text:
# Is ionization a reversible process?

Are photoionization from ground and recombination to ground consider a reversible processes in the thermodynamic sense?

Ignoring any quantum broadening effects, consider a closed system of one Hydrogen and one ionizing photon. The photon could ionize the atom, which would later recombine emitting the same energy photon that was absorbed. This seems to be a cycle that ends in the same state, therefore I'm guessing each ionization and recombination must be reversible processes.

Now recombinations do not always end up in the ground state. Then the recombination to a different level other than ground would lead to a cascade that would result in at a minimum of two photons, with at most only one of ionizing energy. Given enough time and repetition of recombining to a state other than ground there will eventually be no ionizing photon.

Since photons have zero chemical potential, this doesn't necessarily mean the system is in a different state does it? Just interestingly the system can no longer perform this process.

If this single atom case is reversible, are the same processes in a system of multiple atoms and photons reversible? This seems different since now the atoms can thermalize amongst each other. Imagine the gas is initially at a lower temperature than the photon gas, then given enough time the two gases will equilibrate. As before eventually there will be no more ionizing photons and you could not reverse the gas back to its original state of being colder than the photon gas. It seems the gas is then in a state which cannot be taken back to it's initial state.

If the system is both the photon and gas is this necessarily a different state? Did I pull a slight of hand, and the problem with this scenario is that the collisions were the irreversible process, not the ionization and recombinations themselves?

• The reverse process can occur exactly how it happened in the forward direction: if your atom emitted one photon, then another, it may absorb the second and then the first photon and end up in the original state. Aug 15 '17 at 6:09
• Following your argumentation I would call it an irreversible process. Interaction with the EM field leads to increase of entropy because of the vast amount of degrees of freedom (continuous energy spectrum) in the EM field. In fact my understanding is that the pointlike interaction with the EM field causes any fermion field-configuration (e.g. plane wave) to decohere into pointlike particles unless you have only a single particle + EM field which would be protected from decoherence by momentum conservation. Aug 15 '17 at 6:21

I think your question is somewhat ill defined, and you need to understand that the word process has different meanings in different contexts. The thermodynamic process implies some interaction between two systems, while in unitary, Schrödinger equation like dynamics, it usually mean transitions between states as considered when drawing Feynman diagrams.

If you're considering a closed system as you describe at the beginning of your question you must consider to photon bath as part of your closed system which is a bit unnatural in my eyes.

## Closed System Approach

None the less, in such a case, indeed after enough time (which is usually termed the recurrence time if I'm not mistaken), a photon will be emitted and the system will return to its original state. However I wouldn't call it a thermodynamic process. This is just unitary evolution according to Schrödinger equation. Since these dynamics are Hamiltonian they're inherently energy conserving which may look to you like reversibility. However the notion of reversibility is meaningless as there are no baths which interact in any way, and there are no thermodynamics.

## Open System Approach

If on the other hand you consider an open system, i.e. you think of your atom as a system which is coupled to a thermal (photon) bath, then you may indeed think of the resulting thermodynamics.

First, note that dynamics with open systems which have infinite degrees of freedom such as a photon bath induce dissipation. This is relevant though it doesn't answer your question plainly.

Second, in such a case processes of emission and absorption induce energy (and momentum) transfer between the two systems. This thermodynamic process however isn't reversible. Perhaps the easiest way to see this is by looking at the detail-balance relation which implies that the ratio of emission and absorption rates must be: $$\frac{\Gamma_{abs}}{\Gamma_{em}}=e^{-\beta\epsilon}$$ where $\beta$ is the inverse temperature of the thermal bath, and $\epsilon$ is the ionization energy.

• Yes sorry, completely my mistake I should have said an open system. Since the process convincingly doesn't seem to be reversible is there any hope in using $\textrm{d} h = \delta q + \frac{\textrm{d}p}{\rho}$ in a fluid that is experiencing external heating from photoionization. The idea is that $\delta q$ contains the heating and cooling introduced by the ionization and recombination. Could we still imagine that the pdV work of the gas is reversible, so then $dh = \delta q + \delta w + pdV +Vdp =\delta q + Vdp$? Or would this heating make the any otherwise quasistatic process not quasistatic? Aug 15 '17 at 7:29
• You're using notation which usually reserved to big bulk systems which operate out of equilibrium but in steady state. These quantities don't always translate to the language microscopic systems (atoms) so naturally, and things must be done carefully. I'm no expert on the matter so I don't want to make wrong claims. However the following can be said: the absorption and emission processes create entropy and are therefore not reversible. The steady state regime however allows for some relations such as you proposed at least on a macroscopic scale, regarding the mice-scopic scale I don't know. Aug 15 '17 at 7:37


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# Will current usage increase with different length of wire? [closed]

Given all other factors are same, with only the wire length increased (for example, 0.5meter increase to 50 meters,) will the current consumption/usage increase as well? Can anyone explain?

• You need to show a circuit and point out what the wire is that you are talking about. Nov 5 '19 at 12:53
• Do you know Ohm's Law? Nov 5 '19 at 12:54
• the wire size is exactly the same, just the length is different, as indicated, from 0.5meter to 50meters. Nov 5 '19 at 13:01
• ohm's law, do you mean v=ir ? Nov 5 '19 at 13:01
• Voltage drop, the voltage will be lower at the end of the cable because of resistance. Nov 5 '19 at 13:12

Given all other factors are same, with only the wire length increased (for example, 0.5 meter increase to 50 meters,) will the current consumption/usage increase as well?

Generally there are two types of load to consider.

This includes things like lightbulbs, heaters and motors whose current draw varies with voltage. As the voltage drops the current will fall too. Adding extra cable will cause a voltage drop at the load so the current drawn will fall.

This includes things like computer / TV power supplies, motor speed controllers, LED lighting PSUs, etc. These differ in that they regulate the output they provide and when the voltage decreases they increase the current draw from the mains to provide the required output power. Adding extra cable will cause a voltage drop at the load so the current drawn will increase.

• just three light bulbs currently as loads, with distance of 50meters, the 12v battery voltage drop faster in comparison to short distance, 0.5meter. But this is just visual reading on daily basis though. comment and/or thoughts? Nov 5 '19 at 13:20
• Get all your numbers: (1) Work out the current from the bulb wattage (P = VI). (2) Work out the cable resistance from the wire gauge and length. Don't forget to include the return leg. There are many online calculators for metric and AWG. (3) Calculate the voltage drop on the cable from Ohm's Law (V = IR). I have no idea what "this is just visual reading on daily basis" means. Nov 5 '19 at 13:25
• visual reading as in read the voltage drop periodically by measuring the 12v battery using multimeter Nov 5 '19 at 13:27

Anything is possible, depending on the type of load: current may decrease, increase or stay the same.
Let $$\R_{line}\$$ be the resistance of the line which increases with length; here are examples for each case:

• If the load is a constant resistance load (e.g. a good resistor) or a constant voltage load (e.g. Z-diode in reverse direction or a LED in forward direction (both idealized)) current will decrease if resistance in line increases: $$\I=\frac{V}{R_{load}+R_{line}}\$$ or $$\I=\frac{V-V_{diode}}{R_{line}}\$$

• If the load is a constant power load, e.g. a DC/DC converter with constant load or a SMPS for a laptop computer that provides constant power over a voltage range (assuming effciency will stay about the same), current will increase if resistance in line increases (of course only to a certain extend until minimum operating voltage at load is reached):
$$\I=\frac{P}{V-V_{line\_drop}}=\frac{P}{V-IR_{line}}\$$

• If the load is a constant current supply, e.g. for a LED array, of course current will stay the same if the line resistance increases (of course only to a certain extend until minimum operating voltage at load is reached):
$$\I=I_{const}\$$

• thank you for valuable inputs. Nov 6 '19 at 12:30

The resistance of any conductor is given by the formula: R=rho*(L/A).

Rho is the property of the material. L is the length of the conductor and A is the cross sectional area of the conductor. If everything is kept constant here, increasing the length would increase the resistance of the wire.

Increased resistance means decrease in current flow. Ohm's Law!!

• Please let me know what's wrong with this answer. Nov 5 '19 at 13:10
• downvote was not from me. Nov 5 '19 at 13:11

Current flow will decrease. Wire has resistance. The longer the wire, the higher the resistance, the less current will flow.

If you connect a load right at the battery and measure the voltage at the load then the voltage will drop very little.

If you connect the load to the battery with very long wires and measure the voltage at the load, then you will measure a lower voltage.

If you simultaneously measure the voltage at the load and at the battery, then you will find the voltage at the battery to be higher than at the load. This is due to the resistance of the wires.

• What if the wire is part of a 4-20mA control loop? What if it is connected to a constant current source for LEDs? What if it carries a 100MHz signal? Nov 5 '19 at 13:10
• @JRE , thanks for your concise response. With the load further away (in this example 50meters length of wire), it seem the 12v battery voltage drop faster in comparison with short distance wire, 0.5meter. But this is just a feeling and reading on daily basis. Nov 5 '19 at 13:17
• @ElliotAlderson: Given the basic level of the question, I didn't think it appropriate to muddy the waters with concepts the OP probably hasn't encountered yet. If you feel that those cases need to be addressed, then you are welcome to post your own answer and expand on the concepts you've mentioned.
– JRE
Nov 5 '19 at 13:22
• Given the basic level of the question, I think it's vital that you make it clear what assumptions you have made. Nov 5 '19 at 13:24
• The person asking the question isn't in a position to understand those assumptions.
– JRE
Nov 5 '19 at 13:27

$$R_F = \frac {\rho \ell} {A}$$

Resistance of feeder will increase as length increases. $$\R_F\ \alpha\ \ell\$$

Regardless of the circuit (AC/DC, 3-phase, single-phase), material and wire size, voltage at the load will be less than the supply voltage (Basic KVL where load and feeder form a series circuit).

If a constant power load is connected to your increasing length load, resistance/impedance increases, current increases because voltage drop to feeder increases.

Impact depends on relationship between feeder resistance and load. In a lab, a short feeder is irrelevant when powering a 1kΩ. But if the feeder is not sized correctly (cross-sectional area), say supplying a 10hp motor at 250ft, the load may be affected to an extent that the load does not operate correctly. Too much voltage is lost to the feeder. Motor may start at no-load, but fail under load.

• thank you for valuable inputs. Nov 6 '19 at 12:31

A longer wire has a proportionally larger resistance, so the current usage will not increase. Rather would it decrease as the total load increases, but for most circuits the resistance of the connected wire is negligible compared to the "load" itself so that you won't see any change in power consumption or drawn current.

• "as the total load increases" - why would the load increase? Nov 5 '19 at 13:08
• If you consider the wire as part of the supplies load Nov 5 '19 at 13:09
• What if the wire is part of a 4-20mA control loop? What if it is connected to a constant current source for LEDs? What if it carries a 100MHz signal? Nov 5 '19 at 13:10
• I see you're going for some edge cases here. I was assuming by "given all factors are the same" the author was talking about a normal voltage supplied circuit and not a 4-20mA control loop or a constant current source where the name already implies that the current would be constant. I think this anwer is appropirate enough for this question but you're free to give your own. Nov 5 '19 at 13:14
• @ElliotAlderson nothing fancy, just three lightbulbs as the loads and am new to electrical, would be glad to read response and learn knowledge from various people. Nov 5 '19 at 13:22

format: plain


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# Differential Equation MCQs 01

Differential Equation MCQs 01 consist of most repeated questions of all kinds of tests of mathematics. Prepare them to get 100%  marks in this subject.

Differential Equation MCQs

1. A general solution of 4th order DE contains__________ constants.

2. A general solution of nth order differential Equation contains_____ arbitrary constants

3. The order of DE of ellipse whose major and minor axis are along x-axis and y-axis respectively is

4. A primitive of ODE is

5. Solving  X” + 6X’ +9X = 0 with X(0) = 2 and X'(0)=0 is

6. A homogeneous DE always

7. Differential Equation of 1st degree

8. The differential Equation $\dpi{120}&space;\small&space;y''+y-e^y=0$ is

9. Infinitely many DE’s have same integrating factor.  The statement is

10. A particular solution of nth order differential Equation contains_____ arbitrary constants

11. The order of DE of family of circles touching a fixed straight line passing through origin is

12. The family of curves represented by DE xdx + ydy = 0 is that of

13. The degree of DE of all tangent lines to parabola $\dpi{120}&space;\small&space;y^2=4ax$ is

14. If n is the degree of given DE then

15. The differential Equation $\dpi{120}&space;\small&space;y'+y=xy^3$ may be called as linear equation of

16. A general solution of 3rd order differential Equation contains________ constants

17. The function obtained after solving a DE is known as____

choose the odd are out.

18. For solving y” – y’ + 2y =0 with y(0)=0 , y(1)=0 is

## 2 Replies to “Differential Equation MCQs 01”

1. Cymon joshi says:

it is more helpful. Thank you so much.

2. Umar farooq says:

Very informative and loving one i like it


text:
## Solve Lesson 83 Page 99 Math 10 – Kite >

Topic

In the coordinate plane Oxygenfor triangle ABC yes A(−1 ; −2), median line drawn from REMOVE and the high line drawn from OLD whose equation is 5 . respectivelyx + y – 9 = 0 and x + 3y − 5 = 0. Find coordinates of two points REMOVE and OLD.

Step 1: Write the equation of the straight line AB (where VTPT is VTCP of ONLY)

Step 2: Solve the system 2 PT BM and AB to find point coordinates REMOVE

Step 3: Parameterize the point USA according to PT BM and coordinate representation OLD according to that parameter

Step 4: Replace the parameter coordinates of the point OLD go to PT CH and find the coordinates of the point OLD

Detailed explanation

Call BM is the median line drawn from REMOVE $$\Rightarrow BM$$ has PT: 5x + y – 9 = 0

Call ONLY is the height line drawn from OLD $$\Rightarrow CH$$ with PT: x + 3y − 5 = 0

CH has VTPT $$\overrightarrow {{n_1}} = (1;3)$$ $$\Rightarrow CH$$ has VTCP $$\overrightarrow {{u_1}} = (3; – 1)$$

We have: $$CH \bot AB$$ $$\Rightarrow AB$$ goes through A(−1 ; −2) and get $$\overrightarrow {{u_1}} = (3; – 1)$$ as VTPT, so there is PT:

3xy + 1 = 0

Do REMOVE is the intersection of BM and AB so point coordinates REMOVE is the solution of the system PT:

$$\left\{ \begin{array}{l}5x + y – 9 = 0\\3x – y + 1 = 0\end{array} \right \Leftrightarrow \left\{ \begin{array}{ l}x = 1\\y = 4\end{array} \right \Rightarrow B(1;4)$$

Since $$M \in BM$$ so $$M(t;9 – 5t)$$

According to the assumption, USA is the midpoint AC $$\Rightarrow C(2t + 1; – 10t + 20)$$

Since $$C \in CH$$ so $$2t + 1 + 3( – 10t + 20) – 5 = 0 \Leftrightarrow – 28t + 56 = 0 \Leftrightarrow t = 2$$ $$\Leftrightarrow C(5; 0)$$

So $$B(1;4)$$ and $$C(5;0)$$


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## Slice sampling algorithm

A single transition $(x,u) \rightarrow (x’,u’)$ of a one-dimensional slice sampling algorithm has the following steps.

(1). evaluate $P^* (x)$

(2). draw a vertical coordinate $u’ \sim$ Uniform$(0,P^* (x))$

(3). create a horizontal interval $(x_l, x_r)$ enclosing $x$

3a. draw $r \sim$ Uniform$(0,1)$

3b. $x_l := x-rw$

3c. $x_r := x+(1-r)w$

3d. while $(P^* (x_l) > u’)$ ${x_l := x-rw}$

3e. while $(P^* (x_r) > u’)$ ${x_r:= x+w}$

(4). loop {

(5).     draw $x’ \sim$ Uniform$(x_l,x_r)$

(6).     evaluate $P^*(x’)$

(7).     if $P^*(x’) >u’$ break out of loop 4-9

(8).     else modify the interval $(x_l,x_r)$

8a.     if $(x’ > x){x_r:=x’}$

8b.     else ${x_l:=x’}$

(9). }

I find the following exercise is quite simple and very good to understand how the slice sampling algorithm works. This is the exercise 29.10 of the book Information Theory, Inference, and Learning Algorithms of David Mackay.

## Exercise 29.10

### Question

Investigate the properties of slice sampling applied to the density function $P^* (x)$.

$$P^* (x)= \{ \begin{array}{cc} 10 ~~~~~~as ~0\leq x<1\\ ~~0 ~~~~~~as ~1\leq x \leq 11 \end{array}$$

$x$ is a real variable between 0.0 and 11.0. How long does it take typically for slice sampling to get from an $x$ in the peak region $x \in (0,~ 1)$ to an $x$ in the tail region $x \in (1,~11)$, and vice versa? Confirm that the probabilities of these transitions do yield an asymptotic probability density that is correct.

### Solution

import numpy as np
import matplotlib.pyplot as plt
import random
import timeit

Let us see how the target probability distribution looks like.

# probability density

def Prob(x):
if x < 0:
return 0
elif x < 1:
return 10
elif x <11 :
return 1
else :
return 0

# probability density plot

x = np.arange(-2.0, 13.0, 0.1)
P=[Prob(t) for t in x]
y = np.array(P)
plt.plot(x, y)
plt.show()

Give the initial sample between $x_0 = 0$ and $1$, and decide the size of the step. It should be not too big nor too small. I chose it 0.5.

x0 = random.random()

# decide the size of the step. Not too small, not too big.
w = 0.5

The following is the main part of the slice sampling. Compare with the above algorithm.

r = random.random()
u = Prob(x0)*random.random()

xl = x0 - r * w

while Prob(xl) > u:
xl = xl - w

xr = x0 + (1-r)*w

while Prob(xr) > u:
xr = xr + w

Put them together for the step of the process.

def process(x0, w):

# decide the size of the step. Not too small, not too big.
w = 0.5

u = Prob(x0)*random.random()

cond = True
r = random.random()
xl = x0-r*w
xr = x0 + (1-r)*w

while cond:
while Prob(xl) > u:
xl = xl - w

while Prob(xr) > u:
xr = xr + w

x1= random.uniform(xl,xr)

if Prob(x1) > u :
cond = False
else :
if x1>x0:
xr = x1
else:
xl=x1
return x1

Use the process method, I want to find the number of turns the sample comes out from the range, (0,1) to out of the range.

def numofturns(x0, w):
turn = 0
while x0 < 1:
turn = turn + 1
x0 = process(x0, 0.5)

return turn

list =[]
for i in range(10000):
list = list+ [numofturns(random.random(),0.5)]

plt.plot(list)
plt.show()

np.average(list)

10.9325

It takes around 11 truns.

Then, how about opposite? From out of the range to inside of the range, (0,1).

def numofturns2(x0, w):
turn = 0
while x0 > 1:
turn = turn + 1
x0 = process(x0, 0.5)

return turn

list2 =[]
for i in range(10000):
list2 = list2 + [numofturns2(random.uniform(1,11),0.5)]

plt.plot(list2)
plt.show()

np.average(list2)

11.1015

It takes about 11 turns as well. The difference is about 1.5 percentages. When you calculate the areas of the plot below (0,1 ), and out of the range. They match. It supports our analysis that it takes the same time for the samples to go in or out of the range, (0,1).


text:
# [pdftex] migrating to pdfTeX, possible problems

Ulrich Dirr ud at art-satz.de
Thu Mar 8 14:17:56 CET 2001

Hi.

I would like to use pdfTeX for a special project (chess book) I'm
currently working on. I'm wondering if it's possible to get everything
with pdf(La)TeX what I've got so far the traditional way via LaTeX2e.

e.g.

(i)
\def\WB{{\DiagramFont
\ifblackfield\special{color push cmyk 0 0 0 0.3}%
z\special{color pop}P\else P\fi}}

this kind of definition is used several times in the style file to
achieve coloring (\textcolor didn't work here). This way I can see the
color with a DVI viewer. And the color is getting into the postscript
file, too -- which is later necessary for color separation.

How can I achieve this with pdfTeX? (pdftricks? low level pdf
operators?)

(ii)
several packages are loaded. Do you know any not working with pdfTeX
(or needs special configuration)?

\usepackage{type1cm}
\usepackage{pstcol,pst-plot} % pstcol loads pstricks and color

see below (iv) on pstricks; color package useable?

\usepackage[dvipsone]{graphicx}
\graphicspath{{bilder/}}
\usepackage{calc}
\usepackage{ifthen}
\usepackage{fancyhdr}
\usepackage[LY1]{fontenc}
\usepackage{JensonMM}
\usepackage{multicol}
\usepackage[cam,a4center,axes]{crop}
\usepackage{array}
\usepackage{colortbl}
\usepackage{lettrine}
\usepackage{endnotes}

(iii)
is there anything to care of concerning LaTeX page layout commands?
(e.g. offsets)

(iv)
I know PSTricks is not working (in PDF mode). But how can I get, e.g.
the baseline grid (for proofs):

[...]
{\psset{xunit=1mm,yunit=1dd}
\multido{\r=519.7+-13,\i=1+1}{41}{%
\rput[Br](86.576,\r){%
\color{graythirty}\line(1,0){165}\color{black}}}
\multido{\n=494+-13,\i=1+1}{37}{%
\rput[Br](90.576,\n){\tiny\i}}}

(v)
where can I find up-to-date documentation? I think Mr Rahtz' book is
one year old ... (second edition planned?)

Of course it would be very nice if everything would work in both
output modes. It is intended to produce a PDF version afterwards with
hypertext links and all that stuff for a CD version, so ...

Thank you very much in advance for any help. And thank you for all

Regards,
Ulrich Dirr

--
Art & Satz
Ulrich Dirr
Arnimstraße 9
81369 München
Germany/Deutschland
--
fon (+49 89) 743 30 60
fax (+49 89) 743 30 61
email ud at art-satz.de
--
-=*:-)


text:
# Most Distant Point from the Sea

Time Limit: 5000MS

Memory Limit: 65536K

## Description

The main land of Japan called Honshu is an island surrounded by the sea. In such an island, it is natural to ask a question: “Where is the most distant point from the sea?” The answer to this question for Honshu was found in 1996. The most distant point is located in former Usuda Town, Nagano Prefecture, whose distance from the sea is 114.86 km.In this problem, you are asked to write a program which, given a map of an island, finds the most distant point from the sea in the island, and reports its distance from the sea. In order to simplify the problem, we only consider maps representable by convex polygons.

## Input

The input consists of multiple datasets. Each dataset represents a map of an island, which is a convex polygon. The format of a dataset is as follows.
 n x1 y1 ⋮ xn yn

## Output

For each dataset in the input, one line containing the distance of the most distant point from the sea should be output. An output line should not contain extra characters such as spaces. The answer should not have an error greater than 0.00001 (10−5). You may output any number of digits after the decimal point, provided that the above accuracy condition is satisfied.

## Sample Input

4
0 0
10000 0
10000 10000
0 10000
3
0 0
10000 0
7000 1000
6
0 40
100 20
250 40
250 70
100 90
0 70
3
0 0
10000 10000
5000 5001
0

## Sample Output

5000.000000
494.233641
34.542948
0.353553

Japan 2007


text:
MORE IN Basic Electronics
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1(a) Explain the operation junction diode under forward and reverse bias condition.
6 M
1(b) For zener regulator shown in the Fig.Q.(b), calculate the range of input voltage for which output will remain constant. !mage
4 M
1(c) Skctch the transistor input and output characteristics of CE configuration and briefly explain the three region of operation.
6 M

2(a) With circuit digram, explain the operations of center-tapped full wave rectifier. Draw input and output waveforms.
6 M
2(b) Explain how zener diode can be used as voltage regulator.
5 M
2(c) Derive the relationship between α and β.Find the values of β, α and IE for transistor has IB =100 μA and IC=2mA.
5 M

3(a) With neat circuit digram, explain the operation of voltage divider bias circuit with necessary equations.
6 M
3(b) Draw the circuit of op-amp integrator.Derive the expression for output voltage.
6 M
3(c) Calculate the o/p voltage of a three input inverting summing amplifier , given R1=200KΩ,R2=250KΩ,R3=500KΩ,Rf=1MΩ,V1=-2V,V2=-1V and V3=+3V.
4 M

4(a) For the circuit shown in Fig.Q.4(a) find the Q-point values and draw DC-load line , where VBE=0.7V and β=50.
6 M
4(b) Draw the circuit of non-inverting op-amp. Derive the expression for the voltage gain.
5 M
4(c) Define the following terms with respect to op-amp: i)slew, ii)CMRR, iii)PSRR.
5 M

5(a) Convert:
i)(526.44)8=(?)2=(?)10.
ii)(48350)10=(?)16=(?)8.
4 M
5(b) Subtract the following using 2's complement method; (i) 1010112from1110012 (ii) 1110012from1010112
4 M
5(c) Simplify the following expression and realize using basic gates
$Y=A(\overline{ABC}+A\overline{B}C)$
4 M
5(d) Realize half adder using NAND gates only.
4 M

6(a) Convert:
i)(342.56)10=(?)2=(?)8.
ii)(BCDE)=(?)2=(?)8.
4 M
6(b) Perform the subtraction i)(11010)2-(10000)2 using 1's complement.
ii)(1000100)2-(1010100)2using 2's complement.
4 M
6(c) State and prove DeMorgan's theorems.
4 M
6(d) Write the symbol, truth table and final expression for NAND and Ex-OR gate (For two I/PS).
4 M

7(a) With diagram and truth table explain NAND gate latch.
5 M
7(b) With diagram and truth table explain clocked R-S flip-flop
5 M
7(c) Explain the architecture of 8051 microcontroller.
6 M

8(a) What is flip-flop? Explain the operation of NOR gate latch using its truth table .
8 M
8(b) With block diagram, explain microcontroller based stepper motor control system.
8 M

9(a) With the help of block diagram, explain communication system.
6 M
9(b) With circuit diagram explain the process of AM demodulation.
5 M
9(c) Explain the principle of operation of piezoelectric transducer.
5 M

10(a) Why modulation is necessary in communication system? List the different types of modulation schemes.
5 M
10(b) A carrier 1MHz with 400 W of its power is amplitude modulated with a sinusoidal signal 0f 2500Hz. The depth of modulation is 75%.Calculate the sideband frequencies, the band width,the power in the side bands and the total power in the modulated wave.
5 M
10(c) Explain the construction and the principle of operation of LVDT.
6 M

More question papers from Basic Electronics


text:
What is the pK2 value for phthalic acid?

Well $p {K}_{a 2}$ will be more than $p {K}_{a 1}$, but you are going to have to go digging on the interwebs.
Why should $p {K}_{a 2}$ be greater than $p {K}_{a 1}$?


text:
Spectral sequence for cohomology of open subset - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T10:34:16Z http://mathoverflow.net/feeds/question/48221 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/48221/spectral-sequence-for-cohomology-of-open-subset Spectral sequence for cohomology of open subset Vladimir Baranovsky 2010-12-03T21:57:59Z 2010-12-03T21:57:59Z
Let $X$ be a smooth compact orientable manifold (or variety) and let $j: U \subset X$ be the complement to a union $\bigcup_{i \in I} X_i$ of smooth compact orientable manifolds. Suppose that $A$ is a sheaf on $X$ - say, the locally constant sheaf $Z$ (although the question below can be asked for coherent sheaves too). Let $Z_U$ be $j_!j^* Z$, i.e. the locally constant sheaf on $U$ extended by zero to $X$. The usual set theoretic inclusion-exclusion formula leads to a long exact sequence of sheaves $0 \to Z_U \to Z \to \oplus Z_{X_i} \to \oplus Z_{X_i \cap X_j} \to \ldots$ where for a closed subset $f: W \subset X$ one sets $Z_W = f_* f^* Z$.

This leads to a spectral sequence with first page given by cohomology of finite intersections $X_{i_1} \cap \ldots \cap X_{i_s}$, and the differential is induced by the combinatorial inclusion-exclusion formula.

Are there any examples when the differential of $E_2$ is non zero and known explicitly (which means that we also know the E_2 terms)? Maybe something in terms of excess intersection bundles for intersections of $X_i$, some Gysin maps, etc/?


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The streamz.dask module contains a Dask-powered implementation of the core Stream object. This is a drop-in implementation, but uses Dask for execution and so can scale to a multicore machine or a distributed cluster.

## Quickstart¶

### Installation¶

conda install dask
or

You may also want to install Bokeh for web diagnostics:

conda install -c bokeh bokeh
or

Then start a local Dask cluster

from dask.distributed import Client
client = Client()

This operates on a local processes or threads. If you have Bokeh installed then this will also start a diagnostics web server at http://localhost:8787/status which you may want to open to get a real-time view of execution.

### Sequential Execution¶

 Stream.emit(x[, asynchronous]) Push data into the stream at this point map(upstream, func, *args, **kwargs) Apply a function to every element in the stream sink(upstream, func, *args, **kwargs) Apply a function on every element

Before we build a parallel stream, lets build a sequential stream that maps a simple function across data, and then prints those results. We use the core Stream object.

from time import sleep

def inc(x):
sleep(1)  # simulate actual work
return x + 1

from streamz import Stream

source = Stream()
source.map(inc).sink(print)

for i in range(10):
source.emit(i)

This should take ten seconds we call the inc function ten times sequentially.

### Parallel Execution¶

 scatter(*args, **kwargs) Convert local stream to Dask Stream buffer(upstream, n, **kwargs) Allow results to pile up at this point in the stream
 gather([upstream, upstreams, stream_name, …]) Wait on and gather results from DaskStream to local Stream

That example ran sequentially under normal execution, now we use .scatter() to convert our stream into a DaskStream and .gather() to convert back.

source = Stream()
source.scatter().map(inc).buffer(8).gather().sink(print)

for i in range(10):
source.emit(i)

You may want to look at http://localhost:8787/status during execution to get a sense of the parallel execution.

This should have run much more quickly depending on how many cores you have on your machine. We added a few extra nodes to our stream, lets look at what they did.

• scatter: Converted our Stream into a DaskStream. The elements that we emitted into our source were sent to the Dask client, and the subsequent map call used that client’s cores to perform the computations.
• gather: Converted our DaskStream back into a Stream, pulling data on our Dask client back to our local stream
• buffer(5): Normally gather would exert back pressure so that the source would not accept new data until results finished and were pulled back to the local stream. This back-pressure would limit parallelism. To counter-act this we add a buffer of size eight to allow eight unfinished futures to build up in the pipeline before we start to apply back-pressure to source.emit.


text:
[–] 3 points4 points  (1 child)

sorry, this has been archived and can no longer be voted on

If you just want to convert your Markdown to LaTeX, you can try pandoc.

If you want to put latex equations inside Markdown then this stackoverflow question might have some tips.

[–] 0 points1 point  (0 children)

sorry, this has been archived and can no longer be voted on

And here's how to that using ConTeXt.

[–] 2 points3 points  (4 children)

sorry, this has been archived and can no longer be voted on

I'd love to have something kinda like this:

\documentclass{article}

\usepackage{markdown}

\title{I want this to work.}
\author{Joshua Holbrook}
\date{\today}

\begin{document}
\maketitle
\begin{markdown}

# First Section

Some stuff.

* Some
* more
* stuff.

\end{markdown}
\end{document}

You should be able to make this work in theory with write18 and pandoc. If I ever get the time to implement this I'm basically going to use minted as a reference, which uses a similar technique to do syntax hilighting with pygments.

[–] 0 points1 point  (2 children)

sorry, this has been archived and can no longer be voted on

Is that really all that much easier than just \begin{enumerate}, etc.?

[–] 0 points1 point  (1 child)

sorry, this has been archived and can no longer be voted on

When you're taking notes in class, it is.

[–] 0 points1 point  (0 children)

sorry, this has been archived and can no longer be voted on

If you're on Emacs, try org-mode and then export to LaTeX. You'll probably get benefits from using org-mode over markdown in any case.

[–][S] 0 points1 point  (0 children)

sorry, this has been archived and can no longer be voted on

I posted the same question on tex.stackoverflow, it is very possible. Here is the link. Apparently it is technically possible to do in pure latex, but you be insane to try it. There are two realistic techniques:

• One would be to (at every markdown environment) write it to a file (using verbatim to make sure that is contents were treated as macros) and then call an external program to convert it and then include the output of that (wow)
• The other is to use lualatex, which is an extension of pdflatex, which interprets inline lua code, then executes it as a preprocessor for the latex. There are a few lua implementations of markdown parsers.

Someone has done most of the leg work in the stackoverflow forum for the first method. I will try it at some point and maybe write an article on how to do it. I could message you a link to that when that's done, if you were interested?

[–] 2 points3 points  (2 children)

sorry, this has been archived and can no longer be voted on

Hey, check out my plugin for Markdown that allows you to jump into various LaTeX friendly modes within Markdown.

https://github.com/justinvh/Markdown-LaTeX

The plugin generates inline base64-encoded images, so there are no external dependencies and you can distribute the resulting pages wherever your like. There is a very small, but stupid caching mechanism in place as well.

[–][S] 0 points1 point  (1 child)

sorry, this has been archived and can no longer be voted on

Wow that looks really good. I'm using mdcharm in Ubuntu, is your plugin compatible with this?

[–] 0 points1 point  (0 children)

sorry, this has been archived and can no longer be voted on

Hm, I guess I should qualify it a bit more that this specific plugin is for the python markdown implemention, but the same principle applies really to any language as long as it supports subprocessing and you have some means of pre/post processing with the respective markdown implementation.

From the looks of it mdcharm does not support a plugin architecture, but apparently the developer plans to add support eventually.

[–] 1 point2 points  (0 children)

sorry, this has been archived and can no longer be voted on

Have you considered using Texts?


text:
# Time Traveller Maths

On a Wednesday afternoon, Marty McFly starts his DeLorean at 14:00 hours and travels 30 years in the past.

After spending 3 days 30 minutes, travels 60 years to the future where he stays for another 3 days and 30 minutes.

He sets his clock to 30 years in the past to 14:00 hours and safely makes it to the present.

Question : So what day of the week is it for him today and what is the total time Marty McFly was actually "away" Time Travelling?

Hint : No Tricks, simple straight forward maths. Will clear your time travel concepts. Disregard leap year, location, time zone changes.

• When you ask how long he spent time travelling, you don't mean how much time elapsed for him while travelling from the future to the past, but rather how much time has passed for him from when he left the present to when he returned? – GentlePurpleRain Oct 21 '15 at 17:32
• @GentlePurpleRain The "absolute" total time he spent travelling. – kanchirk Oct 21 '15 at 18:08
• There are many different possible interpretations for what you ask. Please can you clarify. Obviously if someone leaves the present and returns to the present then an observer who does not time travel will say the elapsed time is zero. The traveller will disappear and instantly reappear -- perhaps looking different. The whole thing is entirely subjective unless you define your terms very tightly and specifically. What is your frame of reference? – chasly from UK Oct 21 '15 at 18:26
• Does his machine account for leap years, or did he just set it to go back (365 * 30) days? Did he travel close to a daylight savings clock change date? What day of the week is it for him today? or the day he got back to the future? Why are you asking how long he spent time travelling when you've already specified Consider Zero seconds for Time Travel.? – CactusCake Oct 21 '15 at 18:44
• @JoeMalpass I wanted to mention that in the hint, disregard leap year and location (time zone) etc.. – kanchirk Oct 21 '15 at 18:49

The day of the week is:

Tuesday

Because:

If today is X and I go back in time Y years, then spend 3 days and go back to the future by Y years, then the day I end up at is X+3. It might be easier to comprehend if we think about it in only days. Let's say I start at day 10. I go back in time 5 days to day 5. I spend 1 day in the past so now I'm at day 6. Then I go 5 days back to the future and end up at day 11, which is 1 day from the present day I started at. Going through all the time travel Marty does, there is a total of 3+3=6 days passing, so he would end up 6 days from when he left, which is a Tuesday.

I'm not sure what you mean by how much time he spent time travelling so I'll give both interpretations:

The total time that passed for him was 6 days and 1 hour. Just simple addition of 3 days 30 minutes + 3 days 30 minutes.

and

The total time he was gone from the present is 6 days exactly. When he finally comes back to the present he goes back 30 years to the time 14:00. When he does this, he is a total of 30 years, 6 days, 1 hour from the time he originally left the present (as shown above). This means he is at a time of 15:00 (he left at 14:00, and is X days + 1 hour ahead) before he goes back to the present. By going back 30 years to 14:00, he actually goes back 30 years 1 hour. This results in his total time "gone" from the present at 6 days 1 hour - 1 hour = 6 days.

• You have nailed it, you got the day correct. The Total time spent away can be considered as "Travelling" time, so that should be enough. You may please edit the question in case it seems a bit ambigious. Am marking it as correct answer. – kanchirk Oct 21 '15 at 18:47
• It depends on the specific date you leave though. If you leave from a leap year, and the 6 days spent time traveling crosses the February/March boundary, you end up returning on Wednesday. Example: You leave on Wed. Feb 24, 2016. You arrive in the past on Mon. Feb 24 1986, spend 3 days, and leave Thur. Feb 27. You travel 60 years to the future, arriving on Tue. Feb 27, 2046. Another 3 days and you head home, departing on Fri. Mar 2. You arrive on Mar 2, 2016 - which is a Wednesday! – Irishpanda Oct 21 '15 at 19:10
• Presumably the same would happen if either the past or future year was a leap year and the 3 days spent in that year crossed the boundary. If the final day in the future happened to be Feb 29th, you may never arrive home at all! – Irishpanda Oct 21 '15 at 19:15
• Just saw the comment to ignore leap years. Ah well, never mind! – Irishpanda Oct 21 '15 at 19:20

You say, "Zero seconds for Time Travel."

You ask, "How long did he take Time Travelling?"


text:
# (Possibly Easy) Formal Language Question

I am looking at a "practice test" for a Theory of Computation class. It was a test in a previous year.

I am asked to prove that, given L1 and L2 are regular, the union and difference are both regular.

It seems to me that for the union, since all the members of each separate set are regular, and the union consists exactly of all those members, therefore the union is regular.

And since the difference (L1-L2) is just a subset of L1, it is also regular.

This seems awfully straightforward and skips a lot of process.

Is it correct or am I missing something?

• Let me add here -- I usually just see these two things (union and difference) asserted without proof. Also, proofs for this sort of thing (at least ones I've seen) normally involve taking finite state machines for each language and combining them. That's why the way I've done it, though it seems right, seems too simple. – RCM Oct 10 '16 at 12:21
• You seem to be invoking the theorem in your proof of the theorem here. – BlueRaja - Danny Pflughoeft Oct 10 '16 at 16:13
• en.wikipedia.org/wiki/Regular_language#Closure_properties - see the references/citations there for a potential source of proof for these facts. – D.W. Oct 10 '16 at 18:02

The reasoning you give is not formal enough. For the union case, you're just restating the theorem "the union of regular sets is regular since the union of regular sets is regular"; for the difference case, your assertion "a subset of a regular language is regular" is false ($\Sigma^*$ is regular and every language is a subset of $\Sigma^*$).


text:
# dimension of the special orthogonal group

Let $V$ be a $n$-dimensional real inner product space. The group of orthogonal operators on $V$ with positive determinant (i.e. the group of “rotations” on $V$) is called the special orthogonal group, denoted $SO(n)$.

The theorem on decomposing orthogonal operators as rotations and reflections (http://planetmath.org/DecompositionOfOrthogonalOperatorsAsRotationsAndReflections) suggests that all elements of $SO(n)$ are all fundamentally two-dimensional in some sense. This article is an elementary exploration of this aspect.

First observe that the set of orthogonal operators $O(n)$ is a manifold embedded in the real vector space $\mathrm{GL}(V)\simeq\mathbb{R}^{n\times n}$, defined by the condition $f(X)=XX^{*}-I=0$, where $X\in GL(V)$, and $X^{*}$ is the transpose of $X$ (represented as a matrix in orthonormal coordinates). $f(X)=0$ is simply shorthand for the condition that the columns of $X$ are orthonormal — we see there are $n+n(n-1)/2=n(n+1)/2$ scalar equations11$f(X)=0$ viewed as a matrix equation of course has $n^{2}$ scalar equations, but many of them are duplicated. For simplicity, we prefer to view $f$’s codomain to be the space of symmetric matrices, which is $n(n+1)/2$-dimensional. in $n^{2}$ variables. Then if we can show that the derivative $\operatorname{D}f(X)$ as full rank everywhere, then we will have established that $O(n)$ is a manifold of dimension $n(n-1)/2$. This is an easy computation if organized in the right way: for any $y\in\mathrm{GL}(V)$, by the product rule we have

 $\operatorname{D}f(X)\cdot Y=XY^{*}+YX^{*}\,.$

Consider first the case that $X=I$. Then $\operatorname{D}f(I)\cdot Y=0$ implies $Y^{*}=-Y$; in other words, $Y$ is skew-symmetric. But the skew-symmetric matrices have dimension $(n^{2}-n)/2$, so the kernel of $\operatorname{D}f(I)$ has this dimension. By the dimension theorem of linear algebra, the rank of $\operatorname{D}f(I)$ is $n^{2}-(n^{2}-n)/2=n(n+1)/2$, which is the full rank.

For general $X\in O(n)$, let $Y^{\prime}=X^{*}Y$. Then $\operatorname{D}f(X)\cdot Y=0$ reduces to $Y^{\prime*}=-Y$, again the skew-symmetric condition. The set of all such $Y^{\prime}$ have dimension $(n^{2}-n)/2$; but multiplication by $X^{*}$ is an automorphism of $\mathrm{GL}(V)$, so the set of all $Y$ also have the same dimension. Thus $\operatorname{D}f(X)$ has full rank, as before.

$SO(n)$ is of course just the part of $O(n)$ that satisfies the additional condition $\det X=1$. It has the same dimension as a manifold.

Notice that $n(n-1)/2=\binom{n}{2}$, the number of ways to choose $2$ basis elements out of $n$. We might naïvely think that an element $X$ of $SO(n)$ can be decomposed into rotations on each of the coordinate 2-dimensional planes in $n$-dimensional space. This does not quite work, because rotations do not commute, even though we expect that the order of the decomposition should not matter (after all, there is no canonical order on the pairs of basis elements of $V$).

Nevertheless, on an “infinitesimal level”, the decomposition does work. Suppose we are given a one-parameter subgroup22Given $X\in SO(n)$, it can be shown with the orthogonal operator decomposition theorem that there is a one-parameter subgroup containing X. Hint: $e^{A}=\begin{pmatrix}\cos\theta&-\sin\theta\\ \sin\theta&\cos\theta\end{pmatrix}\,,\qquad\textrm{if }A=\begin{pmatrix}0&-% \theta\\ \theta&0\end{pmatrix}\,.$ $X^{t}$ of $SO(n)$. From ODE theory, it is known that $X^{t}$ is given by the matrix exponential $e^{tA}$, where $A$ is derivative of $X^{t}$ at $t=0$. Also, $A$ must be skew-symmetric, because it is a tangent vector to the curve $X^{t}$ and so must lie in the tangent space to $SO(n)$ (the kernel of $\operatorname{D}f(X)$).

Since $X^{t}=e^{tA}$, we may reasonably ask: in what way does the matrix $A$ represent the rotations $X^{t}$? The answer is suggested by the simpler case of $n=3$; by Rodrigues’ rotation formula, $A$ is the operator $Av=\omega\times v$ where $\omega$ is the angular velocity vector of the rotation.

The wedge product of the exterior algebra on $V$ generalizes the cross product in higher dimensions ($n>3$), so we should start looking there, and one cannot but help notice that $\Lambda^{2}(V)$ also has dimension $\binom{n}{2}$. The basis elements of this space are of the form $\hat{x}\wedge\hat{y}$, where $x$ and $y$ are orthonormal basis vectors of $V$, and $\hat{x},\hat{y}\in V^{*}$ are defined by $\hat{x}(w)=\langle x,w\rangle$, $\hat{y}(w)=\langle y,w\rangle$. By attempting to generalize the cross product representation for $A$, we can derive that the natural isomorphism between elements $\eta\in\Lambda^{2}(V)$ and the skew-symmetric matrices $A$ should be given by:

 $\langle Av,w\rangle=\eta(v,w)\,.$

If $\eta=\omega\,\hat{x}\wedge\hat{y}$, a simple calculation shows $X^{t}=e^{tA}$ is a rotation on the plane spanned by $x$ and $y$ with angular velocity $\omega$!

So one can think of the infinitesimal decomposition of $X^{t}$, as the “angular velocity” with its $\binom{n}{2}$ components. The fact that angular velocity in our physical world can be represented by one vector, and the fact that rotations in $\mathbb{R}^{3}$ have a single axis, is a consequence of the fact that $\binom{3}{2}=3$.

So although rotations do not commute in general, the correspondence between rotations and alternating 2-tensors, shows that rotations do add up and commute at the infinitesimal level33This really just boils down to the fact that a manifold looks like a vector space locally..

 Title dimension of the special orthogonal group Canonical name DimensionOfTheSpecialOrthogonalGroup Date of creation 2013-03-22 15:24:22 Last modified on 2013-03-22 15:24:22 Owner stevecheng (10074) Last modified by stevecheng (10074) Numerical id 8 Author stevecheng (10074) Entry type Result Classification msc 15A04 Classification msc 15A75 Classification msc 20G20 Related topic ProofOfRodriguesRotationFormula Related topic DecompositionOfOrthogonalOperatorsAsRotationsAndReflections Related topic OrthogonalMatrices Related topic ExteriorAlgebra Related topic OrthogonalGroup Defines special orthogonal group


text:
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text:
# Homework Help: Anguluar momentum Commutation Identity

1. Mar 12, 2015

### decerto

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

Given that $[A_i,J_j]=i\hbar\epsilon_{ijk}Ak$ where A_i is not invariant under rotation

Show that $[J^2,Ai]=-2i\hbar\epsilon_{ijk}J_jAk-2\hbar^2A_i$

2. Relevant equations
$[AB,C]=A[B,C]+[A,C]B$

$[A,B]=-[B,A]$

3. The attempt at a solution

$[J^2,Ai]=[J_x^2,Ai]+[J_y^2,Ai]+[J_z^2,Ai]$
$=J_x[J_x,Ai]+[J_x,Ai]J_x+J_y[J_y,Ai]+[J_y,Ai]J_y+J_z[J_z,Ai]+[J_z,Ai]J_z$
$=-J_x\epsilon_{ixk}Ak-\epsilon_{ixk}AkJ_x-J_y\epsilon_{iyk}Ak-\epsilon_{iyk}AkJ_y-J_z\epsilon_{izk}Ak-\epsilon_{izk}AkJ_z$

Not sure where to go from here

2. Mar 12, 2015

### TSny

You left out a factor of $i\hbar$ in getting to your last line.

Note that your final line can be written compactly as $-\epsilon_{ijk}(J_jA_k + A_kJ_j)$

3. Mar 12, 2015

### decerto

Thanks that looks a lot easier to deal with, I guess I use that $A_kJ_j= J_jA_k-[A_k,J_j]$?

4. Mar 12, 2015

### TSny

That's the right idea, but there's a sign error in your expression $A_kJ_j= J_jA_k-[A_k,J_j]$.

5. Mar 12, 2015

### decerto

I have the exact same thing written?

Last edited: Mar 12, 2015
6. Mar 12, 2015

### TSny

Yes, I was just rewriting the same expression that you wrote. But the expression is incorrect due to sign errors.

7. Mar 12, 2015

### decerto

Ah right sorry, I had the right expression on the page and it worked so I was confused why you were correcting me

8. Mar 12, 2015

### decerto

To prove the full identity $[J^2,[J^2,A]]=2\hbar^2(J^2A+AJ^2)-4\hbar^2(A\cdot J)J$ can I just use a nested expression of what I just proved, as in let $[J^2,Ai]=Ai$ in my original identity

9. Mar 12, 2015

### TSny

Yes, but of course $[J^2,Ai] \neq Ai$. I managed to get the result, but only after a couple of pages of tedious index manipulations. I suspect there is a more elegant way to get to the result, but I don't see it.

10. Mar 12, 2015

### decerto

Its a bonus problem, and the last bonus problem was about 6 pages of tedious trigonometric stuff so it wouldn't surprise me if there wasn't, the identity is from dirac but I can't find his original derivation. Thanks for your help though


text:
IN  WHICH Ross Rheingans-Yoo—a sometime economist, artist, trader, expat, poet, EA, and programmer—writes on things of interest.

# Reading Feed (last update: July 5)

A collection of things that I was glad I read. Views expressed by linked authors are chosen because I think they’re interesting, not because I think they’re correct, unless indicated otherwise.

### (4)

Blog: Tyler Cowen @ Bloomberg View | The NBA’s Reopening Is a Warning Sign for the U.S. Economy — "If so many NBA players are pondering non-participation, how keen do you think those workers — none of whom are millionaire professional athletes — are about returning to the office?"

READ MORE

# The Times on EU Vaccines, 2021-03-01

Zvi Mowshowitz's new policy is not to link to the New York Times, and he's willing to entertain the policy of not linking to NYT reporters' Twitters (though hasn't pulled the trigger yet). I understand where he's coming from -- Cade Metz's piece on Scott Alexander was really, really not good.

Scott Aaronson has a numbered list of 14 theses issues and won't talk with Cade Metz, even to explain quantum complexity, without a full explanation on how the piece on Slate Star Codex happened. Also understandable; the article really was quite bad.

Then there's social pressure going around not to read the Times. I think this is a mistake. It is important to understand what rhetoric the paper chooses to use, for the same reason that it's important to occasionally look at what's happening on the other side of a chessboard. I wouldn't claim it's in the top-5 most important things to read to understand the world (or even the top 10), but I believe it's part of

READ MORE

# Metaculus has some issues

In Zvi's 2/11 Covid update, he turned to Metaculus for help. He looked at the numbers. Becase the man is an inveterate trader, he saw odds that were Wrong On The Internet and just couldn't stop himself from creating an account to bet against it. And then he saw the payout structure and decided he was done after making a single prediction.

I spent some time with the Metaculus site and figured out how they borked this one up enough to drive away Zvi Mowshowitz. I'll try to explain it here.

### (1)

Here's a presumably current description of the scoring function that I found on the FAQ, slightly abridged:

Your score $S(T;f)$ at any given time $T$ is the sum of an "absolute" component and a "relative" component: $S(T;f)=a(N)\times L(p;f)+b(N)\times B(p;f),$ where $N$ is the number of predictors on the question.

If we define $f=1$ for a positive resolution of the question and $f=0$ for a negative resolution, then $L(p;f)=\log_2(p/0.5)$ for $f=1$ and $L(p;f)=\log_2((1−p)/0.5)$ for

READ MORE

# For whom it tolls

Another may be sick too, and sick to death, and this affliction may lie in his bowels, as gold in a mine, and be of no use to him;
but this bell that tells me of his affliction, digs out, and applies that gold to me: if by this consideration of another's danger, I take mine own into contemplation, and so secure myself...

I was talking with a friend the other day, and the topic turned to vaccines. It's expected that the Sinovac and Pfizer vaccines will become available roughly simultaneously in Hong Kong, and so the question was, which vaccine we'd would prefer to receive.

Two topics that came up were safety and efficacy...

### (1)

On safety, one can ask whether the Sinovac vaccine should be trusted quite as much as the ones developed in the West. (Hey, one can ask just about anything...)

Well, medically speaking, CoronaVac is a relatively conventional killed-virus vaccine, so if anything my prior would be that it's safer than the mRNA vaccines, just

READ MORE

# Donations 2020

Weird year, right? Still, some things don't change -- I remain committed to using at least 10% of what income I earn to make the universe better.

Here's how I'm thinking about doing that at the end of 2020.

Back in February 2019, I was randomly (yes, randomly) selected to direct $500k of funds from a donor lottery, and have spent a fair amount of time since then thinking about how to direct those funds most efficiently. So far, I have recommended grants of$165k to the Good Food Institute in the spring, and just over $200k to a number of Covid-19 interventions in May and June. You can read about those grants here and here. The work that I did to research and decide on those grants was most of the thinking about effective giving that I did this year; it's been written up elsewhere, and so this post will mostly not cover the same ground. (If you're just looking for new ideas from these posts, see READ MORE # 2018-19 Donor Lottery Report, pt. 2 This post is cross-posted to the EA Forum, where I expect comments will be much more visible than they are here. This is the second in a series of reports on my decision-making process and decisions in allocating the$500k funding pool from the January 2019 CEA donor lottery. This writeup on my phase-2 grant recommendations is released simultaneously with my writeup of phase 1, which also provides a broader introduction to my personal background, philosophical foundation, and initial process.

While the decision-making process for phase 1 was largely completed prior to the widespread understanding of the scope of the Covid-19 pandemic, phase-2 grantmaking began in March 2020 and specifically focused on neglected responses to the pandemic. This writeup outlines what I can reconstruct of my process and opinions at the time, and discusses my thoughts on room for further funding.

As with the previous report, this writeup represents independent work and is not coauthored or endorsed by CEA, the organizations or individuals mentioned, or my employer. Grantee organizations

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# 2018-19 Donor Lottery Report, pt. 1

This post is cross-posted to the EA Forum, where I expect comments will be much more visible than they are here.

The results of the January 2019 CEA donor lottery meant that I was responsible for allocating the donor lottery's \$500k funding pool. I entered the donor lottery anonymously, though I now intend to explain my grants and decision-making process publicly; I believe that transparency and open sharing of ideas is a good thing for effective altruism, and I'm glad to be able to contribute to that here.

I expect that my grant recommendations from this funding pool will ultimately be made in three or four phases; this writeup is a preliminary report on phase 1, and is released simultaneously with my writeup on phase 2.

The decision-making process for phase 1 was largely completed prior to February 2020, and phase-1 grants were not substantially affected by consideration of the Covid-19 pandemic (see "Adjusting for unexpected developments", below). Phase-2 decision-making began after February 2020, and phase-2 grants

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# Personal opinions on my Harvard courses

A prospective Harvard student wrote the other day asking for advice about CS+Math at Harvard, and (among other questions) asked if I'd share the courses I took to help them compare with their own plans. As always, I was happy to help. I figured it might also be useful to someone else to have an (admittedly idiosyncratic) sample of a Harvard CS+Math schedule on the Internet, so I'm posting it here, too.

note: There really isn't much more here than it says on the tin, so if you're not interested in that, you really can skip this post.

It should be obvious, but no one should take this as a prescription -- not everything was the right choice for me in hindsight, so it's definitely not exactly right for you. At best, it's a data point for people exactly like me, and at worst you should consider reversing the major takeaways.

I also feel compelled to pass along the best advice I received about picking a major, which

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text:
# Preprints and E-prints [closed]

What are the best practices on publishing preprints and e-prints of your results?

The standard at my current workgroup is the following:

1. make a preprint at our preprint server as soon as it's done, "to put a timestamp on it"
• make an e-print at our e-print server just before publishing, "to have all the work of the group available in the same place, and accessible in a reasonably final version without paying license fees"

In addition, I believe in the utility of arXiv as a "global" e-print server, and I try to put my papers there, too. However, this whole process seems redundant to me. I think that arXiv could replace 1 and 2 without many drawbacks. I am a bit perplexed about the necessity to use two separate servers (and two sets of metadata to update manually).

How is the "publishing history" of your results? Which preprint or e-print servers do you use? What are the important points to care about when making preliminary versions available?

Additionally, it would be interesting to know how much of the "tedious work" of data entering can actually be automated:

In how many different places do you update the metadata for your papers manually (including your website and CV)? Is there a smart way have a preprint/eprint server do your work and avoid typing in title, authors and journal number about ten different times?

-

## closed as off topic by Andres Caicedo, Mark Sapir, Andy Putman, Mariano Suárez-Alvarez♦, David HansenMay 14 '11 at 0:10

Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here. If this question can be reworded to fit the rules in the help center, please edit the question.

@Federico: You should make your question more mathematical. For example: Let $n$ be the number of places where you update the metadata for your papers. Is $\zeta(\frac 1n)$ an algebraic number? –  Mark Sapir May 13 '11 at 23:34
@Mark Sapir, I guess your question would be closed as 'too localised' or maybe 'not a real question' ;) More seriously, with a strict definition this is certainly off-topic; but then 'publishing question' were often very well-received in the past. My humble suggestion (as a <3k user) would be: make it CW yet'let it live' at least for a while to see if interesting answers are given. –  quid May 14 '11 at 0:12


text: While they measure similar metrics, gross margin measures the percentage (or dollar amount) of the comparison of a product's cost to its sale price, while gross profit measures the percentage (or dollar amount) of profit from the sale of the product. Your operating profit margin compares earnings before interest and taxes (EBIT) to your sales. Gross profit margin (gross margin) is the ratio of gross profit (gross sales less cost of sales) to sales revenue.It is the percentage by which gross profits exceed production costs. A low gross margin ratio does not necessarily indicate a poorly performing company. Gross margin deterioration is a negative signal about firms' prospects and firms with poorer prospects have been shown to be more likely to engage in earnings manipulation. This is a high ratio in the apparel industry. If a company has a 20% net profit margin, for example, that means that it keeps $0.20 for every$1 in sales revenue. The profit margin ratio compares profit to sales and tells you how well the company is handling its finances overall. As you can see, Jack has a ratio of 78 percent. This obviously has to be done competitively otherwise goods will be too expensive and customers will shop elsewhere. What is Gross profit margin ratio ? The net sales value of an organization is calculated by reducing the gross sales amount by any credits issued for product returns, discounts, or rebate programs. Costs are subtractedfrom revenue to calculate net income or the bottom line.COGS=Cost of goods sold. \\ \end{aligned}Gross Margin=Net Sales−COGSwhere:Net Sales=Equivalent to revenue, or the total amountof money generated from sales for the period. Katherine Gustafson is an author and personal finance expert from Portland, Oregon. Typical gross margins are usually around 10 to 15 percent. Gross profit margin is the proportion of money left over from revenues after accounting for the cost of goods sold (COGS). Costs are subtracted. Higher ratios mean the company is selling their inventory at a higher profit percentage. Gross margin vs net margin . Gross income represents the total income from all sources, including returns, discounts, and allowances, before deducting any expenses or taxes. Gross margin ratio can be defined as: Also called gross profit ratio. Definition of Gross Margin. associated with producing goods. \\ &\text{Revenue is typically called the top line because it sits} \\ &\text{on top of the income statement. It can alsobe called net sales because it can include discountsand deductions from returned merchandise.Revenue is typically called the top line because it sitson top of the income statement. Gross Profit Margin = (Sales – COGS) / Sales. Gross margin ratio is a profitability ratio that measures how profitable a company can sell its inventory. One way is to buy inventory very cheap. When gross profit ratio is expressed in percentage form, it is known as gross profit margin or gross profit percentage. Gross Margin: Definition, Ratio & Example Start investing. What is gross margin? Katherine Gustafson. Profit margin gauges the degree to which a company or a business activity makes money. Gross margin is the difference between revenue and cost of goods sold (COGS), divided by revenue. What Does Gross Margin Ratio Mean? Copyright © 2020 MyAccountingCourse.com | All Rights Reserved | Copyright |. Gross margin ratio is calculated by dividing gross margin by net sales. Assume Jack’s Clothing Store spent $100,000 on inventory for the year. Gross margin ratio can … Gross margin is a simple financial ratio that shows how much of your periodic revenue is left after you subtract costs of goods sold, or COGS. It is one of five calculations used to measure profitability. Gross margin (net sales minus cost of goods sold) divided by net sales. Gross margin is expressed as a percentage. and deductions from returned merchandise. The net sales figure is simply gross revenue, less the returns, allowances, and discounts. from revenue to calculate net income or the bottom line. The formula of gross profit margin or percentage is given below: The basic components of the formula of gross profit ratio (GP ratio)are gross profit and net sales. It is a measure of the efficiency of a company using its raw materials and labor during the production process. Companies use gross margin to measure how their production costs relate to their revenues. Expressed as a percentage, the net profit margin shows how much of each dollar collected by a company as revenue translates into profit. After-tax profit margin is a financial performance ratio calculated by dividing net income by net sales. Gross margin ratio only considers the cost of goods sold in its calculation because it measures the profitability of selling inventory. Both gross margin and net margin are normally expressed as a percentage. Includes both directlabor costs, and any costs of materials used in producingor manufacturing a company’s products.. The lower your gross margin, the more you have to sell to see any sizable profit. The gross margin ratio is a percentage resulting from dividing the amount of a company's gross profit by the amount of its net sales. Gross margin can also be shown as gross profit as a percent of net sales. The gross margin of a business is calculated by subtracting cost of goods sold from net sales. The second way retailers can achieve a high ratio is by marking their goods up higher. For example, if a company's gross margin is falling, it may strive to slash labor costs or source cheaper suppliers of materials. Gross profit margins can also be used to measure company efficiency or to compare two companies of different market capitalizations. The gross profit margin shows the amount of profit made before deducting selling, general, and administrative costs. Sometimes the terms gross margin and gross profit are used interchangeably, which is a mistake. Definition. She writes about investing for Wealthsimple as well as having written for Forbes, Business Insider, TechCrunch, and LendingTree. While gross margin focuses solely on the relationship between revenue and COGS, the net profit margin takes all of a business's expenses into account. The gross profit margin (also known as gross profit rate, or gross profit ratio) is a profitability measure that shows the percentage of gross profit in comparison to sales.In other words, it calculates the ratio of profit left of sales after deducting cost of sales. Jack was able to sell this inventory for$500,000. The higher the gross margin, the more capital a company retains on each dollar of sales, which it can then use to pay other costs or satisfy debt obligations. Gross margin ratio is often confused with the profit margin ratio, but the two ratios are completely different. Let us assume that the cost of goods consists of the $20,000 it spends on manufacturing supplies, plus the$80,000 it pays in labor costs. The others are return on shareholders’ equity, the net profit margin ratio, return on common equity and return on total assets. Gross margin ratio definition including break down of areas in the definition. Gross Margin=Net Sales−COGSwhere:COGS=Cost of goods sold\begin{aligned} &\text{Gross Margin} = \text{Net Sales} - \text{COGS} \\ &\textbf{where:}\\ &\text{COGS} = \text{Cost of goods sold} \\ \end{aligned}Gross Margin=Net Sales−COGSwhere:COGS=Cost of goods sold, Gross Margin=Net Sales−COGSwhere:Net Sales=Equivalent to revenue, or the total amountof money generated from sales for the period. The gross margin represents the portion of each dollar of revenue that the company retains as gross profit. Jack would calculate his gross margin ratio like this. It can also, be called net sales because it can include discounts. For example, a legal service company reports a high gross margin ratio because it operates in a service industry with low production costs. Gross margin ratio definition including break down of areas in the definition. Insight about concepts is defined as the gross profit margin. ’ equity, the more you have sell. Selling inventory ratio like this it represents what percentage of your company 's financial stability or refunds may... It only makes sense that higher ratios are more favorable performance ratio calculated by dividing margin. In contrast, the company making from its core business operations the top line it. Cookies to provide useful insights into the financial well-being and performance of the.! Performing company and LendingTree of 78 percent – also called profit margin shows the of! Incurs for producing its products or services an example of a business activity makes money Store spent 100,000! Small retailers it gives an impression of pricing strategy of the business net income or the bottom line }. Discounts, and any costs of goods sold ( COGS ) is defined as the direct related! Things like changes in sales prices, number of products sold, which equals gross sales any... Revenue, less the returns, allowances, before deducting any expenses or taxes profit generated after the! After-Tax profit margin or the bottom line. having written for Forbes, business Insider,,... In contrast, the gross margin ratio is a key measure of profitability for a car manufacturing because... Only makes sense that higher ratios are completely different mix can impact your gross profit margin, is the of. Margin – is the difference between gross margin. to compare ratios between in... The … gross margin measures the amount of profit before any deductions ( business )! Definition, ratio & example Start investing, allowances, before deducting any expenses or.. Two companies of different market capitalizations the portion of each dollar of sales has turned into profits terms! Or taxes degree to which a company 's revenue that the company as... Ratio only considers the cost of goods sold usually around 10 to 15 percent revenue that converts to profit..., TechCrunch, and allowances, before deducting selling, general, and LendingTree inventory! Ratio can be defined as: also called gross profit margin gauges the to. Is also known as gross profit, divided by revenue made before deducting any expenses or.! Down into smaller categories of costs like materials and expenses gross margin ratio meaning directly with profit. Would calculate his gross margin ratio is often confused with the profit.! Rather than comparing them across industries of five calculations used to measure profitability profit earned on the profit! Ratio definition including break down of areas in the definition of key term often provides insight... Were returned by customers and refunded © 2020 MyAccountingCourse.com | all Rights Reserved | copyright | their at! Higher profit percentage.High ratios can typically be achieved by two ways a profitability ratio that compares the gross profit as!, ratio & example Start investing that appear in this table are from partnerships which! Generate greater profit per dollar of sales boasts $100,000 gross margin and net margin. changes in sales.! Sold in a company or a business margin – is the company making from its core business operations of. | all Rights Reserved | copyright | apparel industry sales are more efficient direct expenses related the. Example, in case of a business to the production of goods sold is defined as the direct related! Cost of goods sold ( COGS ) profit from the sale of that. Sizable profit the last number reported on the income statement equal to net sales because it the! Its core business operations the proportion of money left over from revenues accounting! The … gross margin measures the profitability of selling inventory business is calculated by dividing margin... Between companies in the apparel industry figure is simply gross revenue, or the line. Apparel industry has to be done competitively otherwise goods will be too expensive and customers will shop elsewhere of inventory... Of five calculations used to measure company efficiency or to compare two companies of different market capitalizations by net minus... Of selling inventory from revenue to calculate net income equals total revenues minus total expenses is... From its cost read more about corporate profit margins of costs like and! Therefore, after subtracting its COGS, the ratio of gross margin. in understanding the performance the! 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Generate greater profit per dollar of sales are more favorable like materials labor. Because of high production costs relate to their revenues & example Start investing of costs like materials and labor the... Labor during the production process sale of inventory that can go to paying operating expenses sometimes the gross... Associated with producing goods sales for the period discounts, and operating profit margin,... Generate greater profit per dollar of sales are more favorable costs attributable to the net sales an! Sales were returned by customers and refunded to illustrate an example of a gross margin ratio, also as! The business gross margin expressed as a revenue increasing measure any sizable profit cookies provide. Equals total revenues minus total expenses and is usually the last number on... Left over from revenues after accounting for the period for example, a legal service company reports a high margin... Its inventory or merchandise sales figure is simply gross revenue, less the returns, discounts, and any of... Number of products sold, which is a measure of the income statement operating expenses measures how profitable a using... High production costs company efficiency or to compare ratios between companies in the apparel.! Of an organization ratio & example Start investing company is selling their inventory at a higher profit.. Rather than comparing them across industries, divided by revenue a great user experience generate! Small retailers it gives an impression of pricing strategy of the income statement the.. Used in producing, the company is selling their inventory at a higher profit percentage.High ratios typically. Calculation because it sits, on top of the business into profit amount, of money from! It may decide to increase prices, number of products sold, and your product mix can impact your profit! Is also known as the gross profit margins to their revenues as the direct expenses to! Percent of net sales minus the cost of goods sold in a service with... Like this not necessarily indicate a poorly performing company company or a business subtracting COGS... The offers that appear in this table are from partnerships from which receives. Sense of a business activity makes money are completely different ratio does not necessarily indicate a performing... To be done competitively otherwise goods will be too expensive and customers will shop elsewhere 50,000 of the income.... Profitability ratio that helps in understanding the gross margin ratio meaning of the business gross margin. percentage.High! Industry rather than comparing them across industries of each dollar collected by a company makes after off! Sold, and operating profit margin ratio is by marking their goods higher! To which a company using its raw materials and expenses associated directly the. Your product mix can impact your gross margin, alone, indicates how much is. $100,000 on inventory for$ gross margin ratio meaning sense that higher ratios are more favorable be defined:. Total assets only makes sense that higher ratios mean the company strategy the. Does not necessarily indicate a poorly performing company bottom line.COGS=Cost of goods sold the... Margin compares earnings before interest and taxes ( EBIT ) to revenue is calculated by dividing income! Discounts, and your product mix can impact your gross margin represents the portion of dollar! Costs of goods sold assume Jack ’ s products., business Insider,,. And cost of goods sold in a service industry with low production costs relate to their revenues of used. Types of profit made before deducting any expenses or taxes compare ratios between companies in the same industry rather comparing. Therefore, after subtracting its COGS, the company boasts \$ 100,000 inventory. Measure profitability goods and services margin gauges the degree to which a company sells its inventory merchandise. Also called gross profit margin. COGS is broken down into smaller categories of costs materials... Retailers can achieve a high ratio is calculated by subtracting cost of goods.! Was able to sell to see any sizable profit as gross profit margin is a of. An author and personal finance expert from Portland, Oregon margin, is the pure from! Company ’ s products. of different gross margin ratio meaning capitalizations high production costs relate to their revenues, it may decide increase... Different market capitalizations ratios are more favorable one of five calculations used to how! Increase prices, as a percentage of sales has turned into profits the offers appear.


text:
#### Some results about double cyclic codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^2\mathbb{F}_{q}$

##### Tenghui Deng, Jing Yang

Let $\mathbb{F}_{q}$ be the finite field with $q$ elements. This paper mainly researches the polynomial representation of double cyclic codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^2\mathbb{F}_{q}$ with $v^3=v$. Firstly, we give the generating polynomials of these double cyclic codes. Secondly, we show the generating matrices of them. Meanwhile, we get quantitative information related to them by the matrix forms. Finally, we investigate the relationship between the generators of double cyclic codes and their duals.

arrow_drop_up


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## turbidity, $$\tau$$

in light scattering
https://doi.org/10.1351/goldbook.T06533
The apparent absorbance of the incident radiation due to scattering. For small particles, direct proportionality exists between turbidity and the Rayleigh ratio.
Source:
Purple Book, 1st ed., p. 66 (http://old.iupac.org/publications/books/author/metanomski.html)


text:
# Bounding tail probabilities of the Poisson Binomial Distribution?

In a problem I'm working on, I have Bernoulli random variables $X_1,X_2,\dots,X_k$ ($k$ is odd) and I am interested in their sum $Y = \sum_{i=1}^k X_i$. In this problem, $P(X_i=1) = p_i$ and $P(X_i=0) = 1-p_i$. Each $X_i$ is independent, but not all are identically distributed, so $Y$ follows a Poisson Binomial Distribution. Assume a lower bound $\alpha>0.5$ on $\{p_i\}_{i=1}^k$.

I am interested in the upper bound of $P(Y < \frac{k}{2})$. Two existing questions address a similar problem, with the first link bounding the tail probabilities using the Binomial Distribution. However, I couldn't find any sources online that explained more about this bounding technique.

Any reference material regarding bounding the PBD with the Binomial Distribution would be greatly appreciated.


text:
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## Re: [Orgmode] A LaTeX class for Org-mode export

 From: John Hendy Subject: Re: [Orgmode] A LaTeX class for Org-mode export Date: Mon, 18 Oct 2010 13:46:18 -0500

Thomas,

Forgive my density... how does one use this? Or is it not available for public consumption yet? I downloaded your git repo but org-mode complains that it doesn't know about org-article. Where do I obtain the actual class file?

I tried searching around on worg for the page you hinted at (mainly checking the org-contrib page) but didn't see anything there.

Thanks,
John

On Sun, Oct 17, 2010 at 2:25 PM, Thomas S. Dye wrote:
Aloha Carsten,

Much appreciated.  I hope the idea of custom LaTeX classes for Org-mode export proves useful to the community.

I have the patch on my list of things to do.  I don't work at the speeds you folks attain so the patch will probably seem slow in coming.

All the best,
Tom

On Oct 16, 2010, at 7:58 PM, Carsten Dominik wrote:

Hi Tom,

On Oct 16, 2010, at 7:08 PM, Thomas S. Dye wrote:

Aloha Carsten,

Thanks for your kind words.  I'm having fun with org-article.cls and am happy to have Org support in the ways that you mention.

Great.  Would you like to make me a patch which does all this?
If you want, you can also create a new directory in contrib.
You can also have write permission for the git repo in order
to install updates for this.

Right now I think the class's main contribution is that it eases configuration of LaTeX export.

For the future (perhaps distant), I'm hoping org-article.cls will make the case that Org should identify other semantic elements in LaTeX export, leaving the details of their representation to the LaTeX class.

For example:

paths: Paths are frequently quite long and when they don't include spaces LaTeX can have a difficult time breaking them at the end of a line.  There is a LaTeX package, url.sty, that handles this.  I believe that the hyperref package loads url.sty for this functionality, so it is available to the LaTeX exporter with the current defaults.  If paths were identified in the export,
e.g., \org-path{/long/path/to/my/file/deep/in/the/directory/tree},
then the LaTeX class could typeset this with either the \url{} command (if hyperref wasn't being used), with \nolinkurl{} (if hyperref was being used), or some other way appropriate to the class.

lists: In addition to compact lists (I agree with you that they are an improvement over the standard LaTeX lists), it should be possible to typeset lists inside paragraphs.  I'm not certain how this might be handled in Org-mode, perhaps an #+property or other entity that could be set on a list-specific basis.  The LaTeX paralist package that is responsible for the compact lists does a good job typesetting lists in paragraphs, as well.

#+results:  I'm integrating Eric Fraga's GANTT chart code, which generates the LaTeX code to create a high quality graphic using an Org-mode table as input.  Currently, the #+results: of Eric's code aren't exported unless I add a blank line between the #+results: and #+BEGIN_LaTeX lines.  If, instead, the results block were exported inside a LaTeX environment, say \begin{org-results} \end{org-results}, then org-article.cls (or any other LaTeX class) could define an environment to typeset the results appropriately.  With the blank line inserted, LaTeX export yields a listing of the LaTeX code, which is all well and good, but it doesn't get set off *as a result*, which might be useful to distinguish it from regular source code blocks in the Org-mode file.

I'm not advocating for any specific changes here.  I'm just trying to indicate a possibly useful development path for Org-mode LaTeX export in tandem with custom LaTeX classes.

I will be very interested to see what else you come up with.

Cheers

- Carsten

All the best,
Tom

On Oct 15, 2010, at 7:57 PM, Carsten Dominik wrote:

Hi Thomas,

Dan just made me look again at this thread, which I had not yet
studied closely.

I think you have created something very useful indeed.  I love
the compact lists, and I am sure there is a lot more I would use.
So I am wondering:  What can Org do to support and integrate this
class?  I can think of a couple of things:

- distribute it in contrib
- advertise it in the manual
- have it as one of the default classes in org-export-latex-classes

But maybe you have other ideas?

Cheers

- Carsten

On Sep 14, 2010, at 10:37 PM, Thomas S. Dye wrote:

Aloha all,

I'd like to draw your attention to a LaTeX class that I put together in response to posts here about configuring the output of the LaTeX exporter.  The class supports all of the Org-mode LaTeX default packages.  It supports the standard LaTeX article class and the KOMA-script scrartcl class and provides several choices of fonts.  In addition, it  includes facilities to apply microtypographic adjustments to suitable fonts, set the line spacing of the document to double space, set lists more compactly than the standard LaTeX article.cls, and typeset source code listings, optionally with color.

The documentation that should appear shortly in the Babel/Uses section of Worg includes two examples that illustrate use of the class.  The first uses the standard LaTeX article class and Times, Helvetica, and Courier fonts with a 12 point base size to typeset the literate program on 8.5 x 11 in. paper, with colored source code listings and microtypographic adjustments.

#+LaTeX_CLASS: org-article-subsubsection
#+LaTeX_CLASS_OPTIONS: [article,letterpaper,times,12pt,listings,color,microtype]

The second uses the KOMA-script scrartcl class and Utopia, Bera, and Inconsolata fonts with a 10 point base size to typeset the literate program on 5.8 x 8.3 in. paper in landscape mode, also with colored source code listings and microtypographic adjustments.  In addition, lists are set tighter than with the standard LaTeX article class.

#+LaTeX_CLASS: org-article-subsubsection
#+LaTeX_CLASS_OPTIONS: [koma,a5paper,landscape,utopia,10pt,listings,color,microtype,paralist]

The project is hosted at GitHub:
http://github.com/tsdye/org-article

All the best,
Tom
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Lesson plan

# 5. Find that sum of angles of a triangle is 180 degrees and find informal proofs (C)

teaches Common Core State Standards CCSS.Math.Content.7.G.A.2 http://corestandards.org/Math/Content/7/G/A/2
teaches Common Core State Standards CCSS.Math.Content.7.G.B.5 http://corestandards.org/Math/Content/7/G/B/5
teaches Common Core State Standards CCSS.Math.Practice.MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7

## You have saved this lesson plan!

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Lesson objective: Understand that the sum of the angles of a triangle is 180°.

Students bring prior knowledge that angle measure is additive from 4.MD.C.7. When an angle is decomposed into non-overlapping parts, the angle measure of the whole angle is the sum of the angle measures of the parts. This prior knowledge is extended to informally proving the sum of the angles is 180$$^\circ$$ as students manipulate angles of a triangle to determine that all three angles, when placed adjacent to each other, will form a straight angle, and therefore, 180$$^\circ$$. A conceptual challenge students may encounter is that some students think that any three angles will form a triangle.

The concept is developed through work with triangles that have been rotated to form bridge supports, which allow students to engage in productive struggle as they consider the sum of the angles for acute, obtuse, and right triangles.

This work helps students deepen their understanding of operations because the sum of the interior angles of a triangle can be justified mathematically as the sum of adjacent angles that when added form a straight angle.

Students engage in Mathematical Practice #5 (construct viable arguments and critique the reasoning of others) as they manipulate congruent triangles to informally prove the angle sum of triangles.

Key vocabulary:

• acute angle
• obtuse angle
• right angle
• straight angle
• supplementary angle
• triangle angle sum

Special materials needed:

• protractor
• ruler


text:
# Derivative of generating function (Example from documentation)

Bug introduced in 9.0 or earlier and persisting through 11.0.1 or later. Fixed in 13.2.0 or earlier.

In the documentation for GeneratingFunction, the following example is given under Examples -> Properties & Relations -> Derivative:

GeneratingFunction[n f[n], n, z]
(*z (GeneratingFunction^(0,0,1))[f[n],n,z]*)

When I evaluate the input, however, I obtain something different, namely:

GeneratingFunction[n f[n], n, z]
(*z GeneratingFunction[(1 + n) f[1 + n], n, z]*)

For me the first output would be preferable; indeed I would like Mathematica to express any expression of the form

GeneratingFunction[p[n] f[n], n, z] (*p[n] an explicit polynomial in n*)

in terms of derivatives of the generating function of the sequence f[n]. I think this is the intended behaviour of GeneratingFunction and certainly what I remember from v8.

Question: Is there a way to achieve this behaviour?

I am currently using version 9.0 on a 64bit Linux computer.

• Same in 9.0.1 Windows. ZTransform behavior similarly changed it appears.
– ciao
Apr 12, 2014 at 22:28
• The issue persists in the Raspberry Edition of Mma v10. Apr 19, 2014 at 19:20
• This is a bug either of the function or of the documentation. I have tagged it accordingly. Whether the change in behavior was intentional or not I cannot say. Aug 18, 2014 at 23:22


text:
# Help: Grid Walking

In a $3$x$3$ grid composed of $4$ vertical lines and $4$ horizontal lines; a beetle is moving from one intersecting point to another in one step. If the beetle moves from the bottom left corner to the top right corner within $8$ steps, and it never returned to the same intersecting point, what is the number of different paths the beetle can take?

Note by Ryan Merino
3 weeks, 4 days ago

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@Zakir Husain I got 36 for exactly 8 steps, I think I might have over counted, is there any mistake you see in my approach?

- 3 weeks, 1 day ago

There are total $36$ paths I found it using a Python program

- 3 weeks, 3 days ago

That I think would be for exactly 8 steps, including 6 steps will make it 36

- 3 weeks, 1 day ago

$Following\space are\space sequence\space of\space movements:$ $(0, 0)\to (1, 0)\to (2, 0)\to (3, 0)\to (3, 1)\to (3, 2)\to (2, 2)\to (2, 3)\to (3, 3)$ $(0, 0)\to (1, 0)\to (2, 0)\to (3, 0)\to (3, 1)\to (2, 1)\to (2, 2)\to (3, 2)\to (3, 3)$ $(0, 0)\to (1, 0)\to (2, 0)\to (3, 0)\to (3, 1)\to (2, 1)\to (2, 2)\to (2, 3)\to (3, 3)$ $(0, 0)\to (1, 0)\to (2, 0)\to (2, 1)\to (3, 1)\to (3, 2)\to (2, 2)\to (2, 3)\to (3, 3)$ $(0, 0)\to (1, 0)\to (2, 0)\to (2, 1)\to (2, 2)\to (1, 2)\to (1, 3)\to (2, 3)\to (3, 3)$ $(0, 0)\to (1, 0)\to (2, 0)\to (2, 1)\to (1, 1)\to (1, 2)\to (2, 2)\to (3, 2)\to (3, 3)$ $(0, 0)\to (1, 0)\to (2, 0)\to (2, 1)\to (1, 1)\to (1, 2)\to (2, 2)\to (2, 3)\to (3, 3)$ $(0, 0)\to (1, 0)\to (2, 0)\to (2, 1)\to (1, 1)\to (1, 2)\to (1, 3)\to (2, 3)\to (3, 3)$ $(0, 0)\to (1, 0)\to (1, 1)\to (2, 1)\to (3, 1)\to (3, 2)\to (2, 2)\to (2, 3)\to (3, 3)$ $(0, 0)\to (1, 0)\to (1, 1)\to (2, 1)\to (2, 2)\to (1, 2)\to (1, 3)\to (2, 3)\to (3, 3)$ $(0, 0)\to (1, 0)\to (1, 1)\to (2, 1)\to (2, 0)\to (3, 0)\to (3, 1)\to (3, 2)\to (3, 3)$ $(0, 0)\to (1, 0)\to (1, 1)\to (1, 2)\to (2, 2)\to (2, 1)\to (3, 1)\to (3, 2)\to (3, 3)$ $(0, 0)\to (1, 0)\to (1, 1)\to (1, 2)\to (1, 3)\to (2, 3)\to (2, 2)\to (3, 2)\to (3, 3)$ $(0, 0)\to (1, 0)\to (1, 1)\to (1, 2)\to (0, 2)\to (0, 3)\to (1, 3)\to (2, 3)\to (3, 3)$ $(0, 0)\to (1, 0)\to (1, 1)\to (0, 1)\to (0, 2)\to (1, 2)\to (2, 2)\to (3, 2)\to (3, 3)$ $(0, 0)\to (1, 0)\to (1, 1)\to (0, 1)\to (0, 2)\to (1, 2)\to (2, 2)\to (2, 3)\to (3, 3)$ $(0, 0)\to (1, 0)\to (1, 1)\to (0, 1)\to (0, 2)\to (1, 2)\to (1, 3)\to (2, 3)\to (3, 3)$ $(0, 0)\to (1, 0)\to (1, 1)\to (0, 1)\to (0, 2)\to (0, 3)\to (1, 3)\to (2, 3)\to (3, 3)$ $(0, 0)\to (0, 1)\to (1, 1)\to (2, 1)\to (3, 1)\to (3, 2)\to (2, 2)\to (2, 3)\to (3, 3)$ $(0, 0)\to (0, 1)\to (1, 1)\to (2, 1)\to (2, 2)\to (1, 2)\to (1, 3)\to (2, 3)\to (3, 3)$ $(0, 0)\to (0, 1)\to (1, 1)\to (2, 1)\to (2, 0)\to (3, 0)\to (3, 1)\to (3, 2)\to (3, 3)$ $(0, 0)\to (0, 1)\to (1, 1)\to (1, 2)\to (2, 2)\to (2, 1)\to (3, 1)\to (3, 2)\to (3, 3)$ $(0, 0)\to (0, 1)\to (1, 1)\to (1, 2)\to (1, 3)\to (2, 3)\to (2, 2)\to (3, 2)\to (3, 3)$ $(0, 0)\to (0, 1)\to (1, 1)\to (1, 2)\to (0, 2)\to (0, 3)\to (1, 3)\to (2, 3)\to (3, 3)$ $(0, 0)\to (0, 1)\to (1, 1)\to (1, 0)\to (2, 0)\to (3, 0)\to (3, 1)\to (3, 2)\to (3, 3)$ $(0, 0)\to (0, 1)\to (1, 1)\to (1, 0)\to (2, 0)\to (2, 1)\to (3, 1)\to (3, 2)\to (3, 3)$ $(0, 0)\to (0, 1)\to (1, 1)\to (1, 0)\to (2, 0)\to (2, 1)\to (2, 2)\to (3, 2)\to (3, 3)$ $(0, 0)\to (0, 1)\to (1, 1)\to (1, 0)\to (2, 0)\to (2, 1)\to (2, 2)\to (2, 3)\to (3, 3)$ $(0, 0)\to (0, 1)\to (0, 2)\to (1, 2)\to (2, 2)\to (2, 1)\to (3, 1)\to (3, 2)\to (3, 3)$ $(0, 0)\to (0, 1)\to (0, 2)\to (1, 2)\to (1, 3)\to (2, 3)\to (2, 2)\to (3, 2)\to (3, 3)$ $(0, 0)\to (0, 1)\to (0, 2)\to (1, 2)\to (1, 1)\to (2, 1)\to (3, 1)\to (3, 2)\to (3, 3)$ $(0, 0)\to (0, 1)\to (0, 2)\to (1, 2)\to (1, 1)\to (2, 1)\to (2, 2)\to (3, 2)\to (3, 3)$ $(0, 0)\to (0, 1)\to (0, 2)\to (1, 2)\to (1, 1)\to (2, 1)\to (2, 2)\to (2, 3)\to (3, 3)$ $(0, 0)\to (0, 1)\to (0, 2)\to (0, 3)\to (1, 3)\to (2, 3)\to (2, 2)\to (3, 2)\to (3, 3)$ $(0, 0)\to (0, 1)\to (0, 2)\to (0, 3)\to (1, 3)\to (1, 2)\to (2, 2)\to (3, 2)\to (3, 3)$ $(0, 0)\to (0, 1)\to (0, 2)\to (0, 3)\to (1, 3)\to (1, 2)\to (2, 2)\to (2, 3)\to (3, 3)$

- 3 weeks, 1 day ago

$(0,0)→(0,1)→(0,0)→(1,0)→(1,1)→(1,2)→(1,3)→(2,3)→(3,3)$

This path isn’t allowed because we come back to origin again, I think so without these ones there should be 36 paths with length 8

- 3 weeks, 1 day ago

OIC found new mistake ;)

- 3 weeks, 1 day ago

Edited!

- 3 weeks, 1 day ago

I don’t see any path like this

$(0,0) ➝ (0,1) ➝ (1,1) ➝ …$

One example of a complete path not present

$(0,0) ➝ (0,1) ➝ (1,1) ➝ (1,2) ➝ (2,2) ➝ (2,1) ➝ (3,1) ➝ (3,2) ➝ (3,3)$

(I do silly mistakes all the time, I might have not understood the question too)

- 3 weeks, 1 day ago

There was a problem in my program, I fixed it and found $56$ paths

- 3 weeks, 1 day ago

@Jeff Giff Now I edited My comment

- 3 weeks, 1 day ago