwise} \end{cases} \end{align}

In this settings, I'd like to derive $P(XY > z)$ for some $z > c$.

Using independence of $X$ and $Y$,

\begin{align} P(XY > z) &= \int_{c}^\infty f_X(x) [1-F_Y(\frac{z}{x})] \ dx \\ &= \cfrac{\theta_x \theta_y c^{\theta_x+\theta_y}}{z^{\theta_y}} \int_{c}^\infty x^{\theta_y - \theta_x - 1} \ dx \end{align}

It looks like the integral part will diverge in some parameter settings.

My question is: why $P(XY > z)$ cannot be appropriately defined in such cases? My calculation is not correct at some point?

• Your mistake is to use the identity $$1-F_Y(z/x)=(cx/z)^{\theta_Y}$$ for every $x>C$ while this holds only if $$x\leqslant z/c$$ – Did Jun 23 '17 at 15:59
• I understand. Thank you for your clear answer. – myuuuuun Jun 23 '17 at 16:16
• Your use of $C$ and $c$ for the Pareto lower bounds is about the worst visual combination one could think of. How about $b$ and $c$? – wolfies Jun 23 '17 at 16:36
• I'm sorry for making you confusing. $C$ and $c$ indicate a same constant ($C$ is a typo, I modified). Of course I can use different lower bounds for $X$ and $Y$ but I thought it's not essential to my problem. – myuuuuun Jun 23 '17 at 17:55


text:
# Convergence criterion

#### ssss

##### New member
|f(x0)f''(x0)|<|f'(x0)|^2 where I is the interval containing the approximate root x0, is the convergence criterion of ..........

(a) Newton - Raphson method
(b) Iteration method
(c) Secant method
(d) False position method

According to me its (a), but I confused because this formula is not directly given anywhere I had searched a lot on the internet, can anybody confirm what is the correct answer

#### chisigma

##### Well-known member
|f(x0)f''(x0)|<|f'(x0)|^2 where I is the interval containing the approximate root x0, is the convergence criterion of ..........

(a) Newton - Raphson method
(b) Iteration method
(c) Secant method
(d) False position method

According to me its (a), but I confused because this formula is not directly given anywhere I had searched a lot on the internet, can anybody confirm what is the correct answer

Wellcome on MHB $SS^{2}$!...

... remembering the Newton iterations...

$$x_{n+1}= x_{n} - \frac{f(x_{n})}{f^{\ '} (x_{n})}\ (1)$$

... if is...

$$\frac{|f(x_{0})\ f^{\ '}(x_{0})|}{|f^{\ '\ 2}(x_{0})|}= \frac{|f(x_{0})|}{|f^{\ '}(x_{0}|}= a < 1\ (2)$$

... and that holds for any $x_{0}$. then the sequence of $x_{n}$ obeys to the difference equation...

$$x_{n+1} - x_{n}= (\pm a)^{n}\ (3)$$

... and it converges...

Kind regards

$\chi$ $\sigma$

Last edited:

#### ssss

##### New member
Wellcome on MHB $SS^{2}$!...

... remembering the Newton iterations...

$$x_{n+1}= x_{n} - \frac{f(x_{n})}{f^{\ '} (x_{n})}\ (1)$$

... if is...

$$\frac{|f(x_{0})\ f^{\ '}(x_{0})|}{|f^{\ '\ 2}(x_{0})|}= \frac{|f(x_{0})|}{|f^{\ '}(x_{0}|}= a < 1\ (2)$$

... and that holds for any $x_{0}$. then the sequence of $x_{n}$ obeys to the difference equation...

$$x_{n+1}= \pm a\ x_{n}\ (3)$$

... and it converges...

Kind regards

$\chi$ $\sigma$
so I was right answer is Newton Rapshon option a, Thanks a lot for explanation


text:
# The dusty environment of the young galactic cluster NGC 2264.

http://hdl.handle.net/10150/187282
Title:
The dusty environment of the young galactic cluster NGC 2264.
Author:
Meyers-Rice, Barry Allan.
Issue Date:
1995
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
This is a study of the young galactic cluster NGC 2264. In it 12-100 $\mu$m IRAS data are used to analyze emission from the cluster dust. This dust is warmed by the young point sources in the cluster. Images of the region were obtained in the V, R, and I bands, and the point source data extracted are combined with a pre-existing J-H-K database to produce a six-band photometric survey of the cluster. This 4900-entry catalogue and methods to eliminate spurious detections and non-cluster stars from it are discussed. The cluster is estimated to consist of 350-650 members. A device to produce polarimetric images was designed, built, and used to obtain data to explore star formation environments. The nature of one such region in NGC 2264 is discussed, and the sources responsible for illuminating this reflection nebula are identified. It is concluded that multiple scattering and a disk geometry can explain the features observed. Spectra of 361 stars in the cluster region were obtained and by extending the MK system to the red part of the spectrum their spectral types are determined. Many T Tauri stars are identified and aspects of their emission lines are analyzed. It is shown that the spectral lines of many cluster stars of types later than G9 are in emission while those of earlier-type stars show incipient emission diluted by stellar flux. An evolutionary sequence of stars based upon photometry and spectroscopy is proposed. Stars from this spectral survey are dereddened and the extinctions obtained are interpreted. Spectral energy distributions are produced for the dereddened stars, revealing infrared excesses in many. These excesses are modelled by disk-star systems, and it is shown that inner holes are required in the disks to explain the observed levels of short wavelength emission.
Type:
text; Dissertation-Reproduction (electronic)
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Degree Grantor:
University of Arizona

DC FieldValue Language
dc.language.isoenen_US
dc.titleThe dusty environment of the young galactic cluster NGC 2264.en_US
dc.creatorMeyers-Rice, Barry Allan.en_US
dc.contributor.authorMeyers-Rice, Barry Allan.en_US
dc.date.issued1995en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThis is a study of the young galactic cluster NGC 2264. In it 12-100 $\mu$m IRAS data are used to analyze emission from the cluster dust. This dust is warmed by the young point sources in the cluster. Images of the region were obtained in the V, R, and I bands, and the point source data extracted are combined with a pre-existing J-H-K database to produce a six-band photometric survey of the cluster. This 4900-entry catalogue and methods to eliminate spurious detections and non-cluster stars from it are discussed. The cluster is estimated to consist of 350-650 members. A device to produce polarimetric images was designed, built, and used to obtain data to explore star formation environments. The nature of one such region in NGC 2264 is discussed, and the sources responsible for illuminating this reflection nebula are identified. It is concluded that multiple scattering and a disk geometry can explain the features observed. Spectra of 361 stars in the cluster region were obtained and by extending the MK system to the red part of the spectrum their spectral types are determined. Many T Tauri stars are identified and aspects of their emission lines are analyzed. It is shown that the spectral lines of many cluster stars of types later than G9 are in emission while those of earlier-type stars show incipient emission diluted by stellar flux. An evolutionary sequence of stars based upon photometry and spectroscopy is proposed. Stars from this spectral survey are dereddened and the extinctions obtained are interpreted. Spectral energy distributions are produced for the dereddened stars, revealing infrared excesses in many. These excesses are modelled by disk-star systems, and it is shown that inner holes are required in the disks to explain the observed levels of short wavelength emission.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineAstronomyen_US


text:
# Semiclassical strong-field theory of phase delays in $\omega -2\omega$ above-threshold ionization

@inproceedings{Arbo2022SemiclassicalST,
title={Semiclassical strong-field theory of phase delays in \$\omega -2\omega\$ above-threshold ionization},
author={Diego G. Arb'o and Sebasti'an D. L'opez and Joachim Burgdorfer},
year={2022}
}
• Published 8 August 2022
• Physics
Phase and time delays of atomic above-threshold ionization were recently experimentally explored in an ω − 2 ω setting [Zipp et al , Optica 1 , 361 (2014)]. The phases of wavepackets ejected from argon by a strong 2 ω pulse were probed as a function of the relative phase of a weaker ω probe pulse. Numerical simulations solving the time-dependent Schr¨odinger equation (TDSE) displayed a sensitive dependence of the doubly diﬀerential momentum distribution on the relative phase between the ω and 2…

## References

SHOWING 1-10 OF 46 REFERENCES

### Phase delays in ω−2ω above-threshold ionization

• Physics
Physical Review A
• 2021
Relative phases of atomic above-threshold ionization wavepackets have been investigated in a recent experiment [L. J. Zipp, A. Natan, and P. H. Bucksbaum, Optica 1, 361-364 (2014)] exploiting

### Probing electron delays in above-threshold ionization

• Physics
• 2014
Recent experiments have revealed attosecond delays in the emission of electrons from atoms ionized by extreme UV light, offering a glimpse into the ultrafast nature of light-induced electron

### Multiphoton interaction phase shifts in attosecond science

• Physics
• 2021
This paper shows that interferometric experiments in attosecond and free-electro lasers are subjected to large phase effects due to the accumulation of interaction phases with each exchanged laser

### Intracycle and intercycle interferences in above-threshold ionization: The time grating

• Physics
• 2010
Within a semiclassical description of above-threshold ionization (ATI) we identify the interplay between intracycle and intercycle interferences. The former is imprinted as a modulation envelope on

### Laser-assisted photoionization: Streaking, sideband, and pulse-train cases

• Physics
• 2020
We present a theoretical study of atomic laser-assisted photoionization emission (LAPE). We consider an atom driven by a linearly polarized XUV laser in two different scenarios: i) a single

### Spiral-like holographic structures: Unwinding interference carpets of Coulomb-distorted orbits in strong-field ionization

• Physics
Physical Review A
• 2020
We unambiguously identify, in experiment and theory, an overlooked holographic interference pattern in strong-field ionization, dubbed the spiral,'' stemming from two trajectories where the

### Application of the saddle-point method to strong-laser-field ionization

• Physics
Journal of Physics A: Mathematical and Theoretical
• 2020
The quantum-mechanical transition amplitude of an ionization process induced by a strong laser field is typically expressed in the form of an integral over the ionization time of a highly oscillatory

### Time Delays from One-Photon Transitions in the Continuum

• Physics
2020 Conference on Lasers and Electro-Optics (CLEO)
• 2020
We experimentally resolve the time delay of electron wave packets arising from one-photon transitions in the continuum. This allows us to determine and quantify the angular momentum dependence of the

### It is all about phases: ultrafast holographic photoelectron imaging

• Physics
Reports on progress in physics. Physical Society
• 2019
A historic account in which a connection with laser-induced electron diffraction (LIED) is established is established, a summary of the main holographic structures encountered and their underlying physical mechanisms, and a broad discussion of the theoretical methods employed.


text:
# Thread: Approximate Each Number...Part A

1. ## Approximate Each Number...Part A

The instructions given in the textbook are as follows:

Approximate each number using a calculator. Express your answer rounded to three decimal places.

My Question:

Is there a way to approximate each number below WITHOUT usinga calculator?

If so, how is this done?

(1) pi^(e) =

(2) e^(pi) =

2. Originally Posted by magentarita
The instructions given in the textbook are as follows:

Approximate each number using a calculator. Express your answer rounded to three decimal places.

My Question:

Is there a way to approximate each number below WITHOUT usinga calculator?

If so, how is this done?

(1) pi^(e) =

(2) e^(pi) =
$\pi$ is approximately 3.141592 and e is approximately 2.71828 so [tex]\pi^e= \pi^2 \pi^.718[tex], approximately. .718= 718/1000 and 1000 is close to $1024= 2^10$. $\pi^e$ will be approximately 3.14 to the 718 power, then square root 10 times. That won't be very good approximation. You might see if you can find a higher power of 10 that is closer to a power of 2. Of course, that's going to be an awful lot of work!

Originally Posted by HallsofIvy
$\pi$ is approximately 3.141592 and e is approximately 2.71828 so [tex]\pi^e= \pi^2 \pi^.718[tex], approximately. .718= 718/1000 and 1000 is close to $1024= 2^10$. $\pi^e$ will be approximately 3.14 to the 718 power, then square root 10 times. That won't be very good approximation. You might see if you can find a higher power of 10 that is closer to a power of 2. Of course, that's going to be an awful lot of work!

Something is wrong with your math reply when saying "so [tex]\pi^e= \pi^2 \pi^.718[tex], approximately"

Why is the word math in brackets?

4. Originally Posted by magentarita
Something is wrong with your math reply when saying "so [tex]\pi^e= \pi^2 \pi^.718[tex], approximately"

Why is the word math in brackets?
He/she happened to forget a forward slash in the last bracket. It would have generated the image $\pi^e= \pi^2 \pi^{.718}$

--Chris

5. ## ok....

Originally Posted by Chris L T521
He/she happened to forget a forward slash in the last bracket. It would have generated the image $\pi^e= \pi^2 \pi^{.718}$

--Chris
Thanks for clearing that up for me.


text:
# Quantum relative phase, m-tangle, and multi-local Lorentz-group invariant

Quantum relative phase, m-tangle, and multi-local Lorentz-group invariant In this paper we define a family of hermitian operators by which to extract what we call quantum-relative-phase properties of a pure or mixed multipartite quantum state, and we relate these properties to known measures of entanglement, namely the m-tangle and the invariant $${S_{(m)}^2}$$ of the multi-local Lorentz-group $${SL(2, \mathbb{C})^{\otimes m}}$$ . Our construction is based on the orthogonal complement of a positive operator valued measure on quantum phase. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Quantum relative phase, m-tangle, and multi-local Lorentz-group invariant

, Volume 9 (2) – Oct 22, 2009
6 pages
Loading next page...

/lp/springer_journal/quantum-relative-phase-m-tangle-and-multi-local-lorentz-group-f2h0Ml1At9
Publisher
Springer US
Copyright
Copyright © 2009 by Springer Science+Business Media, LLC
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-009-0150-9
Publisher site
See Article on Publisher Site

### Abstract

In this paper we define a family of hermitian operators by which to extract what we call quantum-relative-phase properties of a pure or mixed multipartite quantum state, and we relate these properties to known measures of entanglement, namely the m-tangle and the invariant $${S_{(m)}^2}$$ of the multi-local Lorentz-group $${SL(2, \mathbb{C})^{\otimes m}}$$ . Our construction is based on the orthogonal complement of a positive operator valued measure on quantum phase.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 22, 2009

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text:
# Price, Variable Cost per Unit, Contribution Margin, Contribution Margin Ratio, Fixed Expense For each of the following independent situations, calculate the amount(s) required. Required: 1. At the break-even point, Jefferson Company sells 115,000 units and has fixed cost of $349,600. The variable cost per unit is$4.56. What price does Jefferson charge per unit? 2. Sooner Industries charges a price of $120 and has fixed cost of$458,000. Next year, Sooner expects to sell 15,600 units and make operating income of $166,000. What is the variable cost per unit? What is the contribution margin ratio? ( Note: Round answer to four decimal places.) 3. Last year, Jasper Company earned operating income of$22,500 with a contribution margin ratio of 0.25. Actual revenue was $235,000. Calculate the total fixed cost. 4. Laramie Company has a variable cost ratio of 0.56. The fixed cost is$103,840 and 23,600 units are sold at break-even. What is the price? What is the variable cost per unit? The contribution margin per unit?

### Managerial Accounting: The Corners...

7th Edition
Maryanne M. Mowen + 2 others
Publisher: Cengage Learning
ISBN: 9781337115773

### Managerial Accounting: The Corners...

7th Edition
Maryanne M. Mowen + 2 others
Publisher: Cengage Learning
ISBN: 9781337115773

#### Solutions

Chapter
Section
Chapter 7, Problem 36E
Textbook Problem

## Expert Solution

### Want to see the full answer?

Check out a sample textbook solution.

### Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times vary by subject and question complexity. Median response time is 34 minutes and may be longer for new subjects.


text:
Hide

# Appalling Architecture

Photo from Carlos ZGZ.

You have recently been hired as an architect for the BAPC (Bureau of Architecture and Promising Constructions), responsible for top-quality buildings such as the Tower of Pisa. However, in the past couple of weeks, some of the structures that the BAPC have made have collapsed! It is up to you to figure out whether any other structures are in danger.

After some research it seems like the $x$-coordinate of the centers of gravity of some of the structures are off: if the center of gravity is too much to the left or to the right, the structure will fall over. Hence, you decide to check all the blueprints and see whether the structures are stable or not.

Given is a grid of up to size $100$ by $100$, using characters in .#/\_|-. The $\texttt{.}$ characters denote empty space, while each other character represents a completely filled $1\times 1$ box (any difference in symbols used is due to the artistic freedom of the other architects), whose center of mass is at the center of the box.

Every structure forms a single connected component that touches the ground, i.e. the bottom layer of the grid.

The structure falls to the left if the $x$-coordinate of the center of gravity is less than the $x$-coordinate of the leftmost point of the structure that touches the ground, and it falls to the right if the $x$-coordinate of the center of gravity is larger than the $x$-coordinate of the rightmost point of the structure that touches the ground. It is guaranteed that the center of gravity is never exactly above the leftmost or rightmost point where the building touches the ground.

Given a blueprint, is the structure balanced, does it fall to the left, or does it fall to the right?

## Input

• The first line has $1\leq h \leq 100$ and $1\leq w\leq 100$, the height and width of the grid.

• Then follow $h$ lines with $w$ characters each. Each character is either ., indicating empty space, or one of #/\_|-, indicating a filled $1\times 1$ box .

## Output

• Print a single line containing left, balanced, or right.

Sample Input 1 Sample Output 1
3 3
/-\
|.|
#.#

balanced

Sample Input 2 Sample Output 2
3 3
...
___
..|

left

Sample Input 3 Sample Output 3
3 3
./\
.\/
.|.

balanced

Sample Input 4 Sample Output 4
20 19
...................
.........-____---..
........._/\\////-.
.......--//#\#\/_..
......._/\///////_.
......-/#######\/-.
......////\/#\#/_..
....../\#\#/////_..
....._/#####\#\/...
....._/\////////-..
...../########/-...
...._///\/#\#\/....
...._/#/#/\/\/_....
..._/\#######/-....
..._/\////////-....
.../\#\#\#\#/-.....
.._///\\\\#\/-.....
.._//////////-.....
..////##////-......
.-____##____.......

balanced

CPU Time limit 1 second
Memory limit 1024 MB
Difficulty 4.2medium
Statistics Show


text:
# 教師資料查詢 | 類別: 期刊論文 | 教師: 林莊傑CHUANG-CHIEH LIN(瀏覽個人網頁)

o(|D|) elements in D, determine if ψ satisfies P or differs from any one which satisfies P in at least \epsilon |D| elements. We focus on consistency of quartet topologies. Given a set Q of quartet topologies over an n-taxon set and an upper bound k on the number of quartets whose topologies are missing, we present a non-adaptive property tester with one-sided error, which runs in time O(1.7321^k kn^3/\epsilon) and uses queries, to test if Q is consistent with an evolutionary tree.

ISSN1872-6119

SDGs
• 優質教育


text:
# American Institute of Mathematical Sciences

June  2005, 4(2): 311-339. doi: 10.3934/cpaa.2005.4.311

## Method of the distance function to the Bence-Merriman-Osher algorithm for motion by mean curvature

 1 NTT Comware, Minato, Tokyo, 108-8019, Japan 2 Faculty of Maritime Sciences, Kobe University, Higashinada, Kobe 658-0022, Japan 3 Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan

Received  March 2003 Revised  May 2004 Published  March 2005

A new proof of the convergence of the Bence-Merriman-Osher algorithm for the motion of mean curvature is given. The idea is making use of the approximate distance function to the interface and analogous argument in the singular limiting problem for the Allen-Cahn equation via an auxiliary function given by the primitive function of the heat kernel.
Citation: Y. Goto, K. Ishii, T. Ogawa. Method of the distance function to the Bence-Merriman-Osher algorithm for motion by mean curvature. Communications on Pure & Applied Analysis, 2005, 4 (2) : 311-339. doi: 10.3934/cpaa.2005.4.311
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2019 Impact Factor: 1.105


text:
# Question concerning L'Hospital's rule

I know that L'Hospital's rule is applied when $\lim \frac{f'(x)}{g'(x)}$ must exist.

Then, is there an example that $\lim \frac{f'(x)}{g'(x)}$ does not exist but other conditions of L'Hospital's rule hold ?

i.e. for example) Are there functions $f$ and $g$ such that

$\lim f(x) = \lim g(x) = + \infty$ and $f$, $g$ are differentiable but $\lim \frac{f'(x)}{g'(x)}$ does not exist?

I don't speak english very well. I'm Sorry if you don't understand.

-

We can use $f(x)=x+\sin x$, $g(x)=x$. In that case, the limit as $x\to\infty$ of the ratio exists, but the limit of the ratio of the derivatives does not.


text:
# Clarifying “What topics can I ask about here?” from the help center

This is pretty much a continuation of JBH’s post but it is narrowed down to a specific issue. It also comes after a suggestion from elemtilas to refocus the question.

This is the question that shed light on a problem we have on the site. Despite several edits, it has been closed, reopened, re-closed and now it even has a vote for deletion. I have no idea what is the justification behind the recent trend of deletion votes on questions but that is another issue.

Questions like these get closed but the asker insist that he is building a world. It is not a new issue but it bothers me more now, and it’s hard to justify when there is nothing in the help center to legitimate the closure.

I would summarize the issue like this;

1. The question now has a worldbuilding context, but people still think it is off-topic. I don't know what it takes to change their minds or what needs to be done to make these questions acceptable.
2. People use the lack of context as an argument to close questions but there is nothing in the help center that requires an ** explicit worldbuilding context**. We assume that the questions asked here are about worldbuilding but there is no requirement to have an explicit worldbuuilding context.
3. Worldbuilding in itself is rarely a topic. The question are always about something else like geography, history, linguistic, physics, etc. Some questions might appear to be less focused on worldbuilding but they still are about building a world. If I want to ask a physics question in order to help me build my world, there is again nothing in the rules preventing me to do that.

It has been said countless times that it is not because a question is on-topic on another site that it makes the question off-topic here. Yes, maybe the person will have a better answer on the other site but it’s his/her choice. Questions about building fictional worlds are off-topic on other sites since it’s supposed to be our topic. So asking these questions on other sites is likely to end in closure or migration if there is a slight element of woldbuilding involved.

So, with my understanding of the situation, I see two things that can be done:

1. Stop closing these questions as off-topic because they are on-topic according to the help center.
2. Change the help center to reflect that questions need a clear worldbuilding context, otherwise they will get closed as off-topic.

Right now, we generate a lot of frustration from new users. They get told that they do not follow the rules but when they check the help center, they find nothing. We have to fix it one way or another. Feel free to share your views and solutions to the problem.

Link to the help center for reference.

Edit: JBH's question was not specific enough. By narrowing down the issue, it is more likely to get solved. I felt the other question was not heading anywhere.

• Oml. Maybe it's just me, but that innocent little post I put out on antimatter has sparked something like 5-6 meta discussions and polarized everyone. People, I was just asking a question! I'm not sure whether to feel guilty, glad, bitter, or whether I should just laugh – FoxElemental May 7 '18 at 0:20
• @Anonymous don't feel bad about it, we should have had the conversation a while ago. Sometimes there is a problem but you need time/opinion of others to be able to narrow it down. As I said, it is a trend but eventually, you realize it's to much to ignore. – Vincent May 7 '18 at 0:37
• I haven't read through all the history, but in its current form this seems to be clearly a worldbuilding question. I'm tempted to use my mod powers to reopen it. (And I agree that we need to clarify our scope and documentation.) – Monica Cellio May 7 '18 at 0:57
• Possible duplicate of Enough is enough. NOBODY can obey rules that are only in someone's head – The Square-Cube Law May 7 '18 at 15:01
• @Renan JBH's question was not specific enough. I already explained why they are not duplicate. by narrowing down the issue, it is more likely to get solved. I felt the other question was not heading anywhere. Also, if you are the one casting deletion votes, you should stop this disruptive behaviour. – Vincent May 7 '18 at 15:11
• @Vincent I understand that you are trying to narrow the issue down, and I appreciate that the suggestion on how to solve it is so straightforward. I think the core of this question is the same as JBH's, though, and that reverse rule-lawyering might not solve it. Even if we write down that questions need to have some worldbuilding made explicit in them, people will be questioning what is worldbuilding and what isn't. – The Square-Cube Law May 7 '18 at 15:22
• @Vincent if you are the one casting deletion votes, you should stop this disruptive behaviour. I do not think this is disruptive behavior. According to the Help Center: When should I delete questions? Closed questions that are of no lasting value whatsoever should be flagged and deleted. – The Square-Cube Law May 7 '18 at 17:00
• @Renan trying to fill the breach is better than doing nothing. – Vincent May 7 '18 at 18:57
• @Renan but you should also consider the paragraph following that sentence : "Before voting to delete, please check whether there are any good answers; if so, then the question should be flagged for moderator attention as a potential merge candidate. We don't like to lose great answers!" – Vincent May 7 '18 at 19:28
• The main issue I still see with the original question now edited is that there is still no actual connexion between the question and the action of making a fictional world. I could ask "so, I have this world with Gnomes and I want them to be able to make a chocolate cake; what's the recipe for chocolate cake?" Same exact problem. In both cases, the "worldbuilding context" is a red herring that I think you've been misled by. Like my baking Gnomes, the OP's "need for a source of lots of energy" is irrelevant to the actual question. – elemtilas May 13 '18 at 23:31
• And I see the question that got this started has, for some strange reason, been reopened. Nothing about it has changed: it is still a simple maths question ("how much...") and still lacks any hint of worldbuilding. – elemtilas May 16 '18 at 16:25
• @elemtilas I'm not sure I understand the issue. On one hand, people close the question because it is too simple (not everyone agrees it is the case), on the other hand, questions get closed because they are too complex. Is it because questions need to be in a sweet spot? – Vincent May 16 '18 at 16:45
• @elemtilas by judging from HDE new answer, it doesn't look so simple unless maybe you are already familiar with topic. – Vincent May 16 '18 at 16:49
• @Vincent The issue that I see is that the question has been treated like a football. It's clearly not a worldbuilding related question, has been closed as such. Then it got reopened. Then closed and reopened again. I think this speaks more to us as a community not having consensus as to this forum's purpose, which is why we're actually here in Meta discussing this very question! Also, the fact that the original question has never been substantively edited to make it a worldbuilding question: it should never have been reopened until that happens. – elemtilas May 16 '18 at 17:41
• @elemtilas I believe my initial point still stands: the question does not violate any written rules. Maybe it violates the spirit of the law but it's hard to agree since it's not written anywhere. But after reflection, changing the rules could have bad consequences. Too strict: it becomes harder to ask a question (good ones could get closed because of technicalities) but at least the rules are clear or too slack and it becomes hard to justify the closure of any question. So I think the actual situation, while not ideal, is not so bad. – Vincent May 16 '18 at 18:00

Perhaps an area of focus we need to work on isn't so much "what topics can I ask about here" but rather "What is Worldbuilding Stack Exchange all about?"

Going back the Source, we read here at the Stack Exchange tour: Stack Exchange is a network of 172 communities that are created and run by experts and enthusiasts like you who are passionate about a specific topic. We build libraries of high-quality questions and answers, focused on each community's area of expertise.

I notice two key ingredients to what SE is:

• We are experts in & passionate about a specific topic. In our case, worldbuilding.
• Our task is to provide answers that focus on our community's area of expertise. Again, in our case this is worldbuilding.

There are some commonalities of definition:

• The Font of All Knowledge says: Worldbuilding is the process of constructing an imaginary world, sometimes associated with a whole fictional universe. The resulting world may be called a constructed world. Developing an imaginary setting with coherent qualities such as a history, geography, and ecology is a key task for many science fiction or fantasy writers.[2] Worldbuilding often involves the creation of maps, a backstory, and people for the world.

• Here on Worldbuilding.SE, this question actually came up and we said in response:

• Worldbuilding (noun, verb, adjective) - The act or subject of construction of (fictional) worlds, especially as an aid to the creation of art or to facilitate play

• Worldbuilding (verb) - The creation of lore, history, religions, geography, or any other aspect of a fictional world which is not directly related to the characters in a fictional story

• Worldbuilding (verb) - the creation of the setting of a fictional story

• Worldbuilding is the term used to describe the art of building an imaginary world -- i.e. a setting in which a story or game takes place. This might involve creating fictional geography (maps), biology (races or creatures), politics (kingdoms), history (famous people or events), language, religion, mythology, technology, philosophy, or pretty much any other aspect of the world.

It seems to me, then, that what is on-topic here are those topics, questions and problems directly pertaining to what we have actually self-defined our area of expertise and passion to be.

We certainly may touch on physics and maths and chemistry and even music and literature and sociology. But those really aren't our areas of expertise. Our area of expertise is applying these matters of human lore and science in a fictional direction.

Getting back to the question that got this whole discussion started, I see these ways it can go:

• First, we leave it as is. The problem here is that, in its essence, at the core of its being, that question boils down to "please do this math problem for me". The OP can layer on all the worldbuilding "context" he wants. He can go on ad nauseam about energy sources and mega weapons and whatever else, but that's all my eye and Betty Martin.

• Second, we fix the question. The OP has already (justifiably) complained: No one seems willing to tell me how, exactly, I can fix it. To which I answered: I would think, and this is my opinion, that it is obvious that a question that asks for the answer to a (simple!) physics equation is not related in any way to worldbuilding. Even though you do hint at this being part of some kind of maybe SF story, the question itself doesn't touch upon the construction of fictional worlds & settings. Others disagree with this position, saying that basically anything that can be asked about the primary world touches also upon worldbuilding. Not a really helpful metachat! At this point: plug the numbers into the equation yourself or ask on Physics! I stand by the opinion that this kind of question is by definition off-topic and can't really be "fixed". A non-starter this.

• Third, we fix something about Wordlbuilding.SE that clarifies the basics for those people who are pointed in this direction, who land here accidentally or who do research and find us themselves:

• We clarify what Stack Exchange itself is, and how we at Worldbuilding.SE fit that model;
• We clarify what worldbuilding itself (the art, the hobby) is and what it isn't. The scope of our expertise, in other words.
• We clarify not "what topics" we answer, but perhaps rather what kinds of topics we answer. In other words, we don't want to limit ourselves unnecessarily but also I think we don't want to leave ourselves so broad that we become little more than a dumping ground.

The main problem with the question under discussion is that a serious answer would require a lot of work and a lot of physics; there are not that many people on this site who have the capability to do the work, and, in addition, there are not many people on this site who would appreciate it.

The accepted answer, posted by the inquirer themself, is painfully wrong. One cannot simply take E = mc² and plug in some numbers mindlessly; one must consider what would actually happen. As the planets begin to collide, the energy released would shatter them and vaporize huge amounts of material, which would then proceed to expand; we now have two superhot rapidly expanding spheres of matter and antimatter which will interact in wonderful ways. How it would play out depends on the velocity (speed and direction) of the impactor.

To summarize:

• It's a complicated physics problem.

• The accepted answer, posted by the anonymous inquirer, is wrong.

• I'd say that deleting the question, or, if possible, leaving it closed with a big warning on top, would be justified.

• I don't agree with the first paragraph because we let it happen very often and a lot of people actually like these kind of complex question. Your secound paragraph is off topic, the fact that the answer is wrong is not relevant here. This question is just an exemple and I'm more concerned about how we apply our rules is inconsistent. – Vincent May 13 '18 at 14:45
• Note, though, that the question isn't / wasn't "what would happen if...", but rather "what quantity of energy do I get if..." Now, thát question, what would happen, might actually not have spawned this whole line of discussion! There's actual worldbuilding meat on that bone. – elemtilas May 13 '18 at 23:24

Worldbuilding Stack Exchange is a site for developers, designers, writers and artists to get help creating imaginary worlds.

there is nothing in the help center that requires a worldbuilding context.

is false. There is. At the very, very beginning.

• No, it says they need to build a world, it does not say they have to provide the context surrounding the question. – Vincent May 7 '18 at 14:39
• @Vincent well, if you want to twist it like that then I guess it should be even more explicitly stated that only questions about worldbuilding are on topic on worldbuilding. On the other hand, quite possibly other texts will be twisted later as well... – Mołot May 7 '18 at 14:48
• I am not twisting reality, I just don't put words that aren't there. I don't give it an interpretation, I am reading it as it is written. And I assume people come here with good intentions, to ask questions about worldbuilding. Maybe that is a little naive but I don't see anything against doing so with the rules as they are written. That is why I posted this question. – Vincent May 7 '18 at 14:55
• @Vincent even if the rules state that questions need to have worldbuilding in their context, people will still be rule-lawyering about what constitutes worldbuilding. Rewording the help center pages would be just a token effort. – The Square-Cube Law May 7 '18 at 16:05

The lines will always be blurry on Worldbuilding SE regarding what is on-topic and what isn't.

The community is either divided or doesn't have a strong opinion on how the rules should be understood.

It falls on the responsibility of individual members to judge questions according to what they think is the best thing to do for the community.

Disagreement will continue as users have different closing criteria, bringing confusion for newcomers. But it looks like the community in general is fine with this situation.

• Sadly, I have the feeling this is where the whole issue is going to end up... – elemtilas May 13 '18 at 23:27


text:
Key Exchange vs Key Encapsulation

From what I understand, the steps of a key exchange protocol are

1. Alice and Bob each encrypt something using their public key and private key and send the result to each other

2. Alice and Bob each do some mechanism with their private key and the result sent by the other

3. They should agree on the secret.

Key encapsulation is

1. Alice generates a secret key and public key and sends the public key to Bob.

2. Bob generates his own secret key and encrypts it using Alice's public key. He sends the result to Alice.

3. Alice decrypts the result using her private key and ends up with Bob's key.

Is this correct and if not, could someone clarify which parts I am misunderstanding or missing?

Looking at the Known Answer Tests for NIST PQC KEM Submissions, when a seed is provided, each algorithm returns the secret key, public key, cipher text, and shared secret.

Is the shared secret Bob's private key and the cipher text what Bob sent to Alice? If not, how does the terminology work? How can the seed guarantee the correct public/secret key generation?

Key exchange: I'll use ECC as an example. Alice and Bob generate ephemeral key pairs and sign their ephemeral public key with their static private key, and then send their signed ephemeral public key to each other.

Both parties receive the others signed ephemeral public key and verify it using the others static public key, stored by a CA or in a PKI. Now they combine their own ephemeral private key with the other's ephemeral public key, using EC Point Multiplication (for this example). Now they both have a shared secret, as both multiplications give the same result.

This is then run through a quick hash like SHA2/3 into the correct length for symmetric encryption. For example with AES-256, the shared secret goes through SHA(3)-256 to get a key of the correct length.

Key encapsulation: I'll use the RSA KEM for this example. Bob knows Alice's public key $$(e,n)$$. He creates the symmetric key $$M$$ from a CSPRNG , where $$0, and converts it into a symmetric key with a KDF ie symmetric key $$M=KDF(m)$$. The Ciphertext $$C = m^e (mod \ n)$$ This is transmitted from Bob to Alice, and she can decrypt it by computing $$P = m^d (mod \ n)$$ Alice now has $$k$$, and derives the symmetric key $$M$$ with $$M = KDF(m)$$

Side note: I've seen that you tagged post quantum cryptography, so you could use NTRU for KEM; ECC and RSA can be broken with a powerful enough quantum computer running Shor's algorithm. The NTRU KEM works differently to the RSA KEM however. I'm not familiar with a quantum safe version of the ECC key exchange, though I'm sure one exists.

• Updated the RSA-KEM – SamG101 Jan 23 '20 at 10:36
• Could the downvoter explain the reason here? – kelalaka Jan 23 '20 at 22:38

There is issue in key encapsulation when you say "Bob generates his own secret key and encrypts it using Alice's public key. He sends the result to Alice."

This is encryption not encapsulation. In key encapsulation algorithm, the secret key to be shared by Bob is produced as an output of the “encapsulation” algorithm, which is run on the Alice public key alone. This works as follows:

The input of encapsulation algorithm is the Alice public key and output generated by the encapsulation algorithm on Bob side is the ciphertext c and secret key k. Now, Bob will send ciphertext c to Alice and Alice will decapsulate it with its private key to recover the secret key k.

For more concept clarity see the peikert's KEM and its more clear version by Vikram using lattice based cryptography in post-quantum cryptography. ).


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### Weakening Assumptions for Deterministic Subexponential Time Non-Singular Matrix Completion

Maurice Jansen
Kabanets and Impagliazzo \cite{KaIm04} show how to decide the circuit polynomial identity testing problem (CPIT) in deterministic subexponential time, assuming hardness of some explicit multilinear polynomial family $\{f_m\}_{m \geq 1}$ for arithmetic circuits. In this paper, a special case of CPIT is considered, namely non-singular matrix completion ($\NSMC$) under a low-individual-degree promise. For this subclass of problems it is shown how to obtain the same deterministic time bound, using a weaker assumption in terms of...
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# Homework Help: Velocity From Electric Potential

1. Jul 19, 2016

### PurelyPhysical

1. The problem statement, all variables and given/known data

http://imgur.com/UsKsaOn

2. Relevant equations

Why is the answer in joules multiplied by 2/3 and 1/2? I can follow the rest of the problem.

3. The attempt at a solution

I get the same solution as my teacher if I use the constants 2/3 and 1/2. I just don't understand where they are coming from.

2. Jul 19, 2016

### Divya Shyam Singh

I would want to correct the information you have given by looking at the solved equation.
The ratio of distribution of engergy for particle 1 and particle 2 is 2:1
So the energy of particle 1 will be: 2/(2+1)= 2/3 times the total energy
Energy of particle 2: 1/(1+2)= 1/3 times the total energy.
This "total energy" is basically the change in the electric potential as the particles move from being 0.1m apart to 0.2m apart.

3. Jul 19, 2016

### PurelyPhysical

Thank you very much! This clears it up for me. It never occurred to me to look at ratios that way. Is there a name for what this particular concept is in math?

4. Jul 19, 2016

### Divya Shyam Singh

Ummm....not really. It is generally covered in the topic of ratios and proportions.
I will explain a bit more here for you to have a better understanding:
Suppose a line segment of length A units is to be divided into a ratio of x:y
Then the length of each unit can be calculated as:
Ax/(x+y)
Similarly, the length of the other part will be:
Ay/(x+y)

To check we can easily see that the sum of each of the part of the line segment should be equal to the total length of the line segment.
so
Ax/(x+y) + Ay(x+y)= A

Hope it helped!

5. Jul 20, 2016

### collinsmark

The energy ratios can be calculated by invoking conservation of momentum.

The total momentum of the system starts out as 0 and ends as 0.

$m_1 \vec {v_1} + m_2 \vec {v_2} = 0.$

Placing the particles on a line and noting that they move in opposite directions, we can get rid of the vector notation.

$m_1 v_1 - m_2 v_2 = 0.$ [Edit: I'm just using the magnitudes of the velocities in this equation. If you'd rather allow negative velocities to indicate direction, then use $m_1 v_1 + m_2 v_2 = 0.$ That's arguably the better approach anyway.]

Substituting $m_2 = 2m_1$ you can calculate a simple relationship between $v_1$ and $v_2$ (you can do that for yourself ).

Note that the energy for each particle is

$E_1 = \frac{1}{2}m_1 v_1^2,$

$E_2 = \frac{1}{2}m_2 v_2^2,$

And the total energy is,

$E_T = E_1 + E_2,$

if you make the appropriate substitutions, you'll find the energy ratios are 2/3 and 1/3 of the total.

6. Aug 7, 2016

### PurelyPhysical

This does help, thank you very much :D