Why doesn't homoskedacticity bias an estimator?

Question: I keep reading that homoskedasticity biases the SE, but not the estimator. Why? I'm imagining a plot, where a bunch of errors are clustered on the top left. That would "pull" the OLS line up  towards there, which should affect the estimator right?
Comment: Do you mean heteroscedasticity? In any event what you describe is not just either of them as you are making it depend on values of your predictor.
Answer: What heteroskedasticity describes is that the variation of the errors may depend on the values of the regressors. That is, that for certain values of $x$ we expect that, while we still expect zero errors on average, any given error tends to be further away from the true regression line in either direction.
The situation you describe rather concerns the situation in which the errors systematically deviate from the regression line in one direction (or in one direction for some range of $x$, and in another for another range of $x$), so that errors would no longer have mean zero for such predictor values, for example due to omitted nonlinearities or omitted variables.
Here is an example in which the error term $u$ of the model is generated such that it correlates with the regressor $X$ (see code below). This causes the scatter plot not to scatter around the true (red) regression line, such that, despite the huge sample size of $n=10,000$, the (blue) estimated OLS line is pretty far away from the true value $\beta_1=0.5$.

<code>library(mvtnorm)
# truth
beta0 <- 1
beta1 <- 0.5

# generate some data with correlation between X and u
n <- 10000
errors <- rmvnorm(n, mean = rep(0, 2), sigma = matrix(c(1,-0.5,-0.5,1),2,2))
u <- errors[,1]
X <- errors[,2]
y <- beta0 + beta1*X + u

plot(X,y,xlab="x",ylab="y")
abline(a = beta0, b = beta1, col="red", lwd=4) # the truth
regr <- lm(y~X)
abline(regr, col="blue", lwd=3)
</code>
Comment: Could you further elaborate what would cause the errors not to have a mean zero?
Comment: @Hutchins, I made some edits, which I hope are helpful.
Answer: Consider a heteroskedastic linear regression with model form:
$$\boldsymbol{Y} = \boldsymbol{x} \boldsymbol{\beta} + \boldsymbol{\varepsilon} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \boldsymbol{\varepsilon}  \sim \text{N}(\boldsymbol{0}, \sigma^2 \text{diag}(\boldsymbol{\tau} ) ),$$
where $\boldsymbol{\tau} = (\tau_1, ..., \tau_n) \in \mathbb{R}^n$ gives the underlying variance scales for the variables.  (To simplify our analysis we will also assume that none of these weightings is zero, which means that without loss of generality, we can let $|\text{diag}(\boldsymbol{\tau})| = 1$.)  The ordinary least squares (OLS) estimator is:
$$\hat{\boldsymbol{\beta}} = (\boldsymbol{x^\text{T}} \boldsymbol{x})^{-1} (\boldsymbol{x^\text{T}} \boldsymbol{Y}).$$
Since $\mathbb{E}(\boldsymbol{\varepsilon}) = \boldsymbol{0}$, this has expected value:
$$\begin{equation} \begin{aligned}
\mathbb{E}( \hat{\boldsymbol{\beta}} ) = \mathbb{E}( (\boldsymbol{x^\text{T}} \boldsymbol{x})^{-1} (\boldsymbol{x^\text{T}} \boldsymbol{Y}) ) &= (\boldsymbol{x^\text{T}} \boldsymbol{x})^{-1} \boldsymbol{x^\text{T}} \mathbb{E}(\boldsymbol{Y})\\[6pt]
&= (\boldsymbol{x^\text{T}} \boldsymbol{x})^{-1} \boldsymbol{x^\text{T}} \mathbb{E}(\boldsymbol{x} \boldsymbol{\beta} + \boldsymbol{\varepsilon} )\\[6pt]
&= \boldsymbol{\beta} + (\boldsymbol{x^\text{T}} \boldsymbol{x})^{-1} \boldsymbol{x^\text{T}} \mathbb{E} (\boldsymbol{\varepsilon}) \\[6pt]
&= \boldsymbol{\beta}.
\end{aligned} \end{equation}$$
It also has variance:
$$\begin{equation} \begin{aligned}
\mathbb{V}( \hat{\boldsymbol{\beta}} ) = \mathbb{V}( (\boldsymbol{x^\text{T}} \boldsymbol{x})^{-1} (\boldsymbol{x^\text{T}} \boldsymbol{Y}) ) &= (\boldsymbol{x^\text{T}} \boldsymbol{x})^{-1} \boldsymbol{x^\text{T}} \mathbb{V}(\boldsymbol{Y}) \boldsymbol{x}  (\boldsymbol{x^\text{T}} \boldsymbol{x})^{-1} \\[6pt]
&= (\boldsymbol{x^\text{T}} \boldsymbol{x})^{-1} \boldsymbol{x^\text{T}} \mathbb{V}(\boldsymbol{\varepsilon}) \boldsymbol{x}  (\boldsymbol{x^\text{T}} \boldsymbol{x})^{-1} \\[6pt]
&= \sigma^2 (\boldsymbol{x^\text{T}} \boldsymbol{x})^{-1} (\boldsymbol{x^\text{T}} \text{diag}(\boldsymbol{\tau}) \boldsymbol{x})  (\boldsymbol{x^\text{T}} \boldsymbol{x})^{-1}. \\[6pt]
\end{aligned} \end{equation}$$
As you can see, nothing in the expected value derivation depends on the variance of the error vector in the model.  Heteroscedasticity affects the variance matrix of the OLS coefficient estimator, but it does not affect the expected value.  Intuitively, this is because positive and negative variation in the (symmetric) distribution of the error terms "balance out" in the expected value.
Comment: Shouldn't we solve the weighted least squares in this case, which is equivalent to the log-likelihood?
Comment: Yes, you would usually use WLS estimation in this case.  However, the question at issue here is whether or not heteroskedasticity biases the OLS estimator.
Answer: I would like to go a bit theoretical on this. One of the most important assumptions for the unbiasedness of estimators is:
\begin{equation}
E(u|x) = 0
\end{equation}
This assumption implies that we expect no variance between a parameter's true value and its estimator. This can also be expressed as:
\begin{equation}
E(\hat{\mu}) = \mu
\end{equation}
with $\hat{\mu}$ is the estimator of parameter $\mu$. This is called the zero conditional mean assumption, and it is distinct from the homoskedasticity assumption, which is:
\begin{equation}
Var(u|x) = {\sigma}^2
\end{equation}
Woolridge (2002) clearly distinguishes between the assumptions of unbiasedness and homoskedasticity. The first concerns the expected value of $u$, while the second concerns the variance of $u$. @Christopher Hanck illustrates a good example of heteroskedasticity: the variation of $\hat{\beta}$ should be spread out unequally along the true $\beta line in every direction.
In your case, when you imagine a bunch of errors is clustered on the top left, such data will violate the unbiasedness assumption as the $E(u|x) > 0$. Yet, it does not necessarily means that $Var(u|x)$ is non-constant.


Middle English or Elizabethan English as a second language?

Question: Are there books, web sites, or language courses designed for English speakers who want to learn Middle English or Elizabethan English in the same way that they would learn a foreign language? It would be fun to be able to understand Shakespeare fluently rather than straining to follow what was being said. Chaucer just seems hopeless without such a course, unless you're a college English major taking your upper-division course on Chaucer.
Comment: This question appears to be off-topic because it is a request for resources
Comment: For Shakespeare, I'd highly recommend you familiarise yourself with The King James's translation of the Bible. And while not a course, as such, Owen Barfield's 'History in English Words' may give you a wider view of the subject. I'd also recommend Clare Asquith's 'Shadowplay' which argues for a recusant code embedded in the words he used.
Comment: Look for the side-by-side editions of Shakespeare.  An example on [Amazon](http://www.amazon.com/Romeo-Juliet-Side-By-Sides/dp/1580495176/ref=sr_1_1?ie=UTF8&qid=1392695594&sr=8-1&keywords=shakespeare+side+by+side).
Comment: @DavidM: I'm asking about language courses, not editions of the works.
Comment: @BenCrowell I understand, but it's a good jumping off point.  In lieu of Rosetta Stone Middle English (which should, but, to my knowledge, does not exist), it will at least give you a good foray into understanding Shakespeare.
Comment: This question is probably [too old to migrate](http://meta.stackexchange.com/q/151890/340816) now, but if you're still interested in newer (possibly better) answers, you could try [Language Learning SE](http://languagelearning.stackexchange.com/), which did not exist when this question was submitted.
Answer: Actually engaging with the works is the main thing. Shakespeare's easy. Two paths:

Buy a good lightly annotated edition—Riverside's pretty standard in US colleges—and start reading. By the time you've gotten through 5,000 lines (about two average plays) you'll be moving pretty quickly, and by the time you've gotten through 10,000 you'll easily get through all but the cruxes which have baffled everybody for 400 years.
Try out for a community or college theatre production. If you get cast, you'll be improvising blank verse by the time the piece opens; if you don't get cast, volunteer as AD or ASM, whatever will get you entry to all the rehearsals. Help the cast learn their lines; many of them will be just as lost as you at first, so you won't feel all that stupid.

Chaucer's a bit harder, but not much. The biggest obstacle is the spelling; you might try Michael Murphy's modern-spelling edition of the Prologue and 12 of the Tales. But I think it's more fun just to jump in and start reading; it's not nearly as alien as you think at first. Baugh's Chaucer's Major Poetry was standard for years, and you can find the 1963 edition second-hand on Amazon for $10 or less.
Answer: To my knowledge, there are no courses specifically built around learning Middle or Early Modern English.  Fear not, however, for they are less difficult than they seem.
Obviously, I cannot speak for everyone, but I have found that simply reading Chaucer is enough to learn his language.  I recommend buying yourself a glossed edition of The Canterbury Tales and working your way through that.  I found that, when I first read it, I understood nothing for about the first four hours of reading over two days.  When I woke up on the third day, however, I understood almost everything effortlessly.  There will always be words that are unfamiliar, but you will become more proficient at deciphering the language.  At heart, learning Middle English is less like learning a new language and more like learning a long-sundered English dialect.
As for the grammar itself, some universities have courses on Old English.  Taking one of those will give you all the information you need to understand Middle English; if you can decipher Old English with great difficulty, then you can decipher Middle English with relative ease.
Similarly, if you can read Middle English, then the language of Shakespeare will be far easier.  His style of writing, however, may still prove difficult.  My recommendation is either to buy an annotated edition of his works or to enroll in a Shakespearean course.  The professor will, at least I hope, explain everything satisfactorily.  Additionally, I have found that, after taking Latin, Shakespeare's constructions make far more sense to me.
There are, of course, online resources for learning the languages, but nothing like a complete course.  You mostly need to know what to look for.  You will do well to learn the subjunctive mood and the T-V distinction, and to read annotated editions with those things in mind.  Less important are chiasmus and grammatical case, but they will still help with comprehension.
I know that this is not really the kind of answer that was wanted, but the unfortunate truth is that there is no comprehensive resource for learning those stages of the language.  The best course of action (or at least the 'tried and true' course of action) is to go in prepared as best you may and slog through it until it makes sense.
Best of luck.
Comment: +0.75 Old English is Beowulf and Alfred; Middle English is Chaucer and Gower. Shakespeare is Early Modern English.
Answer: It's not especially detailed, but this website has a set of lessons for learning chaucerian english.
Comment: It has a link to this site http://sites.fas.harvard.edu/~chaucer/pronunciation/ , which seems more directly related to the question.


Can every manifold with torus boundary be cut?

Question: Let $\mathcal{M}$ be a compact, oriented and connected $3$-manifolds, whose boundary satisfies $\partial\mathcal{M}\cong T^{2}$, where $T^{2}:=S^{1}\times S^{1}$ denotes the $2$-torus. If I "cut" through the manifold $\mathcal{M}$, do I always end up  with a well-defined manifold $\mathcal{M}^{\prime}$ whose boundary is a $2$-sphere? For example, if $\mathcal{M}$ is the solid torus (the genus 1 handlebody), then we can just cut along an embeded disk, whose boundary circle lies purely in $\partial\mathcal{M}$. If $\mathcal{M}$ is a manifold obtained by performing the connected sum of the solid torus with some closed $3$-manifold, we can apply the same logic. But it is also true more generally? In general, manifolds with torus boundary can have a highly non-trivial bulk topology, for example manifold with incompressible boundary, etc.
Comment: The question is unanswerable until you define what you mean by "cut." An example is not a substitute for a definition.
Answer: I'm not sure quite what you mean by "cut". If your question is whether there is always a properly embedded surface $S$ in $M$ such that $M\backslash \backslash S$ has boundary consisting of a single 2-sphere, this is not the case: if $\delta S$ is contractible in $\delta M$, then it cuts $\delta M$ into a once-punctured torus and a disc, so the boundary of $M\backslash \backslash S$ has genus.
Otherwise, $\delta S$ cuts $\delta M$ into a single annulus, so $S$ would need to be a disc to cap this off to form a 2-sphere. But, as you note, many 3-manifolds have incompressible boundary, which precisely implies that no non-trivial curve in the boundary bounds a disc in the manifold.


Is this some fungus?

Question: This is one of the leaves of my neon pothos. It's been turning brown since past 2-3 days. This is the only leaf showing this particular issue. Will the  brown wilting continue in the entire branch or will it stop where the leaf ends? What is the cause? Thank you.
Comment: A small trick: for fungus do always photos on the two sides. On one side it is often more easy to identify. I think it is just rot
Comment: Thanks. The other side of the leaf doesn't have anything else except the wilting. Will the rot continue in the whole branch? How do i stop it?
Answer: The common word for the leaf in your photo is leaf "necrosis". But, that word only means that the leaf tissue has died. It is not possible to determine exactly what caused it. It might be caused by many things - heat, cold, too much light, too little light, dryness of the air, one of many diseases, or just plain "old age" to name a few. You should notice that the leaf is white and lacks any chlorophyll, so the leaf itself does not contribute any energy to the plant. The plant may be simply allowing it to die away.
It is unsightly and the best thing to do would be to remove the leaf. That would make the plant look better and prevent any unknown diseases (if responsible) from spreading further.
https://homeguides.sfgate.com/necrosis-plant-diseases-39504.html

Is this some fungus?


Why did Allah make it seem to christians that Jesus died on the cross?

Question: Before I start I ask this in no disrespectful way and ask for that in return in your replies :) So this is something that has been bugging me for a while. I am a Christian who struggles with faith from time to time and whenever I come to reading up on Islam more and more the one thing that I can't understand is why Allah made it seem to Christians that Jesus died on the cross. My reasons for this are: In Allah doing this he essentially created the faith and as he is all knowing he would know that millions of people would follow Jesus. Secondly the Quran and Muhammad coming many years after Jesus makes it hard for me to believe that these words are true. As he couldn't have seen it for himself. Also, before anyone mentions anything about the bible being unreliable and corrupted I know from lots of research that the bible through the thousands of copies of the original new testament that it is not changed how many Muslims say it has been. Finally, with my understanding the Quran has several different versions but muslims only believe in one? If I am correct. Thank you for your help
Comment: There are multiple questions here. It would be better to delete anything except the main question.
Answer: We know that a Christian will struggle with this topic, that's why Allah says:
29:46
۞ وَلَا تُجَـٰدِلُوٓا۟ أَهْلَ ٱلْكِتَـٰبِ إِلَّا بِٱلَّتِى هِىَ أَحْسَنُ إِلَّا ٱلَّذِينَ ظَلَمُوا۟ مِنْهُمْ ۖ

And do not argue with the People of the Scripture except in a way that is best, except for those who commit injustice among them.

Allah is the One whom Christians call father, who according to Acts is Elohim in Judaism, the God of Abraham:

Acts 3:22 For Moses truly said unto the fathers, A prophet shall the Lord your God raise up unto you of your brethren, like unto me.

The reason for God to put the fake Jesus on the cross and save the real Christ are three:

To punish the Jews who planned to kill Jesus and [verbally] attacked the Virgin Mary.
To test the Christians in their faith, which happened with all Christians approaching Islam.
To see the trust of the Muslims, if they should trust Him about Jesus, or the People of the Book.

The problem of the crucifixion started early in the Old Testament, when God threatened the Israelites to break the covenant of Isaac in Jeremiah 33:

25 Thus saith the LORD; If my covenant be not with day and night, and if I have not appointed the ordinances of heaven and earth;
26 Then will I cast away the seed of Jacob, and David my servant, so that I will not take any of his seed to be rulers over the seed of Abraham, Isaac, and Jacob: for I will cause their captivity to return, and have mercy on them.

Jesus comes centuries later and prophesy to Israel that the Kingdom of God will be taken from them in Matthew 21:42-44, and mentions a nation that God will choose to take the covenant of Abraham, which fulfills Israel's prophecy in Genesis 49:10-12 about the appearance of the Shiloh, the figure whom will inherit the Kingdom of God from the Jews.
Jesus also prophesied the Second Temple will be destroyed in Matthew 24, which happened after the crucifixion with 40 years, and inspecting Ezekiel 33:

25 Wherefore say unto them, Thus saith the Lord GOD; Ye eat with the blood, and lift up your eyes toward your idols, and shed blood: and shall ye possess the land?
26 Ye stand upon your sword, ye work abomination, and ye defile every one his neighbour's wife: and shall ye possess the land?

God promised the Israelites to take them out of the Holy Land if they kept transgressing, so when Jesus came, did they obey?
+600 Years later, Allah explained what happened before the crucifixion:
4:155-157

And [We cursed them] for their breaking of the covenant and their disbelief in the signs of Allah and their killing of the prophets without right and their saying, "Our hearts are wrapped". Rather, Allah has sealed them because of their disbelief, so they believe not, except for a few.
And [We cursed them] for their disbelief and their saying against Mary a great slander
And [for] their saying, "Indeed, we have killed the Messiah, Jesus the son of Mary, the messenger of Allah."

Then when we investigate the New Testament around that crucifixion, we find interesting points:
First, the one who taught Christians about the sin atonement by Jesus death is not Jesus himself, but Saul of Tarsus, Jesus has different teachings about repentance in Mark 1:14-15 and Mark 2:15-17.
Second, Jesus prayed God to save him in the endings of the Synoptic Gospels. Exempli gratia, in Luke 22:43-44, an Angel appeared to Jesus in that prayer, but what was the Angel [actually] doing? ... And what did God reply to Jesus for the prayer?
What the angel did with Jesus is explained in Psalm 91: https://www.kingjamesbibleonline.org/Psalms-Chapter-91/
But what was God's reply to the prayer is not in the Bible, it's in the Qur'an:
3:55
إِذْ قَالَ ٱللَّهُ يَـٰعِيسَىٰٓ إِنِّى مُتَوَفِّيكَ وَرَافِعُكَ إِلَىَّ وَمُطَهِّرُكَ مِنَ ٱلَّذِينَ كَفَرُوا۟ وَجَاعِلُ ٱلَّذِينَ ٱتَّبَعُوكَ فَوْقَ ٱلَّذِينَ كَفَرُوٓا۟ إِلَىٰ يَوْمِ ٱلْقِيَـٰمَةِ ۖ ثُمَّ إِلَىَّ مَرْجِعُكُمْ فَأَحْكُمُ بَيْنَكُمْ فِيمَا كُنتُمْ فِيهِ تَخْتَلِفُونَ

[Mention] when Allah said, "O Jesus, indeed I will take you and raise you to Myself and purify you from those who disbelieve and make those who follow you [in submission to Allah alone] superior to those who disbelieve until the Day of Resurrection. Then to Me is your return, and I will judge between you concerning that in which you used to differ.

Then when we see the ending of Luke 22, the "strange" Jesus makes important statements to the Jewish crowd:

He refused to answer if he is the Jewish Messiah.
When they asked him if he is the "son of god" [i.e. the messenger], he refused to admit anything about his real identity.
In between the words, he said that the son of man is now sitting on the right hand of God, i.e. the real Christ has ascended the heaven.

This is definitely against the Christian belief, we certainly know that, but you must bear in mind that the Gospels are the oral tradition of early Christians who heard about Jesus, see Luke's introduction and the ending of John.
The Gospels and the Torah we have today indeed hold many of God's words, and these words were transmitted by scribes and people of tradition to us, and we as Muslims believe in God's revelation, but we also take caution that the Bible authors were writing what they heard, not the ultimate truth about Jesus and the crucifixion:

Matthew 28:17 And when they saw him, they worshipped him: but some doubted.

Id est, the Disciples didn't literally worship him, they prostrated to honour him, and this was allowed in the old law before Islam stops it, look Qur'an [2:34] & [12:100].
The early Christians doubted the crucifixion, and Allah knows that:
4:157
وَمَا قَتَلُوهُ وَمَا صَلَبُوهُ وَلَـٰكِن شُبِّهَ لَهُمْ ۚ وَإِنَّ ٱلَّذِينَ ٱخْتَلَفُوا۟ فِيهِ لَفِى شَكٍّ مِّنْهُ ۚ مَا لَهُم بِهِۦ مِنْ عِلْمٍ إِلَّا ٱتِّبَاعَ ٱلظَّنِّ ۚ وَمَا قَتَلُوهُ يَقِينًۢا

And they did not kill him, nor did they crucify him; but [another] was made to resemble him to them. And indeed, those who differ over it are in doubt about it. They have no knowledge of it except the following of assumption. And they did not kill him, for certain.

Allah has showed mercy to Christians [who didn't know] before the emergence of His Kingdom, so don't ask about their fate, God is Merciful:
2:62
إِنَّ ٱلَّذِينَ ءَامَنُوا۟ وَٱلَّذِينَ هَادُوا۟ وَٱلنَّصَـٰرَىٰ وَٱلصَّـٰبِـِٔينَ مَنْ ءَامَنَ بِٱللَّهِ وَٱلْيَوْمِ ٱلْـَٔاخِرِ وَعَمِلَ صَـٰلِحًا فَلَهُمْ أَجْرُهُمْ عِندَ رَبِّهِمْ وَلَا خَوْفٌ عَلَيْهِمْ وَلَا هُمْ يَحْزَنُونَ

Indeed, those who believed and those who were Jews or Christians or Sabeans - those [among them] who believed in Allah and the Last Day and did righteousness - will have their reward with their Lord, and no fear will there be concerning them, nor will they grieve.

God tested the Christians with Jesus, in the same way He tested the Jews and the Muslims, and we have no issues if Christians disagree.
Christ was not sent to die for anyone, but to tell you the +600 years difference were worth the wait:

Luke 4:43 And he said unto them, I must preach the kingdom of God to other cities also: for therefore am I sent.


How can I remove the finish of hardwood flooring before installation?

Question: I bought 500 sq ft of used engineered hardwood flooring, about 7 inches wide. It is stained a very dark color and I'd like to sand off / remove the top layer to reveal the natural color.
Any suggestions for sanding each board before laying the floor down?
Comment: You'd need to tell us more about the product.
Answer: Whooaa!
It may be hardwood but it most likely - 95%+ - engineered hardwood.   First 7" is not common at all for pure hardwood and would cost a fortune.   Second you almost never float pure hardwood.
So let's assume it is a nice engineered floor.   The wear layer on these range between 1/32nd to a 1/4" and hardly any of them can be sanded, even once.   So chances are you are going to sand, get beyond the veneer and quickly move to the "plywood" type wood underneath the wear layer.    You will ruin the floor quickly - and you cannot fix it.
Answer: Make sure its not a veneer.
If it's nail-free and doesn't have any other embedded hard things maybe rent a planer
If it's not free of nails it will probably be easier to sand it after it's installed.
Comment: it is nail free, it's "floating" install, tongue and groove together. I do have a gigantic floor standing planer buried under stuff in the shed, I'm gonna give it a go!
Answer: Are you sure it's "hardwood"? If it was nailed to a sub-base, the tongue edge would be fastened to the floor and extremely difficult to remove without breaking the "tongue" off.
I'd also check to see if there's enough wood left from the tongue up to the surface…minus the depth of the dark stain you're trying to remove. (Often the boards have been sanded in the past which reduces this dimension to an unacceptable height.)
Often a major problem with hardwood flooring is that it tends to move and squeak after it's installed. In order to check this condition, you hold two pieces vertical and push one tongue into the other groove. Then hold one board and see if the other board falls to the floor. If so, the lumber is not satisfactory for hardwood flooring. I'd check several boards…about 1/4 the load.
For sanding, I'd install all the wood first, then sand so the edges are all level. (Sanding individual boards will create some boards to be thicker than other boards.)
Do all this testing in the room that it will be installed in…acclimate it for about 2-3 weeks.
Comment: Seems like the "factory" stain and there's more than enough thickness left to sand, something like 5mm. Im gonna try a few boards in a planer and report back, thanks!
Answer: I tested it in the planer, I only took off a tiny amount like 1/32 and it revealed the bare wood under beautifully! Now I only need to get new planer knives so it comes out super smooth, old knives are shot


What is a "TV-L 13" position?

Question: I just received a PhD invitation letter from a German University which mentions that my remuneration will be 2/3 of full TV-L 13 position. I do not know what a TV-L 13 position is (Google is of no help here), and didn't want to be rude, so I am asking here first.
Is this a common position or specific to Germany? If anyone knows, currently how much remuneration corresponds to a TV-L position?
Answer: TV-L is the German public servant remuneration grade table (Tarifvertrag für den Öffentlichen Dienst der Länder (TV-L)). It is how civil servants Germany are graded for their salaries and similar conditions for their work.
Depending on where your position is, you'll be under TV-L West, or East, or Berlin, or Hessen. Something in your letter might specify this. Either way, there is information on the details at the Öffentlicher Dienst website.
Assuming you'd be in West Germany, taxed as a single (i.e., not married or living with a life partner or children), this boils down to a basic salary of €2103/month with a net salary after all taxes and health insurance payments of €1383/month.
This will increase as you remain hired, you'll go up the staircase of salaries, going from 1 to 2 after 1 year, from 2 to 3 after an additional 2 years, etc. Each step is a monthly salary increase of about €150/month net.
Comment: @PaulHiemstra: I was expected to work full time for my half salary. The argument was that I was being paid for my teaching, teaching prep, and the assistance I rendered my advisor; while my own thesis work was in my spare time but mandatory… or something like that.
Comment: Yes, I plugged in 66% in the box at that webpage. It is very common with less than full salaries in Germany -- my own position back when I did my PhD was a 1/2 position on TV-L (Ost) level 11.
Comment: If you are paid a fraction of the full salary, your hours are supposed to be reduced correspondingly. However, since most graduate students don't normally work 40 hours per week at any rate, the actual number of hours to be worked is somewhat open to interpretation. The official number, however, is scaled.
Comment: It is worth noting that I did bring the working hours up with central HR when signing my contract. They told me I had to be at my desk 4h/day every day.
Comment: Just curious, the pay is a fraction of a salary scale, but is the work week also that fraction of, say, 40 hours, or is it a full time position.
Comment: @aeismail: Reduced hours? Good one.
Comment: It is not unusual for research groups with less funds to offer so-called "2/3 (or even 1/2) positions", in which you unfortunately get only a part of the full position salary. I think that Mikael's figure is already for the 66% salary - Mikael, can you confirm it?
Comment: Yes Federico is right, this is especially the case for PhD students. In the page Mikael mentioned, you can also put the percentage of full-time work, in this case 67%). This amounts to about 1400 netto a month (after taxes and health insurance).
Comment: @KonradRudolph This very much depends on the subject. In maths, it is usually 1/2, while in engineering, it is usually a full-time position.
Comment: For those interested in more information: I tried to give a detailed explanation how the calculator works in my answer to a related (but curiously not linked) question: http://academia.stackexchange.com/a/44699
Comment: I've *never* heard of this being paid in full, it's always just a fraction (often 1/2).
Answer: Found this link after Googling for "Tarifvertrag für den Öffentlichen Dienst der Lände" (Thanks to Mike for explaining first )
Tarifvertrag für den öffentlichen Dienst der Länder (Collective agreement for the public sector in the countries)
According to this, 13 is the pay group for Ph.D. students and postdoctoral associates. And the gross pay is from 3200 Euros upwards. (Basically it would be about 2000 Euros for 2/3 of that).
BTW, in one of the invitations, it says "E13". I'm not sure what this refers to but, I guess it's same as TV-L 13.
Hope this helps, and if you took this position, please explain further about TV-L 13.
Cheers....
Comment: "E13" stands for "Entgeltgruppe 13 TV-L" (as found on the contract) that literally translates to "Remuneration group 13 TV-L"

What is a "TV-L 13" position?


Can a homogeneous chemical solution really not be split by centrifuge?

Question: Assuming I have a homogeneous solution such as salt in water. My intuition tells me that gravity or centrifugal forces would affect sodium ions more than water molecules. Theoretically, if I could centrifuge salt water fast enough for the pulling forces to surpass the forces of the hydrogen bonds between salt and water, would I be able to seperate it? Or is there some theoretical reason for why no amount of centrifugal force would be able to split it up?
Answer: The issue is that salt ions, while heavier than individual water molecules (they are after all an ion surrounded by coordinated molecules) are not much heavier, and the diffusion rate due to thermal motion is faster than the settling drift. Hence they do not pile up well at the bottom of the container. Most use of centrifuges in desalination are using them to drive salt water through osmotic filters instead.
Sedimentation equilibrium happens when a suspension of particles needs up in an equilibrium where the sedimentation rate equals the diffusion rate. The volume fraction of the particles is given by the Laplace-Perrin equation:
$$\Phi(z)=\Phi_0 \exp\left(-\frac{4 \pi g \Delta \rho R^3}{3 k_B T} z \right)$$
Here $\Delta \rho$ is the density difference - in this case at most a few times, and $R$ the radius of the particle. Note that if $R$ is very small, then the fraction in the exponential becomes very small, and the concetration changes very slowly with $z$. A criterion is that if $\frac{3 k_B T}{4 \pi g \Delta \rho R^3} \gg R$ there will not really be any sedimentation since diffusion dominates. This seems likely here, unless the centrifuge can make $g$ very large.
Comment: It's also a fact that the sodium and chloride ions in a salt water solution are hydrated.  They are surrounded by water molecules and do not exist as individual ions, as shown here: https://chem.libretexts.org/Bookshelves/General_Chemistry/ChemPRIME_(Moore_et_al.)/11%3A_Reactions_in_Aqueous_Solutions/11.04%3A_Hydration_of_Ions
Comment: @David - Yes, I was aware of the hydration. I actually looked for estimates of the local density of a hydrated ion complex, but did not find any good data then. This paper https://www.sciencedirect.com/science/article/pii/S0921452697004997 seems to suggest $\Delta \rho \sim 2$.


Dust Estimation technique

Question: I'm comparing different coating agents for ammonium sulfate fertilizer granules, coating agent is an additive to limit the dust emission, so I have a new coating agent that is lower cost and more effective, but the problem is I need to prove experimentally that the new one is more effective than the one we use. so is there any way ( experimental technique ) to estimate the amount of dust to prove that the new agent is effective?
Comment: Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer.
Answer: A very simple method for measuring dust in the air is to draw the air through a filter using a pump and then weigh the filter.
Answer: If enough dust is suspended in air then it could impact the optical properties of the air, so you can simply measure changes in the apparent brightness of a light source, picked up on the other end of a controlled environment.
Alternatively, just consider weighing samples (of controlled total mass) before and after some controlled time of exposure to a controlled environment. With precise enough measuring equipment, a loss of mass via dust emission could be detectable.

Dust Estimation technique


Hagen-Poisseuille volumetric flow and Darcy Weisbach equation

Question: For the pressure drop in a cylindrical pipe we can use
$$dQ=2 \pi rdr$$
to arrive at the Hagen-Poiseuille equation
$$Q= \frac{\pi R^4}{8 \mu} \left( - \frac{dp}{dx} \right)$$
but I have also found
$$Q=\frac{\pi d^2}{4} U$$
in literature. Why there are two different formulas for volumetric flow rate $Q$?
Comment: In your first equation for dQ, you are missing the axial velocity v(r).
Answer: Your first equation should read $$dQ=2\pi r v(r) dr$$where $$v(r)=2U\left[1-\left(\frac{r}{R}\right)^2\right]$$and where U is the average velocity.  This leads to your third equation $$Q=\pi R^2U=\pi\frac{d^2}{4}U$$The Hagen-Poiseulle equation gives the average velocity as a function of the pressure gradient:  $$U=\frac{R^2}{8\mu \left(-\frac{dp}{dz}\right)}$$These lead to your second equation.
Answer: The Hagen-Poiseuille equation
$$ -\frac{d p}{dx} = \frac{8 \mu Q}{\pi R^4}$$
can be derived analytically assuming laminar steady-state flow of an incompressible and Newtonian fluid in a pipe of constant cross-section. As axisymmetry and steady-state are assumed in the derivation, the description fails for low viscosities $\mu$ ("low damping") and large radii $R$ as the pipe flow might turn turbulent for
$$ Re_D \geq Re_D^{crit} \approx 4000 $$
with the Reynolds number in terms of the tube diameter $D = 2 R$
$$Re_D := \frac{U D}{\nu} = \frac{\rho U D}{\mu}.$$
It allows you to determine the pressure drop from the volumetric flow rate or vice versa for any flow that fulfills the previously mentioned assumptions. For any flows that do not fulfill these requirements you might find empirical correlations (approximations) such as the empirical Darcy-Weisbach equation that might account for turbulent pipe flow (again with constant cross-section) or the Ergun equation for flows in porous media.

The formula
$$Q = \frac{\pi D^2}{4} U$$
on the other hand holds for any one-dimensional incompressible flow
$$Q = \frac{dV}{dt} = \frac{d (A x)}{dt} = A \underbrace{\frac{dx}{dt}}_U = A U.$$
In particular for a pipe flow you get $A = \frac{\pi D^2}{4}$. It is a basic manifestation of the one-dimensional incompessible continuity
$$ \dot m = \frac{dm}{dt} = \frac{d (\rho V)}{dt} = \frac{d \rho}{dt} V + \rho \frac{d V}{dt}$$
for constant density $\frac{d \rho}{dt} = 0$. For your formula you basically assume a constant velocity across the entire cross-section but this approach may also be extended to a cross-section with an arbitrary velocity profile by averaging over the cross-section.

Summing up: Both are formulas allow you to determine the approximate volumetric flow rate (with several limitations) from the pressure drop or the velocity profile. As see you can see two different formulas with different parameters, different assumptions and thus different limitations.


Geocentric Ecliptic to Perifocal Coordinate Transformation

Question: I'm self-studying elementary orbital mechanics and am experimenting with transforming satellite position and velocity vectors between different coordinate systems.  I know there are coordinate transformation matrices between Geocentric Ecliptic and Geocentric Equatorial coordinates (simple rotation around one axis), and between Geocentric Equatorial and Perifocal (P, Q, W) coordinates (utilizing inclination, longitude of the ascending node, and argument of periapsis data).  But I can't seem to develop a single coordinate transformation matrix from Geocentric Ecliptic directly to Perifocal.  Is there an Euler angle rotation sequence that accomplishes this?
Answer: After thinking about this problem further I finally figured out that making the coordinate transformation from ecliptic to perifocal is nearly the same as from geocentric to perifocal.  The only difference is that you use an inclination value 23.4 degrees less, which is the angle between the ecliptic plane and the equatorial plane.  Not sure why I didn't see in the first place.
Comment: Don't forget to check your answer as accepted so they close the question.


want email from my server (postfix) to an email address on my domain to be delivered to google apps

Question: I have google apps for receiving email.  I get inquiries from people on info@[my-domain.com], which email is hosted on google.
Sometimes, I want my rails set-up to send emails from my own server, and that works fine.  But when I want to send to an email address on my own domain, such as email@example.com, postfix sees the my-domain.com and tries to deliver locally.
I understand that's normal, but I'd like to have those emails go to google apps rather than try to be delivered locally.
I know there's a postfix config file for aliases, but here, the email addresses are the same, just need to tell postfix not to try to deliver locally.
Any way to do this?
Answer: It sounds like you have two mail servers set up to act as the primary destination for email to your domain: Google Apps and your postfix server. You can't do that because, as you've found, mail sometimes gets delivered to one server and sometimes the other.
Presumably you want Google Apps to be the primary destination. That is, mail for your domain should go to the Google servers, not yours. You will need to re-configure postfix so that it is not the mail server for your domain.
Edit the /etc/postfix/main.cf file and look for the mydestination line. Remove your domain from that line.
I don't normally use postfix, but I think if the line looks like this, you'll be good:
mydestination = $myhostname localhost.$mydomain localhost

Let's say your server name is "test1" and your domain is "example.com." The following addresses would be delivered locally:
info@test1
email@example.com
info@localhost

But mail to email@example.com would go to Google Apps because postfix is not configured to accept mail for simply "example.com."
Comment: Thank you, was looking for the exact same thing and your solution hit the spot.
Answer: I get around it by doing this http://souptonuts.sourceforge.net/postfix_tutorial.html.  Basically have that mail sent through one of your google domain accounts instead of locally.
Answer: Either, as Barry Brown suggested, tell postfix that my-domain.com is not local by removing it from $mydestination on the postfix box, or if that's not practical, use virtual aliases in Postfix to rewrite that specific address (firstname.lastname@example.com) to the google-hosted address you want to deliver it to.
Virtual aliases in Postfix are not just for the virtual alias address class; they are a general-purpose pre-queue address rewriting mechanism. Sendmail-style aliases (depending on your distribution, either /etc/aliases or /etc/postfix/aliases) are used by the local delivery agent and only apply to the local address class. You could, of course, use sendmail-style aliases to forward mail for "info" to some-address@your-google-hosted-domain.
The documentation at postfix.org is pretty good. Try
http://www.postfix.org/STANDARD_CONFIGURATION_README.html
http://www.postfix.org/ADDRESS_CLASS_README.html
http://www.postfix.org/ADDRESS_REWRITING_README.html
http://www.postfix.org/VIRTUAL_README.html


Why was the Sea of Galilee called so?

Question: We see the mention of a freshwater lake of 167 km square in Israel called as the Sea of Galilee or the Sea of Tiberias at Mtt 4:18, Mtt 15:29, Mk 1:16, Mk 7:31 and Jn 16:1. I wish to know the logic behind calling a lake a sea.
Comment: I'm voting to close this question as off-topic.
Comment: I'd be interested to know what the Greek name was. Because the word "Sea" here is just what the Bible translators used to put the Greek into then current English.
Comment: Removed references to "error" and "Catholic Church" as this has neither to do with either errors or the Catholic Church.
Comment: @djclayworth good point. I'll add that to my answer.
Comment: It was interesting to research this question, see below. (+1).
Answer: This is not an unusual usage, nor one that needs a specifically religious explanation. "The Sea of Galilee" is the standard English translation of the original Greek θάλασσαν τῆς Γαλιλαίας ("thalassan tes Galilaias"); that is, "the θάλασσα of Galilee"). One sees this usage, for example, in Matthew 4:18.
Liddell and Short, a commonly used Greek-English lexicon, defines θάλασσα as "the sea", using primarily references to the Mediterranean.
Merriam-Webster gives a usage of "sea" to mean

a great body of salt water that covers much of the earth

that is, a synonym of "ocean". However, it also describes "sea" as used to mean

an inland body of water—used especially for names of such bodies

It is in this sense that the body of water you mention is called "the Sea of Galilee".
Comment: I think another issue is that we too often try to impose our very well defined and regimented world today (filled with borrowed words and refined meanings from many languages) onto ancient civilization (and then wonder why they did what they did).  I wouldn't be at all surprised if 2,000 years ago θάλασσα simply meant "a large body of water."
Answer: θαλλω, thallo, Strong 330 is the Greek word used in relation to plants, that they 'flourish', as described in Thayer's Lexicon. It may well be that the word was used, not of individual plants, but of fields of growing crops.
A field of flourishing corn or wheat, stretching out before the eyes, moving and rippling in the wind, appears like a body of water.
Thus the word θαλλασσα, thallassa, may not refer to the size of the body of water, it may just refer to the characteristics of a large body of water in the way it appears and in the way it moves.
The θαλλασσα (the 'sea') of Galilee at 33 miles (see Wikipedia) is large enough to have an horizon. Which only requires a distance of about three miles, when viewed at ground level (see Wikipedia). One cannot see the farther shore. Thus 'sea' seems, to me, a perfectly correct translation.
It is a body of water, moving in the wind, rippling like a field of standing corn, and stretches as far as the eye can see.

If this derivation and interpretation is correct, then it would have implications in those instances where it is mentioned in scripture - the underlying meaning of flourishing crops and plentiful supply of food.
And there may well be a spiritual allusion in the fact (as reported by Wikipedia) that the sea of Galilee is freshwater, so crops could flourish right up to (and, possibly, into) its very waters.
Comment: Do you have any evidence that the two Greek words are related?
Comment: @MattGutting The close similarity of the words would lead me to expect someone to prove that they are _not_ related.
Comment: The Greek word *thallos* comes from [an Indo-European stem meaning "to bloom"](https://www.etymonline.com/word/thallus#etymonline_v_39145). The IRS *thalassa* comes from [a word that appears to have been used in the area of Greece before the Indo-European speakers came there](https://www.etymonline.com/word/thalasso-#etymonline_v_49491).
Answer: It's fairly simple.  The Sea of Galilee is the second lowest body of water under sea level.  The lowest is the Dead Sea.
The reason they are called "seas" is because of their salinity content.  In the Sea of Galilee's case, the weight of the fresh water suppresses the salty springs under her.

[because of the drought and lower lake levels] In February 2018, The city of Tiberias requested a desalination plant to treat the water coming from the Sea of Galilee ...
  -ibid-
The Sea of Galilee is at risk of becoming irreversibly salinized by the salt water springs under the lake, which are held in check by the weight of the freshwater on top of them.
  -idid-

At the same time, the brass laver in Solomon's temple is also called the sea.

And the pillars of brass that were in the house of the LORD, and the bases, and the brasen sea that was in the house of the LORD, did the Chaldees break in pieces, and carried the brass of them to Babylon.
  2 Kings 25:13

So, it's not like the wording of sea is a definitional or geographic error of distinction.
Comment: Although I agree with you that the Sea of Galilee is saline, and I agree that your sources demonstrate that statement, I don't think they demonstrate that it is called "sea" *because* it's saline. Can you add a source that shows that connection?
Comment: I was of the opinion like OP that Sea of Galilee is freshwater what source do you have that the SOG was salt water?  https://www.google.com/search?q=sea+of+galilee&ie=UTF-8&oe=UTF-8&hl=en-us&client=safari.   Wikipedia states it is freshwater
Comment: The sea being at risk of riding salinity in 2018 is not relevant to the question
Comment: If one assumes that things remain static, what happens in 2018 may have no bearing on what happened in the time of its naming.  OTOH, it's obvious there is drought and change, which may account for the word.  In my answer, I also noted the wording of "sea" is not an error.

Why was the Sea of Galilee called so?


Skipped והוא רחום in Tachanun

Question: If one skipped והוא רחום and the extra paragraphs in Tachanun on Monday and Thursday should he go back to say them if he finished Tachanun or even the rest of Davening?
Comment: https://judaism.stackexchange.com/questions/23490/im-in-the-middle-of-tachanun-when-they-take-out-the-torah-what-do-i-do
Comment: @GershonGold I don't see anything in that question that is relevant to answering this one. What would be an accurate definition of poretz geder ?
Answer: See Mishnah Berura commentary #3 on O.C. 134:1. He explains that one who didn't say Vehu Rachum at all is called poretz geder - "breaching the fence".
The term poretz geder is used regarding anyone who violates a strongly established custom. Even if the environment or conditions that established a custom no longer exist, we are extremely reluctant to abolish the custom without the ruling of a Sanhedrin. This term is used selectively, and it seems that it's a fairly severe term.
While there is nothing specific in O.C. stating what to do if one accidentally skips Vehu Rachum, I think that the labeling of someone as a poretz geder would obligate him to repeat it at some point during davening.
Comment: What are your sources for the second paragraph?
Comment: @mevaqesh My apologies. I had the site on Friday, and I forgot to add that. It was from a book on Google books. I'll try to hunt that down.

Skipped והוא רחום in Tachanun


LED power consumption in theory and reality

Question: In theory if one LED consume 10mA so 17 parallel LEDs consumed 170mA, but in reality when i connect 17 parallel LEDs they only consumed 100mA not 170mA
why there are difference between theory and reality?
Comment: How much voltage does an LED produce when light is hitting it from its neighbour? Will it be enough to significantly reduce the forward current?
Comment: @Andyaka I would be surprised if that effect was on the same order of magnitude of the issues mentioned.
Comment: Note: The intensity of the light recorded in the image is visually greater in the set of 9 to the left of the bridging jumpers in the center of the power rails. This makes it nearly certain that [Passerby's point](http://electronics.stackexchange.com/a/222432/53747) of there being resistance in your setup and a drop in the voltage between your power input and, at least, the second set of LEDs.
Answer: Your PSU meter is only has resolution to 0.01 A (10 mA). The actual current could be anywhere between 5 mA and 15 mA for the single LED.
Switch your yellow multimeter to mA range, connect the leads into the correct sockets and wire the multimeter in series with the one LED and get a more accurate measurement.
Paralleling LEDs in this fashion is not recommended. The ones with the lower forward voltage drop will hog the current. Either connect them in series with a current limited supply or put a resistor in series with each LED to limit the current.
Answer: transistor and Passerby have both made perfectly good answers to the question you've asked, but let me try something a bit more comprehensive.
You seem to have goodly number of LEDs, and if you have a few spares, try this experiment. Drive 1 LED at 1.9 volts. Record the current. Increase the voltage to 2.0. Now try 2.1. You'll see that the current increases very rapidly, and I'd be surprised if 2.1 volts doesn't kill the LED. Now replace the LED with a 200 ohm resistor and repeat the test. This establishes that current rises much more rapidly with an LED than with a resistor once the turn-on voltage is reached.
Now, here's something you don't know - for a fixed voltage, the current through an LED will increase as the LEDs temperature increases.
Because it's getting hotter, its current will increase, and so will its temperature. Which, of course, means that its current will increase still more. You can see where this is leading - the technical term is thermal runaway. So this leads to the first and most important rule: never try to drive an LED from a voltage source. Always limit the current. This is most easily done by providing a higher voltage and using a current-limit resistor in series. In your case, a 5-volt supply and a 300 ohm resistor will give about 10 mA safely.
Furthermore, your setup shows that you got lucky in your choice of LEDs - they all seem to be about the same brightness. As Passerby stated, this is not generally true. So don't tie a bunch of LEDs together and drive them from a single resistor. Doing so will invite a range of brightness in the LEDs. If you don't want uniform brightness, you might think that this is OK, but there is one more thing to consider.
Let's say you have 10 LEDs in parallel, each drawing (you hope) 10 mA, for a total of 100 mA. To do this you use a 5 volt supply and a 30 ohm resistor. You're fine with the non-uniform brightness. Is there a problem?
Quite possibly. Just as the LEDs are not uniform in brightness for the same voltage, neither do they draw the same current at the same voltage.
Let's say that one of the LEDs naturally draws a bit more current than the others at the common voltage. This means that, since power equals voltage times current, it dissipates more power than the others, and this means it will get hotter. In turn this drops its voltage more, and it draws more current. In the worst case, the weakest LED will hog more and more current until it burns out, and it will probably fail open. This means that the next-weakest LED will start hogging current, and in the worst case the process will continue until all the LEDs are dead. This process can occur with other components as well, and has gained the nickname "firecracker mode". It is made possible in this case by a current limit which is set too high: that is, the 100 mA current limit set by the 30 ohm resistor allows a worst-case current distribution to kill the LEDs.
This leads to the other rule you should follow: limit the current to each LED separately. This usually means one resistor per LED, or string of LEDs in series. For instance, if you have a 12-volt source, you could put 4 or 5 LEDs in series, and use a single resistor to limit the current in the string. You can often get around this for small numbers of LEDs, as long as you are aware of the consequences. With 2 LEDs in parallel, you probably don't have to worry about firecracker mode failures, since not many LEDs will die at twice the normal operating current, but you will still probably get unequal brightness. The more LEDs you put in parallel, the greater the odds of catastrophic failure. The choice is up to you, and you will probably want to take chances until you've been burned a few times.
"Good judgement comes from experience. Experience comes from bad judgement."
Comment: All your missing is the keyword `led thermal runaway`
Answer: You are assuming that each of these leds have perfectly identical IV curves. The stated specs are nominal, typical figures, and there will be variations.
One LED may be 10mA at 1.9 VF, but another may be 8 or 12 mA or different at the same VF. That's not even taking brightness into account. Two leds with the same IV curve can be noticeably different in color and brightness too.
You also have to account for your supply's precision or rounding. It only measures to the 100th of an Amp. Not enough for proper single milliamp range.
Also take into account the resistance of the breadboard you are using. If you measure the voltage across the first led and the last led, you may notice a difference.
You should use a good ammeter or multimeter in current mode, and individually measure each of the leds in this circuit to see how much each led is actually consuming.
Answer:
The simple answer is rounding error with only "1 significant figure" in 0.01 A which ought to read 0.0058 A
But you can now compute the current 100/17=5.8mA per LED due to lack of 3 significant figures from a single LED reading.

Furthermore you can predict the current rise with voltage rise.
Nominal 5mm Ultrabright LED has internal ESR of 15 Ω.  With 15 LEDs in //, the ESR would be ~ 1Ω. ( & 17 slightly less.) Thus every precise rise of 0.10 V results in a rise of ~0.10A which suggests the "knee" of the Vf curve is 1.8V, where ESR rises dynamically.
To safeguard against mismatched ESR in LEDs, I recommend adding a minimum of 50% of the ESR or 8Ω approx when driving them to max in parallel.
This affects Vf vs If and can have a narrow tolerance <1% from a single batch or wide tolerance on the high side from mixed batches. ergo this affects current sharing and only becomes significant when self heating reduces the Vf.  This difference is accelerated with rising current above 20mA especially where the internal threshold voltage reduces (Shockley Effect) thus the voltage across the internal ESR bulk resistance rises and draws more current from the supply's constant voltage.
IN effect, LED's are just as accurate as Low voltage Zeners, which also have similar tolerances, often worse, due to rising improvements in supplier quality in high luminance LEDs.
THe approximate formula for this RED LED becomes

Vf=1.8+If*ESR

Naturally adding a series small series R eliminates the sensitivity w.r.t. mismatch induced "current sharing diode thermal runaway".
NAturally efficiency is lost by adding a small series R but at the benefit of stabilizing the expected current.
Now the formula becomes;

Vout = 1.8 + If*(ESR'+Rs)

... where Vout is a driver or Vcc which also has ESR that could be included with the ESR' above. e.g. 5V CMOS is ~50Ω while CMOS <=3.3 max Vcc is ~ 25Ω ESR.
. then choose If and solve for Rs.
But most people simply use the nominal Vf@20mA and compute RS from

Rs= (Vcc-Vf)/If

then choose If and solve for Rs using worst case maximum Vcc.

ESR is simply a convenient term for differential resistance otherwise known as RdsOn in CMOS and MOSFET's.

For white 5mm LEDs
it is Vf=2.85+If*15Ω
for nominal good parts with similar tolerances.
Answer: I think as resistance of individual LED is greater and as we connect them in parallel So, resistance in parallel is decreased from individual value that's why current of 10 LED is less.
1/Rt = 1/R1 + 1/R2 + ..........
Comment: Your explanation would explain why LEDs in parallel should draw more current, not less.  Resistors in parallel have a lower total resistance, so more current will flow.


Is there a hard upper bound to the deBroglie wavelength of a particle with vanishing momentum?

Question: This is probably a stupid and simple question, but does the heisenberg uncertainty principle set this upper bound? That knowledge of the momentum is limited, so it can't reach a very low value and thus have a very large (visible) debroglie wavelength? I am figuring if you wanted to test this on a macroscopic particle you would need it frozen to near-absolute zero, but I assume QM comes in and makes it impossible to see visible wavelengths with the naked eye. Thanks!
Comment: possible duplicate of [Validity of naively computing the de Broglie wavelength of a macroscopic object](http://physics.stackexchange.com/q/57390/)
Comment: Interesting, one of the comments leads off to the question I pose:

"You are correct, but I don't know if it is due to the present limitations in knowledge or technology or there is a fundamental theoretical limitation of decoherence. In the first case it might be possible in the future to increase the experimental bounds where interference is observable."

 I suppose my question is better framed in terms of decoherence.
Answer: No there isn't.
QM imposes limitation on the accuracy of the "measured" momentum, but that doesn't mean at all that in some moment of time it can't be smaller than what Heisenberg principle tells us, so de Broglie wavelength can be any value (maybe up to universe' scale, but that another question), indeed, we can generate photons of any wave length.
BUT don't mix photon's wave length with de Broglie wave length: Photons are actually exception because they are bosons and massless, in other words, deBroglie wave length is not a physical thing that can be measured by it self, it's actually wave function's wave length, i.e it describes probability wave length, and you can't measure it directly, maybe only indirectly by determining how big/small the objects that particular particle will interact with at highest probability (roughly speaking).


How to properly use my Multi effects processor which has no send/receive with a guitar amp? (in terms of tone)

Question: I've just bought my first multi-effects processor which is the "Zoom G1X Four" and it has no send/receive for an effects loop. It only has input, output and AUX Input. How should I use my processor with the amp on stage? Should I turn off the cabinet mic of my processor? Should I connect my processor with the amp in a specific way like connect the processor with the amp cabinet replacing the amp head? (as the option for fx loop isn't available) or do something else? I'd describe myself as an intermediate guitarist but I'm pretty new to electric guitar area. So, I still have many misconceptions. Please help me out.
Answer: Only you can answer that one. With only guitar in, and processor out, it can only go in series with your amp. Which appears to have input only. That means any sound the guitar sends into the amp will be sort of re-processed, tone-wise, by the pre-amp, which will send that straight to the power amp part, and on throug the speaker/s.
You know what sort of tones you want for stage work, so you will have to play around with it, balancing what the effects produce with what the amp tone controls do. If yu are using two or three different effects simultaneously, it may be possible with the Zoom to put them in a particuar order. By cahnging the order the signal goes through, you may find better (or worse) sounds. You'll have to experiment. But that's part of the fun - isn't it? Also bear in mind that a fabulous sound you create in your front room may well not be the same fabulous sound that appears on stage at the next gig. Rooms have an uncanny knack of changing tone, etc.
Comment: Seconded - don't try to pre-program compressor settings in the living room for live work… unless you really want to try holding down the squealing on stage ;-))
Answer: It depends on what you're looking for, and what's available at the site. I could see using this device in a variety of ways.
First, I'll say that I looked up the device and it costs $90. I have analog OD pedals that cost twice that. So if you can get any kind of full signal through this thing, that's kind of amazing right off the bat. But I will assume the reason you bought this device and are committed to using it, is budget.
Moving on, I'll give three options...
...it has amp models in it. It says "up to five effects simultaneously", but I'm assuming one of those is going to be the amp model, meaning you get four other effects. Still, that's not bad. I can confidently get away with almost any live gig if I only have four effects, even three will do the job if that's all I've got.
It also says you can put them "in any order". I will assume this means that you can put effects post-amp. That's not insignificant to your sound at all, it gives you sonic options. Not an FX loop that's true, but it is some flexibility. For instance, if one of your effects is an EQ, and you put that post-amp you can pretty robustly adjust your tone (e.g. boost the mids, cut the bass and high end). You could also put your reverb post-amp. That only gives you two front-of-amp effects, but it might be worth cutting back the fireworks to dial in a decent tone.
So, option 1: run the device straight into a board. You'd hear yourself through a monitor. Alternatively, if you're just jamming or working a venue without monitors etc, you could run the device out to a full-range-flat-response speaker (you would not want to run into an amp, because you are already modeling one in the device). A decent speaker of this nature can cost you a couple of hundred bucks on the low end, and it will have more than enough decibel horsepower.
Anybody that tells you the above setup is unrealistic or is guaranteed to sound like shit, probably doesn't have a lot of experience operating this way. I've been running modelers since the Line 6 Guitar Port. I've owned Digitech, Roland, PODs, and now the Helix and Helix Stomp, the latter being a device not much bigger than your Zoom (though admittedly a higher quality device, you get what you pay for). I have run the Stomp direct, and/or into a full range flat response speaker, many times. Some years ago, yes, modelers were about convenience and "lots of effects for little money." But the quality was dodgy. That's over now. An up-to-date modeler, even a cheapy, is usable these days. Sure, Bonamossa wouldn't do it, but I'd be willing to bet if he had to, he'd make it work.
Anyway, after working with the device for a while, you find a usable amp-modeled sound, and off you go. If I know they have a PA with monitors, I just bring the device, an expression pedal, and my guitar. If I'm not sure they have a monitor for me, I'll bring a speaker, and depending on the setup, either Y-out the device (one split to the board, the other to my speaker), or just run into my speaker and let 'em mic it.
This is by far the most portable, and cheapest, way to get the full bang for your buck out of the device. I don't know this device, but I do know a fairly well respected NYC guitar player (specializing in the Beatles) that used a Zoom device the way I describe above, and his sound was always acceptable.
Option 2: the device is just front-of-amp. You use it like a pedal board and run it into an amp of your choice. I'll make a point here that I have consistently found to be true:
A guitar player's sound primarily relies on the amp. Not the guitar, not the pedals. It is all about the amp. I can take a $300 dollar guitar that stays in tune, run it through a good tube amp (none of which are "cheap"), and sound fine. But hand me a $2.4k Les Paul and run it through a Gorilla, and I will sound horrible. Period.
The principle; do NOT attempt to fix your sound with pedals or an expensive guitar. If you are going to play through an amp, INVEST IN THE AMP. It took me years to realize this because I never had the money all at once to buy a decent amp. But the day I did, I knew: it's all about the amp.
Anyway, that's the most expensive way to use this device, because it relies on the amp (you are not using an amp model, just the effects in the device).
Options three, which exists nowadays but did not exist in the past, and is ultimately how I would use this device probably because unless I'm wrong, the amp emulations are probably not the quality I'd go for (though I don't know this device well enough to say that for sure, but it's $90 bucks...):
Get a lunchbox head. I highly (HIGHLY) recommend the Orange Microdark, specifically for four reasons: it is tiny (laughably so, but don't be fooled), it has an FX Loop, it has a headphone jack that also has cabinet emulation, and it sounds GREAT. Of course if Orange isn't your thing, there's lots of other options, but many of them don't have a cab-emulated out and/or FX loop. This one does, which is kind of incredible.
Done this way, you can run the Zoom into the Orange, use the FX loop on the Orange if you have any pedals you want to run this way, AND you can either run the head into a regular amp cab, or (lots of people don't know this) you can use the headphone out to run direct into a speaker or a board.
I say this with authority because I have done it, people have heard it, and they can't believe it:
I run my Stomp, into the Orange, with a reverb in the FX Loop, then out the headphone jack (again, which has cabinet emulation), into a Line 6 Stagesource L3t speaker (which is a full range flat response speaker pumping out SERIOUS volume), and I could play any mid sized club confidently. If they have good monitors, I wouldn't even need the speaker, I'd just run the Orange out to the board.
The microdark and zoom fit into a backpack easily, and if you shop around the total cost would be around $300 bucks. With a couple of cables, as long as they have a PA and monitors, you could play anywhere. No PA/monitors, get a speaker, there are plenty of acceptable ones, and just run the Orange out the headphone jack into it. If the speaker is loud, you will be loud.
There's lots of lunchbox heads out there, but quality vs. value, the Microdark is unbelievable bang for your buck. And, it can confidently drive a nice 2x12 cab if you need it to with surprising volume. I use it for silent recording, everything. It's an unbelievable value and only weighs a few pounds.
Also worth noting: option 1 and 3 set you up for silent recording. Option 1, you run your device into an interface and a laptop running Garageband or whatever. Option 3, you run the Orange out the headphone jack into an interface, into a laptop running GB or whatever.
So, lots of options. Again, my preferred (for either live or silent running) is to run the effects device without an amp model into the Microdark, put reverb in the FX loop, and run it out the headphone jack (which has cabinet emulation) into the board and/or a speaker. But if budget is the concern, option 1 should be workable unless the amp emulations in the device are just unusable (which again, can be mitigated somewhat with post-eq, though only to a point).
Comment: I'm kinda using option 1 for the last few months because there were no amps at the gigs I was performing at. (Low mediocre budget shows). But the next gig which was supposed to happen before this corona situation was supposed to have good amps. That's the reason for this post. And I think that option 2 is the most suitable one for my situation.
Comment: Problem there though, is you don't know those amps. House back lines are always tricky. They have a Marshall...which one? Is it well maintained? How's that amp sound in that room? How does my effects signal chain sound through it? I love my tube amps (I have four), and if I can I'll use one, but these days, I have to acknowledge that if I have a choice of using my own signal via a modeler, or an amp I know nothing about, I will get a more consistent sound via the modeler. It's one of the reason I love lunchbox heads with cab emulation. Easy to carry and get me a known tube signal.
Comment: Thanks for all the help. I got to know a lot. I'll try out the things you suggested but can't buy anything in this situation or go out or get an online delivery. So, maybe after Corona if I survive. :3 Thanks, man.


Emacs detaching from launcher

Question: I have just upgraded to Ubuntu 12.04 and I am having an issue with emacs and the Unity launcher. When I start up emacs from the launcher it opens a new window but the typical little arrows do not appear on either side of the emacs icon. When I minimize the emacs window clicking the Unity icon does not maximize it, it opens a new window instead. So once I have minimized emacs there is no way to retrieve my current session. Any ideas on what might be causing this? Thanks.
Answer: This is a known bug of bamf (the window matching library of ubuntu).
Currently I know no workaround for having the emacs icon in the launcher, but I can tell you that when you start emacs from the command-line, you do get a working launcher icon for the current session (arrows, focus, etc.).
Comment: Thank you for linking the error. Strangely enough I restarted my computer a few minutes ago and when I started up emacs the problem was gone. Not really sure why but I guess the problem is fixed :P

Emacs detaching from launcher


Best way to pass options from backend to frontend in Wordpress

Question: i have a doubt that bothers me. I have added options pages in my Wordpress backend. Now i am wondering, what is the best way to pass their parameters to frontend?
For example, let's say i have a color field in my backend that saves its value to mysql.
If i wanted to assign such a color to a div,i could just get the value from mysql and echo it as a variable in my php file:
echo '
';

But is it considered a good practice? I reckon there must be other prettier and better performing alternatives, such as exporting all the variables in a static css file everytime i save my options page.
Would love to hear suggestions!

Edit. I'm adding this to my original question to help others understand what i'm asking:
Hello! I probably wasn't clear in my request. I already know how to create an admin-side options page (in fact, i am using Redux, which is based on the framework you suggested). I also know how to retrieve the variables in my front-end with:
$options = get_option('theme_name');
$single_option_value = $options['unique_id_of_the_admin_option_form'];

What i don't know is the correct way to implement them.
I'll make an example. Let's suppose i want to give my user the possibility of setting a custom background for a section.
Admin-side, i have a media uploader form (unique id: div_background_url ).
Right now, in my front end i have the options retrieved like this:
<?php
$options = get_option('my_theme');
$section_background_url = $options['div_background_url'];
?>

and then the section echoed, with its custom background in the style tag:
<?php echo '

';

But i reckon that this method could generated i huge number of server requests.
Wouldn't it be better if all of the options were saved in a css file whenever the admin changes them, and then having this file loaded in my frontend website?
Hopefully it's a lil clearer now, i'm not a native english speaker so explaining complex stuff sometimes gets tricky.
Answer: Read this tutorial on wordpress, this tutorial also shows how to set and get option.
http://codex.wordpress.org/Creating_Options_Pages
I suggest you to use Option framework
http://leemason.github.io/
This option framework is easy to use and very flexible.


How can I prevent my furnace exhaust pipe from freezing?

Question: My furnace keeps on turning off because my air intake freezes. The reason it freezes up is because my neighbors exhaust vent blows directly on it. What can I do to prevent this?
Comment: There are codes about how far apart furnace air intakes and exhausts must be.  Depending on wording, it may regulate the distance between the outlet of a furnace and the intake of ***any*** furnace...
Comment: Which was installed later, your intake or their exhaust?
Answer: You can extend the pipe along the outside wall away from the neighbor's vent to prevent it from causing the freeze.
you can also have the neighbor's vent extended away from your pipe depending on what is easier/how willing your neighbor is.
the separation can be as easy as hanging a piece of plywood to redirect his air away.


Understanding Text Encoding (In .Net)

Question: I have done very little with encoding of Text.  Truthfully, I don't really even know what it means exactly.
For example, if I have something like:
Dim myStr as String = "Hello"

Is that 'encoded' in memory in a particular format?  Does that format depend on what language I'm using?
If I were in another country, like China, for example, and I had a string of Chinese (mandarin?  My apologies if I'm using the wrong words here) would the following code (that I've used fine on English strings) still work the same?
System.Text.UTF8Encoding encoding=new System.Text.UTF8Encoding();
return encoding.GetBytes(str);

Or would it lose all meaning when you convert that .Net string to a UTF8Encoding when that conversion isn't valid?
Finally, I've worked with .Net for a few years now and I've never seen, heard, or had to do anything with Encoding.  Am I the exception, or is it not a common thing to do?
Comment: good question... Many developers struggle with this, in my experience.
Answer: The .NET string class is encoding strings using UTF16 - that means 2 bytes per character (although it allows for special combinations of two characters to form a single 4 byte character, so called "surrogate pairs") .
UTF8 on the other hand will use a variable number of bytes necessary to represent a particular Unicode character, i.e. only one byte for regular ASCII characters, but maybe 3 bytes for a Chinese character. Both encodings allow representing all Unicode characters, so there is always a mapping between them - both are different binary represenations (i.e for storing in memory or on disk) of the same (unicode) character set.
Since not all Unicode characters were able to fit into the original 2 bytes reserved by UTF-16, the format also allows to denote a combination of two UTF-16 characters to form 4 byte characters - the so formed character is called a "surrogate" or surrogate pair and is a pair of 16-bit Unicode encoding values that, together, represent a single character.
UTF-8 does not have this problem, since the number of bytes per Unicode character is not fixed. A good general overview over UTF-8, UTF-16 and BOMs can be gathered here.
An excellent overview / introduction to Unicode character encoding is The Absolute Minimum Every Software Developer Absolutely, Positively Must Know About Unicode and Character Sets
Comment: Thank you for that link (and the rest of your answer)
Comment: awesome article!!  ("The Absolute Minimum...")
I thought I had a good understanding and still learned something.
Read it!!!
Answer: First and foremeost: do not despair, you are not alone.  Awareness of the treatment of character encoding and text representation in general is an unfortunately uncommon thing, but there is no better time to start learning than right now!
In modern systems, including .NET, text strings are represented in memory by some encoding of Unicode code points.  These are just numbers.  The code point for the character A is 65.  The code point for the copyright (c) is 169.  The code point for the Thai digit six is 3670.
The term "encoding" refers to how these numbers are represented in memory.  There are a number of standard encodings that are used so that textual representation can remain consistent as data is transmitted from one system to another.
A simple encoding standard is UCS-2, whereby the code point is stored in the raw as a 16-bit word.  This is limited due to the fact that it can only represent code points 0000-FFFF and such a range does not cover the full breadth of Unicode code points.
UTF-16 is the encoding used internally by the .NET String class.  Most characters fit into a single 16-bit word here, but values larger than FFFF are encoded using surrogate pairs (see the Wiki).  Because of this encoding scheme, code points D800-DFFF cannot be enocded by UTF-16.
UTF-8 is perhaps the most popular encoding used today, for a number of reasons which are outlined in the Wiki article.
Answer: UTF is a specific type of encoding with multiple different sizes. Each encoding type is how much memory and what representation in that memory the characters will take.
Generally we work with Unicode and Ascii.
Unicode is 2 Bytes per character.
Ascii is 1 Byte per character.
Ascii can be represented in unicode. however Unicode cannot be represented in ascii without being encoded.
UTF encoding uses a special character '%' to tell you that the following is the hex value of an encoded character.
%20 for instance is the character 32, which is actually a space.
http://www.google.com?q=space%20character

placing that url in a browser would UTF-8 decode that string and q= would actually be interpreted as "space character" notice the %20 is now a space.
UTF-16 uses 2 Bytes and is represented as such.
http://www.google.com?q=space%0020character

this example would actually fail as the URI is actually supposed to use UTF-8, But this example demonstrates the point.
The Unicode character would be 0020 or two bytes with values 0 and 32 respectively.
Mandarin would be some type of unicode characters, and UTF-16 would encode the Unicode so it would be representable in Ascii.
Here is a wiki article explaining a little more in depth
http://en.wikipedia.org/wiki/UTF-8

Understanding Text Encoding (In .Net)


Any way to run shell commands on android programmatically?

Question: Is there any way to run terminal commands on my application and then access the data on my UI? Specifically top.
Answer: Check out Log Collector as an example. Here is the relevant file.
The key is here:
ArrayList<String> commandLine = new ArrayList<String>();
commandLine.add("logcat");//$NON-NLS-1$
[...]

Process process = Runtime.getRuntime().exec(commandLine);
BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(process.getInputStream()));

Comment: This is now banned by Google
Comment: so basically if I would like to run top, I could just replace commandLine with top and it should work fine right? I am getting an error so I guess I will need a little more help.. thanks..
Comment: Do I need to surround the Process process = Runtime.getRuntime().exec(commandLine); with a try and catch because I keep getting this throws IOException. I have looked at the java examples seem to handle it that way...
Comment: Yes.. again, check out the link to see everything they do. You definitely need to do error checking - don't expect 'top' to be there on all phones.
Answer: Okay this is what exactly worked for me just in case anyone needs it in the future... :)
Surround in try and catch
try {
    Process process = Runtime.getRuntime().exec("top -n 1 -d 1");
    BufferedReader in = new BufferedReader(new InputStreamReader(process.getInputStream()));
} catch (InterruptedException e) {
    e.printStackTrace();
}

Comment: When I do that followed by String result = null;  result = bufferedReader.readLine(); Log.i("OnClickListener", "result: " + result); It displays only "result:" (the 'result' string is empty). Any thoughts as to why this would be? Also, when I try process = Runtime.getRuntime().exec("/system/bin/ping abc"); instead, the 'result' string is null. Both of those commands work as expected from an 'adb shell' terminal.
Comment: I got it working. The problem was the that the first line from 'top' WAS empty (a new line, to create the table). The case of it returning null when there was actually output was because I needed to get stderror (getErrorStream) instead of stdout (getInputStream).
Comment: Sorry @DavidDoria, I have not touched android in 2 years now. It was something I tried my hand at while in college. You would be better off posting it as a question.
Answer: We, can execute commands as follow, i was succesfull in doing this....! try like this, here we need to specify the complete path of command. to get the complete path of commmand, at ur terminal (android) type
*$ which ls
/system/bin*
try {

    // Executes the command.

    Process process = Runtime.getRuntime().exec("/system/bin/ls /sdcard");

    // Reads stdout.
    // NOTE: You can write to stdin of the command using
    //       process.getOutputStream().
    BufferedReader reader = new BufferedReader(
            new InputStreamReader(process.getInputStream()));
    int read;
    char[] buffer = new char[4096];
    StringBuffer output = new StringBuffer();
    while ((read = reader.read(buffer)) > 0) {
        output.append(buffer, 0, read);
    }
    reader.close();

    // Waits for the command to finish.
    process.waitFor();

    return output.toString();
} catch (IOException e) {

    throw new RuntimeException(e);

} catch (InterruptedException e) {

    throw new RuntimeException(e);
}

Answer: it also depends on what you are running in the terminal... if you are running "cat" on a file you can also do it like this.
final private String MEM_FILE = "/proc/meminfo";

public Long readMem() {
    String[] segs;
    FileReader fstream;
    try {
        fstream = new FileReader(MEM_FILE);
    } catch (FileNotFoundException e) {
        Log.e("readMem", "Could not read " + MEM_FILE);
        return false;
    }
    BufferedReader in = new BufferedReader(fstream, 500);
    String line;
    try {
        while ((line = in.readLine()) != null) {
            if (line.indexOf("MemTotal:") > 0) {
                Log.e("MemTotal", line);
                segs = line.trim().split("[ ]+");
                memTotal = Long.parseLong(segs[1]);
            }
            if (line.indexOf("MemFree:") > 0) {
                Log.e("MemFree", line);
                segs = line.trim().split("[ ]+");
                memFree = Long.parseLong(segs[1]);
            }
        }
        updateMem(); //call function to update textviews or whatever
        return true;
    } catch (IOException e) {
        Log.e("readMem", e.toString());
    }
    return false;
}

EDIT:
There is a perfect example for you in the android labs project called netmeter. There is a class called Top.java that actually does exactly what you want and it is used in TaskList.java to be displayed.
http://code.google.com/p/android-labs/source/browse/#svn/trunk/NetMeter/src/com/google/android/netmeter
Comment: Not cat, I specifically want to run top and get the live results displayed on the screen. I am aware of applications which emulate the terminal on which I have found top working, so I was wondering how I could just pull the results of top and display them on the UI.
Comment: See my edits above for a working example of exactly what you want.
Comment: Hey thanks... Need to spend some time here, but I think this is it... You have been a great help!
Comment: `line.indexOf` should be `> -1` instead of `> 0`. -1 mean not found
Answer: For Kotlin enthusiasts, you can use the following
fun executeShell() {
    val command: String = "top -n 1"
    try {
        val process: Process = Runtime.getRuntime().exec(command)
        // Read the lines using BufferedReader
        BufferedReader(InputStreamReader(process.inputStream)).forEachLine {
            // Do something on each line read
            Log.d(this::class.java.canonicalName, "$it")
        }
    } catch (e: InterruptedException) {
        Log.w(this::class.java.canonicalName, "Cannot execute command [$command].", e)
    } catch (e: Exception) {
        Log.e(this::class.java.canonicalName, "Cannot execute command [$command].", e)
    }
}

You won't even have to take care of closing the buffer, as forEachLine extension function takes care of it.


Ubuntu 16.04 Display Setting while Ubuntu 18.4 scalling is missing, Where is the Scalling?

Question: Here I have Ubuntu 16.04 LTS and I can adjust the scaling. In 18.4 LTS the scaling is missing?????
Answer: Ubuntu switched from the Unity desktop to the Gnome Shell Desktop. Scaling works differently in Gnome Desktop than it did in Unity.

You can set overall scaling, but only by integers (i.e. 100%, 200%) in Settings - Displays
You can further adjust font scaling after installing Gnome Tweaks by changing "Scaling factor" on the Fonts tab.


Name of this plant

Question: Saw this succulent at nursery quite liked it so i purchased it. Looks like sansevieria (Snake Plant) but dwarf there is also little pup coming from side
Answer: Yes this is Sansevieria, the species might be Sansevieria trifasciata hahnii. However, hard to tell for sure. It is clear that your plant is not variegated, you often see Sansevieria with yellow bands, but yours doesn't have those. The plant is very easy to maintain, it doesn't need much water, and half shade is also fine.
Also known as mother-in-law's tongue.
Comment: Thanks @benn I also have the Sansevieria trifasciata with yellow edges growing beautiful every month
Comment: @OmiPenguin, yes me too, I have one with yellow stripes as well. Your plant in the picture might a Hahnii, a dwarf type. You'll have to wait and find out if it stays small.

Name of this plant


View and Synonym hirarchy oracle

Question: The Dba of our company has created views for the tables for all the users.
We have 230 users, he has created 230 views for each tables!
I want to replace this by public synonym and grant select to the users.
Example:
Create public synonym emp to scott.emp
grant select on scott.emp to public;
When I query synony after droping view it works.
Without dropping the view If I query emp oracle does the select on the view.
When we have a view and synony in the same name, what is the hirarchy between this?
Is there a workaround for this problem.
Because when I modify a table I have to correct 230 view scripts!
Answer: The resolution order is described in the documentation:

Oracle Database attempts to qualify the first piece of the name
  referenced in the SQL statement. For example, in scott.emp, scott is
  the first piece. If there is only one piece, the one piece is
  considered the first piece.
A) In the current schema, the database searches for an object whose name
  matches the first piece of the object name. If it does not find such
  an object, it continues with step b.
B) The database searches for a public synonym that matches the first
  piece of the name. If it does not find one, it continues with step c.
C) The database searches for a schema whose name matches the first piece
  of the object name. If it finds one, it returns to step b, now using
  the second piece of the name as the object to find in the qualified
  schema. If the second piece does not correspond to an object in the
  previously qualified schema or there is not a second piece, the
  database returns an error.
If no schema is found in step c, the object cannot be qualified and
  the database returns an error.

View and Synonym hirarchy oracle


How do I move large manta flow files safely?

Question: I have a blend file that has a really large manta flow fluid bake in it. It's saved in another folder. Currently I don't have the capacity to render it and I want to save it on an external hard drive to free up some space. I want to put all the source files and the blend file into the same folder before I move them. How do I do this without screwing everything up. The last thing I want to do is destroy this sim/.blend before I have a chance to render it.
Comment: I actually found I could just update the folder. I saved a duplicate of both the cache and the blend file. Put them both in one folder and then when blender said it  couldn't find them I just updated the folder. And the data worked just fine.
Answer: I think the safest way to do this is to change the file destination of bake files in blender, begin a bake but cancel it and then move the original bake files in place of the old ones
Comment: Cool I'll give this a shot.


RDP fails to connect across L2TP VPN

Question: I have a working L2TP VPN that I can ping all clients once connected, name resolution does not work but I believe that is a separate issue. I cannot connect using RDP between two Windows 10 machines. I can RDP connect from a Windows 10 laptop to an old Windows Home 2012 Server across the VPN, I can also use the following 'telnet (IP address) 3389' to verify the connection to the Windows Home Server. Inside both local LANs, RDP works fine between Windows 10 machines, just not across the WAN/VPN. Both networks connected over the VPN have different IP address ranges. I also have 'Require computers to use Network Level Authentication to connect' turned off on the machines I am trying to connect to. I am using a centrally managed Bitdefender firewall on each machine at both sites. I have opened ports 3389 TCP/UDP for all IP addresses on the local machines, as well as the for the RDP service at '%WINDIR%\system32*svchost.exe*'. (svchost.exe should be mstsc.exe) I have a setting set on the Home Server to allow all versions of RDP to connect but I have not found anything similar on the Windows 10 RDP settings. I have verified that the machines in question are listening on 3389 as well. Any ideas, I am all ears? Thanks in advance for any help.
NEW INFO as of 12/31/2020: Okay, some critical updates and what I have figured out so far. I know the problem is with Bitdefender and allowing edge traversal with RDP. I did several tests and here is what I found. First I turned off all local (machine) firewalls and everything works fine. I then found some articles on configuring the Windows firewall (after turning off Bitdefender firewall on local machines) for RDP and turned on the three rules needed to allow incoming RDP connections. In addition, I discovered that this is not enough you must also allow Edge Transversal (One subnet to another) within each of the RDP protocol settings. Okay fair enough I can get everything to work with the Windows Firewall and RDP across an l2dp VPN connection into the network. The problem is I cannot figure out how to set this up on Bitdefender. Also as a point of clarity, I have laptops connecting via a VPN to a Hardware firewall router that terminates the incoming VPN. Then RDP is used to connect to the user's machine inside the network. Only on the user machine inside the network do I have the rules allowing for incoming RDP connections. The laptops can be in a public or private connection state and have a separate firewall profile/policy that does NOT allow RDP incoming connections. So what I am saying is users are using a laptop to take over their office computers via RDP through a secure l2dp VPN. Any suggestions would be great, thanks in advance. Also, I had the wrong file listed for the RDP application it is mstsc.exe not svchost.exe
Answer: I finally heard back from Bitdefender Enterprise and they sent me a fix. Basically, I had to add a rule to allow traffic from the VPN subnet and make that the first rule in the firewall ruleset. In my case, I just made the remote address 192.168.x.x/25 and allowed that traffic on the local subnet. Once I did this RDP worked just great over the l2dp VPN. I hope this helps other people with this problem. The same rule also fixed name resolution but with a slight modification. I can now type "machine name".local and it goes right to the right machine.

RDP fails to connect across L2TP VPN


Problems on submanifolds

Question: I am learning differential geometry and a basis of the theory of smooth manifolds but i'm feeling a lack of practice in solving problems on submanifolds in $\mathbb{R}^n$ (problems like 'prove that $SL_n(\mathbb{R})$ is a closed submanifold' or 'prove that preimage of a regular value is a submanifold' etc). Books i am reading are also poor in such problems.
Can you offer such problems or give a link to any problem sheets? Thank-you!
Comment: What sources are you using? I like John Lee's "Introduction to Smooth Manifolds". Chapter 8 of this book is fully devoted to submanifolds and it includes a section with problems.
Answer: As a set, the special linear group $SL(n,\Bbb R)$ is the subset of $GL(n,\Bbb R)$ consisting of matrices of determinant 1.
 Since $det(AB) = (det A)(det B)$ and $det(A^{−1}) = 1/det A$
$SL(n, \Bbb R)$ is a subgroup of $GL(n,\Bbb R)$.
To show that it is a regular submanifold, we let $f : GL(n, \Bbb R) → \Bbb R$ be the determinant map $f (A) = det A$, and apply the regular level
set theorem to $f^{−1}(1) = SL(n,\Bbb R)$.
We need to check that 1 is a regular value of $f$. Let $a_{ij}$,
$1 ≤ i ≤ n, 1 ≤ j ≤ n$, be the standard coordinates on $\Bbb R^{n×n}$, and
let $S_{ij}$ denote the submatrix o $A = [a_{i j} ] ∈ \Bbb R^{n×n}$ obtained by deleting its ith row and jth column.
Then $m_{ij} := det S_{ij}$ is the $(i, j)$-minor of $A$. From linear algebra we have a formula for computing the determinant by expanding along any row or any column:
if we expand along the ith row, we obtain
$f(A) = det A = (−1)^{i+1}a_{i1}m_{i1} +(−1)^{i+2}a_{i2}m_{i2} +···+(−1)^{i+n}a_{in}m_{in}$.
Therefore
$∂f/∂aij =(−1)^{i+j}m_{ij}$.
Hence, a matrix $A ∈ GL(n,\Bbb R)$ is a critical point of $f$ if and only if all the $(n− 1) × (n − 1)$ minors $m_{i j}$ of $A$ are $0$. By the above queation, such a matrix A has determinant 0. Since every matrix in SL(n,R) has determinant 1, all the matrices in $SL(n,\Bbb R)$ are regular points of the determinant function. By the regular level set theorem, $SL(n,\Bbb R)$ is a regular submanifold of $GL(n,\Bbb R)$ of codimension 1; i.e.,
$dimSL(n,\Bbb R) = dimGL(n,\Bbb R)−1 = n^2 −1$.
Comment: Thanks a lot! But i meant these problems were examples of problems i need.

Problems on submanifolds