tanach - Why is Chronicles so similar to Kings?

Why is Chronicles so similar to Kings? Consider these two passages:

1. Ⅱ Kings 22


2. Ⅱ Chronicles 34

It's almost the same word for word. Were they originally the same book that got forked out like open source software?

Answer

According to scholarly research, the Book of Chronicles is either based on the Book of Kings, or both works are based on earlier books, which have since been lost. (The book itself names its sources in many places.) It is likely that the book is based on some combination of the above, in addition to commentary (midrash) on the Book of Kings.

I highly recommend that you read the Encyclopedia Judaica article on the Book of Chronicles, as it addresses your question in depth. (Can't post link due to paywall; sorry.) For a list of the sources mentioned in Chronicles, please see the commentary of the "Anchor Bible" or the "Old Testament Library."

For a traditional view on the book, I recommend that you read the introduction in the commentary by "Artscroll" (English) or "Daat Mikra" (Hebrew).

Relevant quotes from the Jewish Encyclopedia:

A superficial examination of the Books of Kings makes clear the fact that it is a compilation and not an original composition. The compiler, or editor, constantly cites certain of his sources. In the case of Solomon it is "the book of the acts of Solomon" (I Kings xi. 41); for the Northern Kingdom it is "the book of the chronicles of the kings of Israel," which is cited seventeen times, i.e., for all the kings except Jehoram and Hoshea (see, e.g., ib. xv. 31); and for the kings of Judah it is "the book of the chronicles of the kings of Judah," which is cited fifteen times, i.e., for all the kings except Ahaziah, Athaliah, Jehoahaz, Jehoiachin, and Zedekiah (see, e.g., ib. xv. 7). Whether the editor had access to these "chronicles," as they were deposited in the state archives, or simply to a history based upon them, can not with certainty be determined. It is generally assumed that the latter was the case (comp. Kuenen, "Historisch-Kritische Einleitung in die Bücher des Alten Testaments," p. 68, and Cornill, "Einleitung in das Alte Testament," p. 123).

Jewish Encyclopedia, "Book of Kings"

It is clear that Chronicles contains matter taken either directly or indirectly from Kings, because it includes verses inserted by the editor of Kings (compare II Chron. xiv. 1, 2 and I Kings xv. 8, 11). Either Chronicles used Kings and "The Book of the Kings," both of which works used the older "Chronicles" (so Driver, "Introduction to the Literature of the O. T." 6th ed., p. 532), or Chronicles used "The Book of the Kings," which had used both Kings and the older "Chronicles," or works based on them.

Jewish Encyclopedia, "Book of Chronicles"

bentching - Why no singular in birchat hamazon for "ours and all that is ours"?

Near the end of the birchat hamazon there is alternate wording for the beginning of a sentence for eating at your own table, or that of another person, but the end of that sentence is always in the plural (see quote below), at least in almost all bentchers. The end of the Horachamon that I refer to is worded "ours and all that is ours". But this ending sometimes does not agree in number with the beginning of the sentence which can read “me and all that is mine" or “head of household”.

So the sentence can read like this, “May the merciful one bless me, all that is mine, ours and all that is ours.” But that makes no sense to me. If the end of the sentence should agree with the beginning of the sentence, why do bentchers not include a singular wording of the end of the sentence? Is the plural wording correct for some reason that escapes me or is there another more proper wording and what might that wording be?

(Related but different question: Why no singular when referring to one parent in the birchat hamazon?)

For example, from Artscroll pg 192:

words - How to say "at this rate"?

One of my friends has been making a real effort talking to me in Japanese every day. I wanted to say something like "If we continue at this rate I will be able to speak by Christmas". The dictionary thinks that at this rate is この分。

So my question is, is it natural correct Japanese if I say

この分に続いたら、クリスマスまで話せるようになるわよ

?

I suspect that not. It feels like there is a word missing like この分のスピードに or something like that.

Answer

There are many ways to say "at this rate" in Japanese but the more common ones are:

「この調子{ちょうし}だと/なら」、「このペースだと/なら」、「このままいけば」, etc.

Any one of these would fit your sentence with no problem.

Regarding 「この分{ぶん}」, you could use it by adding 「なら」 or 「だと」 to it, but not 「に」 as you formed it. You cannot say 「この分に続いたら」, though it was a nice try. You can say 「この分だと」.

Note: It is 「クリスマスまでに」 and not 「クリスマスまで」.

～～までに = by ~~

～～まで = until ~~

Use 「まで」 and you will be saying that you are only allowed to speak Japanese until Christmas. You can speak Japanese after Christmas, too, you know.

halacha - Time dilation and waiting between meat and milk

Suppose Ploni eats some meat. He then gets in a spaceship and accelerates to some significant percentage of the speed of light for a short trip into outer space, and then returns home. At the time when he returns home, exactly six hours have passed from the Earth's reference frame; however, because of time dilation, less than 6 hours have passed for him.

This is not an issue of who is right. On Earth, six hours have actually passed, whereas for Ploni, the amount of time has actually been less than six hours. Now that he has returned home, may he eat something with milk?

Answer

The short answer is no. Waiting between consuming meat and consuming dairy has nothing to do with how much time we perceive to have elapsed but with the experience of the person who consumed it. Spaceman Ploni, who decided to eat meat immediately prior to takeoff (a revolting thought), can still taste it when he returns to earth, despite the fact that his more sensible brother, who ate meat with him but who didn't board the space-ship, is now enjoying a milkshake.

Source:

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  Rambam, Hilkhot Ma'akhalot Asurot 9:28, which gives the reason for waiting six hours as being because of food that is still between the teeth (although see the Kesef Mishna there);

  
  


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  Tur, YD 89:1, which gives the reason as being because of the flavour of the meat that remains in the mouth.

  
  

translation - How to say "to know how to do something"

Is there a generic formula to express "to know how to do something"?

I know how to ask a question in the second person "How do you do something?", e.g.

How do you write "Yasuda" in kanji? 「やすだ」は漢字でどう書きますか。

I also know how to ask

Can he write "Yasuda" in kanji? 彼は「やすだ」を漢字で書けますか。

but I am struggling to put it in the third person:

Does he know how to write "Yasuda" in kanji?

Answer

It's あの人は「やすだ」は漢字でどうやって書くか知っていますか？, generally, to know how to do something is どう（やって）…するか（を）知っている.

several coefficient differences in UV-vis Spectroscopy

Does anyone know what is scattering coefficient, absorption coefficient and extinction coefficient, and how to separate them experimentally?

halacha - Is age a disqualification for Shechita?

Does advanced age disqualify a Shochet from being able to preform the ritual slaughter? If so what is the cut off age?

Related question: What's the youngest that a shochet could be? (lower age limit)

Answer

Strictly speaking, there is no upper age limit, though some have the custom to impose an across-the-board limit of age 70 (perhaps to kindly retire certain aged shochtim who won't admit to their waning stamina, and who cannot be forced out due to political considerations). On the Nirbater Rav's list of policies for the Meal Mart company under his hashgacha, it states that one may not perform shechitah or bedikah (checking for tereifos) after reaching age 70, in accordance with the ruling of the Satmar Rebbe (R' Yoel) zt"l.

orthography - Abbreviating sets of compounds with leading characters in common

I recently asked a question about on- and kun-yomi and in building the title guessed at how the two compounds involved could be contracted; landing on 「音・訓読み」.

Is this indeed the correct way of abbreviating something like 「音読み・訓読み」, and if so, when can it be used?

If not; what construction should be used?

Answer

In general, there is no restriction in making this kind of ad hoc portmanteau compounds, as long as all original words have parallel structure. That said, it's more natural if the non-common parts are contrastive in meaning.

上下水道 "water(works) and sewerage" < 上水道 + 下水道
開閉会式 "opening and closing ceremony" < 開会式 + 閉会式
視触覚 "visuo-haptic" < 視覚 + 触覚

It doesn't need to be exactly two components:

都道府県庁所在地 "seat of the office of 都/道/府/県" (i.e. capitol)

or being the first character:

輸出入 "import and export" < 輸出 + 輸入

But an interpunct (・) is required when the result spelling causes confusion (colliding with existing words):

北{きた}・東{ひがし}アジア "North and East Asia" cf. 北東{ほくとう} "northeast"
環状1・2号線 "the ring road 1/2"

In your case, however, the word 音訓読み is already reserved for "a type of 2-kanji word where the former is read in 音読み and the latter in 訓読み", so you should avoid this wording (but should be understood with aid of the context). Fortunately, as mentioned in a comment, what you mean can be conveyed by another word 音訓.

halacha - Secular Names for Days of the Week

Is there a problem using the secular names for the days of the week?

If there is a problem, is it because:

1) The names originally come from Polytheistic gods

OR

2) The people forbidding them are doing so because they believe we should distance ourselves from anything secular.

I know in addition to the Hebrew names, there are Yiddish names I have seen used.

Answer

Because of the OP's concern, the Pri Megadim actually writes that one should not use the Yiddish names for the days of the week, but this ruling does not seem to be followed. In truth, as other answers mentioned, it is not such a problem because nobody worships those gods anymore.

Moreover, according to the Satmar Rebbe and Rabbi Menachem Kasher, the commandment to start counting the week from Shabbos only means that once a day a person should mention how many days have passed since Shabbos. Because we already do this in the liturgical introduction to the Shir Shel Yom, we need not follow that directive the rest of the day and can use other terms/names for the days of the week.

SOURCE: "Uttering the Names of Idols" by Reuven Cham Klein printed in the Journal of Halacha and Contemporary Society vol. 73, pgs. 5-21.

Why isn't eating milk with chicken kosher?

I remember learning that the reason you don't eat milk with beef is because you shouldn't cook a calf in its mother's milk. However, when you are dealing with two different species, this same logic doesn't seem to hold. Is there another explanation for why this isn't kosher?

shiurim measurements - How much produce becomes bikkurim (first fruits)?

How much produce becomes bikkurim (first fruits)?

Rambam says: Hilchos Bikkurim Chap 2

Halacha 19 How should one separate the first fruits? A person descends to his field, sees a fig tree, a cluster [of grapes], and/or a pomegranate tree that has budded, and ties them with a reed.50 He should say: "These are the first fruits.' They become designated as first fruits even though they are attached to the ground after they have been given that title, even though they have not ripened entirely.51

When they ripen and are reaped from the ground, it is not necessary to designate them again. If he did not designate them while attached or call them first fruits and then he reaped them, he should designate them after he reaps them.52

This implies to me that only some of the fruits are bikkurim.

Rambam continues:

If his entire harvest becomes impure, he should not designate the impure produce as first fruits. Instead, as an initial preference, he should set aside other produce as first fruits for the impure produce. It appears to me that if he does not have other produce, to separate [as first fruits], he should not set them aside to be destroyed.53 Similarly, it appears to me54 that if the first fruits become impure, he should not use them as kindling for a furnace, because they are like objects consecrated for the Temple.55

Halacha 20 When a person set aside his first fruits and they rotted away,56 were taken by others, lost, stolen, or became impure,57 he is obligated to set aside others in place ofthem,58 as [Exodus 23:119] states: '...bring to the house of God your Lord.' This teaches that one is liable to replace them until he brings them to the Temple Mount.59

and now by mentioning the entire harvest I am not sure.

Answer

הבכורים אין להם שיעור מן התורה אבל מדבריהם צריך להפריש אחד מששים והרוצה לעשות כל שדהו בכורים עושהו:‏
The Bikkurim have no measurement from the Torah, but [the rabbis] required separating one sixtieth; and if one wants to make his entire field Bikkurim, he may.

Rambam Bikkurim 2:16

Intuitive interpretation of Fourier transform in beamforming

When applying Fourier transform in time domain the signal will be carried to frequency domain. And when we apply Fourier transform in spatial domain the signal will be carried to directivity domain.

$$ D(\theta) = \sum\limits_{n = \frac{-N}{2}}^\frac{N}{2} v(n) \exp\left(\frac{j2\pi}{\lambda} nd \sin(\theta)\right)\tag{1}$$

And let's simplify $ d = \lambda / 2 $ so

$$ D(\theta) = \sum\limits_{n = \frac{-N}{2}}^\frac{N}{2} v(n) \exp(j\pi n \sin(\theta))\tag{2}$$

I can see the mathematically this is $\rm sinc$ if I take $v(n)$ as a rectangular window. I have no problem with the result.

• 
  

  First $\sin(\theta) $ confuses me extremely how does this $\sin$ performs within Euler's formula ?

  
  


• 
  

  Secondly I can understand clear in time domain - frequency relationship: $\exp\left(\frac{j2\pi}{T}t\right) $. From Euler's formula $\cos$ and $\sin$ waves are created every $\frac{t}{T} $ step from $0$ to $ 2\pi$. I can not understand this when I look at beamforming function above (formulas (1) and (2)).

  
  


• 
  

  And finally why result is in $\theta$ domain how that happened ?

  
  

Answer

The equations relate to how the directivity of a uniformly spaced linear array of sensors works.

Let's start with an array:

where $\theta$ is our "look" direction (where we want to steer the array), $d$ is the sensor spacing, and, for our purposes, the angles of each segment of the array are all 0 (i.e. $\theta_1 = \theta_2 = \ldots = 0$) so the array is in a straight line along the $x$ axis.

In that case, the time at which the incoming wavefront hits each sensor, $t_j$ is: $$ t_0 = 0\\ t_1 = d\sin(\theta)\\ t_2 = 2d\sin(\theta)\\ \vdots\\ t_j = jd\sin(\theta)\\ \vdots\\ $$

The idea is that you delay each signal from each sensor by $t_j$, weight them by $v(j)$ and then sum them you'll get an array response like: $$ a_{\rm tot}(t) = \sum_{j=0}^{N-1} v(j) \delta(t-t_j) $$ in the time domain.

In the frequency domain, this looks like: $$ {\cal F}\left[a_{\rm tot}(t)\right] = A_{\rm tot}(f) = \sum_{j=0}^{N-1} v(j) e^{i2\pi f jd\sin(\theta)} \tag{A} $$

If you now assume that the speed of the incoming waves is $c = f\lambda$ so that $f = \frac{c}{\lambda}$ we get:

$$A_{\rm tot}(\lambda ) = \sum_{j=0}^{N-1} v(j) e^{i2\pi \frac{c}{\lambda} jd\sin(\theta)} \\ = \sum_{j=0}^{N-1} v(j) e^{i\pi c j \sin(\theta)} $$ if we assume that $\lambda = \frac{d}{2}$.

This last assumption means that now our $A_{\rm tot}$ is not dependent on the frequency variable, and just shows us how the array response changes with bearing angle, $\theta$.

So, really, while the Fourier transform is used in this derivation, equations (1) and (2) in your question are not Fourier transforms themselves.

I don't believe I've directly answered your questions, but feel free to comment and see if I can remove your doubts.

---

if beamforming equations are not Fourier transforms why the result of a uniformly weighted beamformer is sinc function in $\theta$ domain just like Fourier transform ? And also does this means equation 11 in the paper is wrong

So equation 11 of that paper is the same as equation (A) in what I wrote above (I just added the tag).

So, no, the equation is not wrong.

The reason there is a $\rm sinc$-like function is simply the maths of summing complex exponentials. The function is actually not a $\rm sinc$ but a only like it for small values of the argument in the denominator.

As you can see from (4.5) in the link, it actually looks like: $$ {\rm asinc(\omega)} = \frac{\sin(N\omega/2)}{\sin(\omega/2)} \approx \frac{\sin(N\omega/2)}{\omega/2} $$ where the approximation only holds if $\omega/2$ is small.

But in the formula there is $\sin(\theta)$ instead of $\theta$ how $\sin$ affects this equation?

As @Marcus says:

using $D(\theta)$ and calling it Fourier Transform is wrong; you could use $D(\sin(\theta))$ and get away with it :)

This just means that the $\theta$ axis is scaled slightly differently and makes it more periodic. See the picture below which plots:

• $\require{color}\color{black}{\bf black}$ : $\rm sinc(\theta)$


• $\require{color}\color{red}{\bf red}$ : $\rm asinc(\theta)$, and


• $\require{color}\color{green}{\bf green}$ : $\rm asinc(\sin(\theta))$.

---

R Code Below

# 30425


M <- 10
N <- 100
theta <- seq(-pi*5,pi*5,pi/N)

sinc <- sin(M*theta/2) / (theta/2)
asinc <- sin(M*theta/2) / sin(theta/2)
asinctheta <- sin(M*sin(theta)/2) / sin(sin(theta)/2)

plot(theta, sinc, col=1, type="l", lwd = 4)
lines(theta, asinc, col=2, lwd = 2)

lines(theta, asinctheta, col=3, lwd = 1)

legend(-10, 10, c("sinc()", "asinc","asinctheta"), col=c(1,2,3), lwd = c(4,2,1))

grammar - Is saying 「XはYは…」 acceptable?

In いっすんぼうし, a very popular fairy tale, this line appears:

だいじんは　からだは　ちいさいけれど　げんきな
いっすんぼうしを　たいそう　きにいり
じぶんの　いえで　はたらかせることにしました。

Is 「だいじんは　からだは」 grammatically correct? What would be done to make this more correct?

Answer

The sequence 体は小さいけれど元気な serves as an adjectival block which modifies [一寸法師]{いっすんぼうし}. 体は小さいけれど元気な一寸法師 is object of the verb 気に入り, in turn. [大臣]{だいじん}(は) is its subject. So, the whole sentence has kind of a nested structure, and the two は belong to different levels respectively.

phrases - Could you repeat that please?

I recently was on the phone with a Japanese customer service representative and I couldn't quite understand what she had said. I wanted her to repeat what she had said so I said something along the lines of 'again please' or 'one more time please'. What I really wanted to say was 'could you repeat that please'.

How do I say the latter in Japanese?

Answer

もう一度説明してくれますか？ is what I was looking for.

explosives - Does the explosion of TNT include oxidation?

This comment below the question Rocket explosion compared to kT of TNT; has one ever knocked something over at a distance? suggests that

...TNT includes it's own oxidizer...

Explosion isn't the same as combustion and you don't need to add a separate oxidizer to an explosive for it to do its thing.

But technically speaking does the explosion of TNT include any steps that could be considered as oxidative? Can some intermediate products be considered to be acting as oxidizers?

Answer

3 nitrogroups of TNT are rich of oxygen, but the aromatic ring has only carbon and hydrogen atoms.

Therefore oxygen of nitrogroups oxidizes carbon and hydrogen atoms.

There is no principle difference between oxidation and reduction agens being separate molecules, or being different parts of the same molecule.

Note that TNT, in contrary to e.g nitroglycerine, is oxygen deficient, so the amount of available oxygen is not enough for complete oxidation to water and carbon dioxide.

TNT:

$$\ce{2 C7H5N3O6 -> 3 N2 + 5 H2O + 7 CO + 7 C}$$ or $$\ce{2 C7H5N3O6 -> 3 N2 + 5 H2 + 12 CO + 2 C}$$

Nitroglycerine

$$\ce{4 C3H5N3O9 -> 6 N2 + 10 H2O + 12 CO2 + O2 }$$

halacha - Can a teen threaten or attack one parent, who is beating or is about to beat the other?

This is relevant in many dysfunctional Jewish homes. Suppose one parent is beating or about to beat the other, and the child has an opportunity to intervene by threatening violence to the abusive parent.

Which has higher precedence in this case, potentially saving a life or honoring parents? May the child intervene if he or she is able, or must the child not interfere?

organic chemistry - Has Crabtree's photochemically-activated mercury-catalysed hydrocarbon activation process ever been used commercially?

In the 1980s, while searching for new hydrocarbon activation catalysts, Crabtree's research group accidentally found that mercury vapour activated photochemically could perform some interesting and unusual alkane activation reactions yielding unusual products.

Some of the work is summarised in this Journal of Chemical Education paper from 1988. The reaction seems to be able to produce some unusual (and hard to get) dimers of hydrocarbons and is also tolerant of other functional groups (eg alcohols, amines) and can also generate cross coupled products (eg it will couple alcohols with hydrocarbons).

At the time it was thought to be an interesting curiosity but with some prospect of yielding easy routes to some hard-to-get targets.

Has it ever been used in a significant synthesis? Or for any industrial processes?

legal documents - need for civil marriage license in the frum world

I spoke with a Rabbi in Far Rockaway NY who indicated that in the frum world civil marriage license is not required. Just the religious ketubah is necessary?

fourier transform - Why are there so many windowing functions?

Many windowing functions are listed here in the Mathematica documentation. I tried using a few to reduce leakage when computing a Discrete Fourier Transform. From what I could tell it made little difference which windowing function is used. Two of them that are very dissimilar are the BartlettHannWindow and BlackmanHarrisWindow. Could someone provide an example where the BarttletHannWindow is a very good choice, and another where the BlackmanHarrisWindow is a very good choice. That might help me understand why there are so many to choose from.

Answer

Aside from reduction of spectral leakage, there is a one major trade-off to be made when choosing a window function. Below you can see a figure with various parameters. Two of them are most important:

• Main Lobe Width


• Peak Side Lobe Level

Width of the main lobe affects resolution of your analysis. I am sure you know that multiplication in time domain is convolution in frequency domain. By default you always use rectangular window, which has frequency response in a form of $\mathrm{sinc}$ function.

For example it might be the case that two pure sinusoids (Fourier Transform being Dirac deltas) with frequencies being very close to each other, peaks can be very hard to distinguish and thus become one. On figure below I compared 4 window functions for two sinusoids separated exactly by 3 frequency bins. You can see how wide is the main lobe of Nuttall window and how it affects the separation, whereas Rectangular window is the window with narrowest possible width of main lobe (i.e. lowest Normalized Equivalent Noise Bandwidth - NENBW)

On the other hand level of first side lobe affects the ability to recognize adjacent frequencies when spectral leakage is present and side lobes of frequency with high amplitude are almost "covering" other frequency next to it with much lower amplitude:

And here is the trade-off... You can't get very low level of side lobes and very narrow main lobe, i.e. it's not possible to have window function with main peak like in rectangular window, and very low level of side lobes as in Nuttal window. Here is the comparison of some windows:

Apart from parameters mentioned above, there is more features such as:

• Side Lobe Roll-off rate (how fast side lobes decrease - for example see Bartlett and Nuttal above)


• Existence of analytical frequency response equation (useful when performing theoretical calculations)


• Summing of window samples to constant value in time domain when doing overlap (for example Hann window with $33\%$ of overlap)

This is extremely useful when you want to perform STFT and then reconstruct time domain signal.

So now to answer your question. Why do we have so many window functions?

Depending on task whether it is simple FFT analysis of: closely spaced sinusoids, white noise, impulsive sounds, or even FIR filter design, different type of window is recommended. Obviously in 90% of cases people are using Hamming/Hanning window or no window at all. Nevertheless for some specific signals you might find that extracted features depending on window choice tend to be more discriminative.

For more info about Window Functions please refer to:

F. J. Harris - On the Use of windows for Harmonic Analysis with the Discrete Fourier Transform

G. Heinzel, et al - Spectrum and spectral density estimation by the DFT, including a comprehensive list of window functions and some new flat-top windows

M. Cerna, A. F. Harvey - The Fundamentals of FFT-Based Signal Analysis and Measurement

H. A. Gaberson - A Comprehensive Windows Tutorial

sound - Why are zero values added in the FFT of a concatenated noise signal?

After concatenating an 11-second *.WAV (sample rate 44100 Hz) file 27 times (just by gluing them head-to-tail), I obtained a ~300-sec noise signal. I used MATLAB(2015b) and the FFT function on both the original file and the concatenated signal. The FFT of the concatenated signal was, as expected, pretty similar to the original. However, for every y-axis point (spectral power) in the concatenated FFT, there were 2 zeros (not precisely zero, but values in the order of x*10^-19, so about 18 orders of magnitude below the 'real' FFT values). The original noise file was specifically designed to allow for looping. Below a close up of the concatenated FFT showing the added zeros:

Hence, the spectral power plot of the concatenated signal looked like the original, but every frequency power point was preceded and followed by two zeros. How can this be? Does it have to do with the fact that lengthening a signal increases the resolution of the FFT and that frequencies are analyzed in the concatenated signal that are not present in the original signal due to resolution restrictions? Or is this rather an error in my script? Other spectra showed up fine, though.

Answer

You're running into a property of the DFT that is usually used in the opposite direction: stuffing zeros between samples in one domain results in replication of the entire sequence in the opposite domain. Let's start in the frequency domain with the signal you plotted, $X[k]$, and look at the inverse transform to see what time-domain signal it corresponds to.

$$ x[n] = \sum_{k=0}^{N-1}X[k] e^{j 2 \pi k n/N} $$

$N$ is the length of the DFT that you apply to the data. Let's say that $X[k]$ consists of sparse values with $M$ zeros between each one, so that $X[k] = 0\ \forall\ k \neq kM$. The above then looks like:

$$ x[n] = \sum_{k=0}^{\left \lfloor{\frac{N-1}{M}}\right\rfloor}X[k] e^{j 2 \pi k M n/N} $$

Do some rearranging within the exponent to get:

$$ x[n] = \sum_{k=0}^{\left \lfloor{\frac{N-1}{M}}\right\rfloor}X[k] e^{j 2 \pi \frac{k n}{\frac{N}{M}}} $$

This is nothing but a $\frac{N}{M}$-point inverse DFT of the nonzero samples in your frequency-domain signal $X[k]$. Due to the periodicity property of the DFT, you can then show that $x[n]$ is periodic with period $\frac{N}{M}$, which is exactly the form of signal that you shoved into the DFT to begin with.

Summary: Replication of the signal in one domain results in a zero-stuffed signal in the opposite domain. This is used in the theory behind interpolating filters and other multirate processing. There is a dual property where if you downsample a signal (by removing $M$ out of every $N$ samples), the data in the opposite domain collapses on top of one another and adds (resulting in aliasing).

particle も - さえ: How to use it?

Hello I'm not sure I have understood well the nuances so I have a few questions:

What is the difference between the sentences below:

ビショップさえ取ればいいよ。

ビショップを取りさえすればいいよ。

I also saw on a site that でさえ is the same as さえ in a sentence like 子供さえわかる. But isn't で the 連用形 of だ? I would translate the sentence as below:

これは子供でさえわかるだろう : Even if you are a kid you should be able to understand this.

これは子供さえわかるだろう : Even a kid should be able to understand this.

And my last question might have nothing to do but I saw a translation for 「日本語さえ話せない」 which is "you can't even speak Japanese", can I express the same thing by saying 「日本語も話せない」? Or does this sentence only mean "you cannot speak Japanese either"?

halacha - What technically constitutes adultery

I would like to better understand what exact physical acts constitute adultery between a married woman and a man that is not her husband?

How do Ethiopian Jews see the Book of Jubilees?

Is the Book of Jubilees considered to be on par with Chumash by the Beta-Israel?

z transform - Minimum number of Poles and zero of transfer function H(z)?

Suppose $G(z)=H(z)(1-\frac{1}{2}z^{-1})$ now in question its saying ROC of G(Z) is entire Z plane except Z=0,so here we need not to add anything because G(Z) already a right sided signal with ROC entire z plane except at z=0.

now $H(z)=\frac{G(z)}{(1-\frac{1}{2}z^{-1})}$, for the input $x(n)=(1+j)^n$, H(z) should become zero.

Now here i am not getting what should be the value of G(z) so that its output becomes zero for the input $(1+j)^n$.

Answer

Restricting the discussion to LTI systems with rational transfer functions, there are various conditions on the placement of poles and zeros of $H(z)$ implied by several properties of the system under concern. Using some of them helps in this question.

Prop 1: Total number of poles equals total number of zeros (including those at $z=0$ and $|z|=\infty$) ,i.e., There are equal number of poles and zeros for any $H(z)$.

Rule 2: For real systems (which has real impulse response $h[n]$) poles (or zeros) exist as either purely real or as complex conjugate pairs.

Now applying these two properties to your system which is real and causal (how?) we reach the following conclusion:

1- If ROC of $(1-\frac{1}{2} z^{-1}) H(z)$ is the entire $\mathcal{Z}$-plane (exc $z=0$), then $H(z)$ has a pole at $z=0.5$

2- If $x[n]=(1+j)^n$ produces zero output, then $z=1 \pm j$ are two zeros of $H(z)$

Are there any more poles of $H(z)$ other than those at $z=0$ ? No. Because if there were so, then part one would indicate it in the ROC of $(1-0.5 z^{-1})H(z)$ which is given as entire $\mathcal{Z}$ plane indicating that there are no more poles of finite, nonzeros values.

Are there any more zeros of $H(z)$ ? The given information is not sufficient to conclude that. There could be more zeros. If they were real then they could be even or odd numbered, if they were complex then they must be in complex conjugate pairs. We only know one complex pair of zeros at $z=1 \pm j$. Note that for each added zero to $H(z)$ there would be one more added pole at $z=0$ (in addition to the existing pole at $z=0$)

Hence we conclude: $H(z)$ has two poles at $z=0$ and $z=0.5$ and at least two zeros at $z=1+j$ and $z=1-j$. If $H(z)$ had any more zeros at $z_k=\alpha_k$ then there would be equal number of poles at $z=0$. And if the zeros were complex they would be in complex-conjugate pairs (and the added poles would be doubled)

parshanut torah comment - Looking for Shadal Al HaTorah

I am looking for Shadal's commentary on the Torah. is it available for free online? If not does anyone know where it can be purchased the cheapest?

Answer

Shadal has two commentaries on Torah:

• a shorter one called Mishtadel


• a longer one, with two printings. One of these printings is a censored text, which leaves out e.g. some of Shadal's citations of gentile scholars. This one is available online in plain text. The other of these printings is the full uncensored version and is available on Google Books (but might then only be accessible if you are in the United States).


• there is also Ohev Ger, which is Shadal's supercommentary on Targum Onkelos, where he tries to establish the correct text.

On parshablog, I have, parsha by parsha, links to a variety of meforshim. For example, here is Bereishit Sources. For Bereishit:

I will give links here to the full commentary for the other four Chumashim. For the rest, you can modify the url yourself, or scroll in the book, or else search parshablog for the Source Roundup for that particular parasha.

Uncensored full commentary for:

1. Bereishit


2. Shemot


3. Vayikra


4. Bemidbar


5. Devarim

meaning - ければ possibly used to link verbs instead of causation? (visual novel, narration)

I apologize if this is a silly question but can ければ be used to simply link two verbs (as in, "and")? It doesn't make much sense (or does it?) in the following sentence for "to scream angrily" making the person to "follow/cling to" to the narrator, that is: "(he) was in the state as if he wanted to say something (but) Shinji didn't shout and didn't follow" as opposed to "didn't shout, so didn't follow me"?

何か言いたげな口調のまま、慎二は怒鳴る事もなければ追いすがってくる事もない。

Couldn't it simply be replaced here by ...怒鳴る事もなくて追いすがってくる事...?

Have I completely misunderstood the sentence?

Thank you.

Answer

Double Negatives:

The structure that you need to be looking at is:

「～～もなければ～～もない」 = "neither ~~ nor ~~"

This has nothing to do with causation. It can link two verb/adjective/noun phrases, not just verbs.

As you mentioned "causation", I think you are thinking of another usage of 「（な）ければ」 as in 「チーズがなければピザは[作]{つく}れない。」 = "If you have no cheese, you cannot make pizza."

「[慎二]{しんじ}は[怒鳴]{どな}る[事]{こと}もなければ[追]{お}いすがってくる事もない」,

therefore, means: "Shinji would neither yell at me nor follow me about"

Example with adjectives:

「このピザはうまくもなければ、まずくもない。」 = "This pizza is neither good nor bad."

Example with nouns:

「あの[人]{ひと}は[男]{おとこ}でもなければ、[女]{おんな}でもない。」 = "That person is neither a man nor a woman."

inorganic chemistry - What does a molecules color have to do with its bond/orbital energies?

For example, elemental iodine is deep violet. Its sigma bond or perhaps the lone pairs are capable of absorbing all visible light frequencies except violet which is why we see it as that color. Lithium, on the other hand, is red which means its valence electrons must be reflecting red frequencies. So, does that mean the valence/bonding electrons of $\ce{I2}$ are higher energy than the lithium valence electrons? In other words, is there a relationship between an orbitals energy and the type of light it can reflect?

You could perhaps compare $\ce{I2, Sn^{II}I2}$, and $\ce{Sn^{IV}I4}$, and which are violet, yellow, orange (in decreasing order of visible light energy).

Perhaps it has to do with symmetry? $\ce{I2}$ is $D_{\infty\mathrm{h}}$, stannous iodide is $C_{2\mathrm{v}}$, and stannic iodide is $T_\mathrm{d}$.

random - Sampling low pass filtered white noise

If we filter out ideal white noise using an ideal LPF of cutoff frequency 10 KHz and then sample it at 30 KHz , is the resulting discrete signal statistically independent? I would like to know the statistical behaviour of the output signal.

I was attending an on-line test. My answer was told wrong.Below is the snapshot from the on-line test.

I would also like to know what would be the result if sampling frequency is below Nyquist frequency?

Answer

The output of your filter is what is sometimes called band-limited white noise. In your particular case, the autocorrelation function of the output noise is a sinc function whose zeroes are every $100$ microseconds, that is, samples taken at the rate of $10^4$ samples/second are uncorrelated. Your samples at $3\times 10^4$ samples per second are closer together and thus are correlated. In fact, the correlation coefficient between successive samples is $\displaystyle \frac{\sin(\pi/3)}{\pi/3} = \frac{3\sqrt{3}}{2\pi} \approx 0.827$

Note added after question was edited: Samples taken $0.03$ milliseconds apart are at a frequency of $33.33\ldots$ kHz, not $30$ kHz as you say in the part of the question that you typed in yourself. Regardless, the answer (B) is incorrect and the reasoning given in support of answer (B) is bogus. What is being sampled is not white noise but filtered white noise, and Answer A is correct.

For (B) to be the correct answer, the sampling rate must be a sub-multiple of $10$ kilosamples per second, that is the samples must be spaced $100$ microseconds apart or an integer multiple of $100$ microseconds apart. Sampling every $0.3$ milliseconds, that is, every $300$ microseconds meets this criterion; sampling every $0.03$ milliseconds does not. Now sampling at $10$ kilosamples/second makes the samples uncorrelated (answer (C)) and to get from this to the stronger result that the samples are statistically independent (answer (B)), we need further assumptions about the noise. The standard assumption is that the noise is Gaussian.

In summary, (B) would be the correct answer if the sampling were done every $0.3$ milliseconds (since the problem statement already includes the assertion that the noise is Gaussian) and (C) would be the correct answer if it did not say that the noise is Gaussian since we could not the make the specialization from uncorrelated to independent. But when the sampling is done every $0.03$ milliseconds, then (A) is the correct answer.

grammar - How do you use 〜と知る?

I've often seen and heard the expression 〜と知る（知っている）. When I think about it, it makes sense in the context of the quoatation-と, like with 〜と言う or 〜と思う. It seems like it means "Know that 〜".

ミユキちゃんが結婚したと知ってる？　→　Did you know that Mikyuki got married?

However, the few times I've tried to use it, I was told I was using it incorrectly, and that I should instead use 〜こと／のを知る.

ミユキちゃんが結婚したこと／のを知ってる？

So what are the rules for using 〜と知る? Do 〜と知る and 〜こと／のを知る have different meanings and rules (they seem the same to me)?

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Update: I've found quite a few examples from my Bible. It's the 新共同訳 version, and I was able to search it here. I searched for ～と知る, ～と知って, and ～と知った. Here are a couple examples:

• 「群衆は、イエスも弟子たちもそこにいないと知ると、自分たちもそれらの小舟に乗り、イエスを捜し求めてカファルナウムに来た。」　－　ヨハネによる福音書 / 6章 24節


• 「けれども、人は律法【りっぽう】の実行ではなく、ただイエス・キリストへの信仰によって義とされると知って、わたしたちもキリスト・イエスを信じました」　－　ガラテヤの信徒への手紙 / 2章 16節


• 「ヨナタンは言った。『そのような事は決してない。父があなたに危害を加える決心をしていると知ったら、必ずあなたに教えよう。』」　－　サムエル記上 / 20章 9節

Answer

The examples are very interesting. It looks like, whenever と知る can be used, it means "find out" rather than "know". Another way to say this is, whenever と知る can be used, you can replace the verb with 分かる. With "find out", you cannot have duration, in other words, you can say:

I knew that theorem for two days, (but I forgot it).

but you cannot say

* I found out that theorem for two days.

the aspectuality matters. Applying this to Japanese, you can use と知る with a simple tense (under which 知る means "find out"):

風の知らせで、みゆきちゃんが結婚したと知った。

but not with perfect (under which 知る means "know"):

* 昨日から、みゆきちゃんが結婚したと知っている。

And indeed this makes sense because と (similar to "to") implies the goal of change of location/state of something. Finding out something is a change of state, but knowing something is not.

PTIJ: Purim- International Forum Day

Is it a bigger mitzvah to post and answer questions on Mi Yodeya on Purim (Furim) because It sounds like Forum? Would that make Purim International Forum Day?

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passover - Why must the child ask these four questions?

The Torah, as explained in the Hagaddah, gives examples of four children. Each asks a question in his own way, and receives an appropriate answer.

However, the Mishnah in Pesachim 116a teaches:

They pour him the second cup, and here the child asks (and if the child doesn't know how, his father teaches him): Why is this night different from all other nights? For on all other nights...

This clearly indicates that the child must ask these questions. This is also brought down in Shulchan Aruch, Orach Chaim 473:7.

Why don't we follow the procedure indicated in the Hagaddah, where a child asks a question he thinks of? Why do we require each child to ask the same four specific questions?

grammar - Difference between 変{か}わり and 変{か}える

What is difference between 変わり and 変える ? 変える means "to change". Maybe 変わり is just a noun? Or maybe there is some grammar rule?

Answer

Japanese has a number of morphologically related transitive-intransitive pairs. The pair of verbs you've discovered, 変わる and 変える, belongs to the largest group, -ar (intransitive) and -e (transitive):

  　Intransitive　　　　　　　　　　　　　Transitive

　  あがる　ag-ar-u　  'rise'　 　　　　　　あげる　ag-e-ru　  'raise'
　  集まる　atum-ar-u　'gather'　　　　　 　集める　atum-e-ru　'gather'
　  溜まる　tam-ar-u 　'accumulate'　 　　　溜める　tam-e-ru　 'accumulate'
　  止まる　tom-ar-u 　'stop'　　　　　　　 止める　tom-e-ru 　'stop'

The romanized versions reflect the actual morphology better than the versions in kana and kanji, but you'll need to recognize the distinction in Japanese spelling, since Japanese isn't usually romanized.

In this case, the root is kaw-, so we end up with the following pair:

　  変わる　kaw-ar-u 　'change'　　　　　　 変える　ka(w)-e-ru 　'change'

In Modern Japanese, /w/ drops out before vowels other than /a/, so we're left with kaeru rather than *kaweru. Historically, however, this root was kap-, and we can see the etymological presence of the original consonant p in both words in the older spellings 変はる and 変へる.

Note that in each -ar / -e pair, the intransitive verb is a consonant-stem verb ending with r-, while the corresponding transitive verb is a vowel-stem verb ending with e-. Consonant- and vowel-stem verbs may be called by another name in your textbook; they're called 五段（ごだん） and 一段（いちだん） in Japanese, and in books for learners they are sometimes called "-u verbs and -ru verbs" or "Group I Verbs and Group II Verbs".

For more information about transitive-intransitive pairs, see Shibatani's 1990 book, The Languages of Japan, pages 235-237. (The chart above is based on the one on page 236.)

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The infinitive form of a verb, called the 連用形（れんようけい） in Japanese, is formed by adding -i to consonant-stem verbs and adding nothing at all to vowel-stem verbs:

　　変わる　kawar-u  　→　　変わり　kawar-i  
　　変える　  kae-ru　 →　　変え　　  kae-

This form can be used like a noun, but it has lots of other uses. For example, it's the form that you add the polite auxiliary 〜ます to:

　　変わる　kawar-u  　→　　変わります　kawar-i-masu  
　　変える　  kae-ru　 →　　変えます　　  kae- -masu

For more information about this form, see your textbook. Besides the names given above, it may also be called the continuative form (a translation of the Japanese name), the "Vmasu stem", or sometimes just "the stem". Unfortunately, different people use a lot of different names for the same things.

organic chemistry - Numbering in chlordiazepoxide

The IUPAC name of chlordiazepoxide is given as : 7-chloro-2-methylamino-5-phenyl-3H-1,4-benzodiazepine-4-oxide, but when I started numbering the structure, I am unable to find chlorine on 7th carbon, it is on 10th. Then why 7-chloro... is given is it wrong? Or I am wrong? Please help by numbering the structure in a diagram even on a paper an upload the photo.

Answer

The parent structure of chlordiazepoxide consist of the heteromonocyclic component 2⁠H-1,4-diazepine that is fused to a benzene ring.

According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), the name of the fused parent structure is generated as follows:

P-25.2.2.4 Heteromonocyclic components fused to a benzene ring

Unless listed as a retained name (…), a benzene ring fused to a heteromonocycle of five or more members (a benzoheterocycle) is named by placing the locant(s) indicating the position(s) of the heteroatom(s) at the front of the name consisting of the fusion prefix ‘benzo’ followed by a retained name, a Hantzsch-Widman systematic name, or a name formed by skeletal replacement (‘a’) nomenclature (…). The locants cited correspond to the full bicyclic structure. As in Hantzsch-Widman names, locants are placed in the order corresponding to the order of citation of the heteroatoms in the heterocyclic component. The locant ‘1’ is always assigned to the atom of the heterocyclic component next to a fusion atom. Heteroatoms are allocated lowest locants as a set, without regard to kind; if there is a choice, lowest locants are assigned in accordance with the seniority of the ‘a’ prefixes (…). In general nomenclature locants may be omitted when the name is unambiguous; for preferred IUPAC names locants must be cited. The letter ‘o’ of the ‘benzo’ prefix is elided when followed by a vowel. Indicated hydrogen is placed at the front of the name, when required.
(…)

Accordingly, the name ‘benzodiazepine’ consists of the prefix ‘benzo’ followed by the name ‘diazepine’. The locant ‘1’ is assigned to the atom of the heterocyclic component next to a fusion atom and the heteroatoms are allocated lowest locants as a set (here: 1,4):

The same numbering of locants applies to the complete structure of 7-chloro-2-(methylamino)-5-phenyl-3⁠H-1,4-benzodiazepine 4-oxide:

pronunciation - When does /r/ become a trill?

In a video that snailboat pointed out in a comment on my question about geminated /r/, at least one speaker of Japanese sounds to me like they trill both the /r/s in タリアテッレ.

It's my understanding that, most of the time, /r/ in Japanese is a flap that freely varies between central and lateral (cf. the answer to R sound vs L sound). For /r/ to transform into a trill, then, is really quite surprising.

In what contexts (social, dialectal, grammatical, whatever) does /r/ become a trill?

I know that /r/ manifests as a trill (巻き舌) in yakuza speech (cf. What are the stereotypical characteristics of yakuza speech?); where else do we find trilled /r/?

(Note: I may just be mishearing the speaker in the Youtube video linked above; if so, just ignore that part. Either way, my question about trilled /r/ in Japanese remains.)

word choice - How to use へ (-e), に (-ni), まで (made) and の方 (no-hō) with destination and direction?

It is common to ask the difference between just "へ" (-e) and "に" (-ni) but it seems to get even more complicated when you also mix in "まで" (made) and even "の方" (no-hō).

When Japanese people ask me where I'm going they always ask "どこまで" (doko made)?" rather than "どこへ" (doko e) or "どこに" (doko ni) that I expected.

I know "まで" (made) can mean "until" but when I ask the difference with "に" (ni) and "へ" (e) I'm told "へ" (e) means "to" and "に" (ni) means "in the direction of" but if this is the case then how do they differ from "の方" (no-ho) which I already learned previously meant "in the direction of"?

Answer

へ and に can both translate as "to" and are often interchangeable. The difference is that へ focuses on the process or course of going in a direction or to a place, while に focuses on the destination itself [1]. まで, being a particle that defines an upper bound, thus focuses on the distance traveled.

The function of ～の方（に／へ） depends on which particle follows. Followed by へ, it does indeed mean "in the direction of" as you previously learned. (東京の方へ行く。) Followed by に, it's harder to pin to a specific meaning, but it often means "in the general area of" or "on the side of" (the latter being when 方 is used to indicate one of multiple options rather than a simple direction of travel). (東京の方にある。)

Sources:

1. 「彼女が待ってる新宿（　）、恋する切符 5,100 円」──格助詞「に」と「へ」のイメージ── (PDF)

manga - Please help me understand this たる?

Please help me understand this たる!

焼きたる
在りたる

Answer

They are the same as 焼いた人器 and いた時, respectively, but said in an archaic fashion.

Several things happening here. First, ある is used instead of いる because ある could safely be used with animate objects in archaic Japanese.

人あり。 (archaic)
≒ 人がいる。 (modern Japanese)
≒ There is a person.

たる is the attributive form of the Japanese archaic auxiliary verb たり, which describes the perfect aspect or the continuation of state (not past tense, strictly speaking). Attributive form is a verb form used to modify the following noun.

声を聞きたり。 (archaic)

≒ 声を聞いた。 (modern Japanese)
≒ I have heard a voice.

聞きたる声 (archaic)
≒ 聞いた声 (modern Japanese)
≒ the voice which I (have) heard

While たり/たる works very similarly to so-called ta-form in modern Japanese, one exception is that it follows the masu-stem of verbs. In archaic Japanese, so-called "te-form" or "ta-form" did not exist. What we know as "te-form" or "ta-form" today is a result of relatively recent sound changes called 音便（おんびん）. See this chart for details. In fact, in Japanese school grammar, 焼き and 焼い or 在り and 在っ are treated as the same conjugation form called 連用形 ("continuative form").

BTW, I feel the latter example, 在りたる時, may not be quite natural from the historical standpoint. It may have to be 在りし時 using し, the attributive form of the archaic auxiliary verb き denoting past. I'd like to see opinions from other people who are better at archaic Japanese.

Is there a different meaning for ごちそうさま!

I have posted a "status" on Facebook:

Dear santa, I would like for you to bring him for christmas

My boyfriend commented:

Your Wish is my command!

And my Japanese manager (from our office) commented:

ごちそうさま!!

In this case, what does ごちそうさま!! mean? I think it is definitely not the meaning "Thanks for the meal".

So, are there any other meanings of ごちそうさま!!？

Answer

Yes, there is! Primary use is the one you are already aware of. ごちそうさま is also used after hearing something lovey-dovey like your boyfriend's "your wish is my command".

halacha - Cookies for kiddush

Many people, including Chabad, eat cookies before shacharis which raises a question about kiddush asked here. I understand that they do this because cookies don't count as a seudah.¹ The flip side of that question is, for those of us who eat mezonot before shacharis, how can we eat the same mezonot for kiddush bemakom seudah?

¹ Orach Chaim 89 (1?) forbids eating before shacharis. Mishnah berurah there permits various things and forbids others on the grounds that they are "like a meal".

Answer

The heter for eating cookies before davening is not based on the idea that it is not a seuda, rather that it is needed to concentrate during davening, despite the fact that it would otherwise be forbidden. As the Alter Rebbe writes:

ואפילו כל מיני אוכלים וכל מיני משקין ששייך בהם גאוה מותר לאכלם ולשתותם לצורך רפואה שאין ברפואה משום גאוה אבל לרעבו ולצמאו אסור אלא א"כ אינו יכול לכוין דעתו בתפלתו עד שיאכל או שישתה ואפילו עכשיו שאין מכוונים כל כך בתפלה מכל מקום אם רוצה לאכול ולשתות כדי לכוין הרשות בידו

Even all types of food and all types of drinks which can create haughtiness, it is permissible to eat them and to drink them for health, as health does not have [concerns] of haughtiness. However for his hunger and his thirst it is forbidden unless he is unable to concentrate his mind in prayer until he eats or drinks. And even nowadays, when we do not concentrate so much in prayer, nevertheless if he wants to eat and drink in order to concentrate, he has permission to do so.

See there for sources.

For those wondering if this is the reason for the leniency, regarding Chabad practice specifically see here: (emphasis added)

הנה לא ירעיב את עצמו עד כמה וכמה שעות על היום, אלא ישתה דבר המחזק את הגוף וגם יאכל מיני מזונות בבקר ואפילו קודם התפלה. וכבר ידוע פתגם רבוה״ק והוראתם, אז מען־ דארף עסין צוליב דאוונען ניט דאוונען צוליב עסן. וכוונתם היתה ג״כ בפשטות, שאם הוא רעב בשעת התפלה, הרי אי אפשר, לאנשים כערכנו — שלא תהי׳ לזה נגיעה בהתבוננות בתפלה והאריכות בה, משא״כ כשיאכל לפני התפלה יסולק בלבול זה, וביכולתו - אם רק ברצונו - לעבוד עבודתו ביותר טוב ובאופן נעלה.

ובתור תיקון על אשר נהג עד כמה באומן אחר, הרי ישפיע גם בסביבתו, אשר כל אלו שאינם בריאים ועפמ״ש באגרת התשובה הנ״ל, לא ירעיבו את עצמם, ויתפללו בבקר וגם ילמדו אז נשמה בגוף שאינו מבלבל, והשי״ת יצליחו

tefilla - Being Shaliach Tzibbur in a Congregation with a different Nusach

In Yalkut Yosef OC 101:10 rules that a Sephardi who is davening in an Ashkenazi minyan should not daven Nusach Ashkenaz as shaliach tzibbur. He can only be shaliach tzibbur if the minyan agrees to let him daven in Nusach Edot HaMizrach, and if not he should refuse the honor.

Among the reasons for this is a very strong preference (for kabbalistic reasons) that Sepharadim should daven in their own nusach, and this overrides being the shaliach tzibbur. But aside from that it would seem that the shaliach tzibbur in any minyan should be proficient in the nusach of that minyan, and therefore "cross-davening" should be problematic even between Nusach Ashkenaz and Nusach Sephard.

Why are Ashkenazim meikil to allow the someone who usually davens Nusach Ashkenaz to be shaliach tzibbur in a Nusach Sephard congregation and vice-versa? And why are they meikil to allow one to daven in a nusach that's not their own in the first place?

halacha - What if the tafel comes to hand first?

Although there are varying opinions among the acharonim, the common practice is that only one b'racha rishona is said before eating a mixture of two items that normally require different b'rachos, where the mixture is such that each spoonful or forkful will include both items. (Sources: Rabbi Yisroel Pinchos Bodner, The Halachos of Brochos, chapter 4, section C; Rabbi Binyomin Forst, The Laws of B'rachos, chapter 7, section Ⅰ.A.)

Suppose one's about to eat such a mixture, takes a spoonful, is about to say the b'racha required, and notices that his spoonful happens to contain only food items whose normal b'racha is not the mixture's. What should he do?

To clarify, I'll pick a specific example, though my question is about the general case. Suppose someone's about to eat a mixture of very small pieces of pineapple (haadama) and apple (haetz). He takes a spoonful and is about to say the haetz required (because, for whatever reason, the apple is considered primary in this case), but realizes his spoon has only pineapple on it. What should he do?

• Say haetz on the spoonful even though it's pineapple? (Seems odd, but I seem to recall hearing that when a primary food's b'racha covers a secondary food, the latter is deemed by some to become a food that actually requires the former's b'racha. In that case, perhaps here one says haetz on the pineapple even if eaten alone first.)


• Say haadama on the spoonful and haetz on the next spoonful (if it contains apple)? (Seems odd also, but it would seem the ideal according to the acharonim, alluded to above, who don't hold only one b'racha is made on the mixture. Note that my question includes the case in which the primary ingredient requires haadama and the other requires haetz (the reverse of the example I gave), which may affect the appropriateness of this option.)


• Put the spoonful back and take another that contains apple so he can say haetz? (Seems like it should be valid, but I wonder whether it's required.)


• Something else?

spectroscopy - What is an exocyclic double bond?

I have been tasked to find the $\lambda_{\text{max}}$ of 3,4-dimethyl-1,2,3,4,4a,5-hexahydronaphthalene.

This was supposed to be fairly easy. I used the base value for homoannular diene ($\pu{253 nm}$) and added the increments for the three ring residues attached to the diene ($\pu{+(3\times 5) = +15 nm}$). This should get me a value of $\lambda_{\text{max}}=\pu{268 nm}$. However, checking the solution this question, they have also added the increment for an exocyclic double bond, and have got the answer to be $\pu{273 nm}$ instead.

As far as I know, an exocyclic double bond means exo+cyclic, where exo means "outside" and cyclic means, well "cyclic", or more simply, a double bond that is outside the ring. I'm looking at this compound, and I dont see any exocyclic double bond at all.

Am I dealing with a key mistake here or is there something that I'm not aware of?

Answer

Surely you are aware that the calculation of this sort is but a very rough estimate, yet still I feel the urge to stress that once more. Having said that, let's look at the double bond in the first cycle: isn't it exocyclic with respect to the other cycle?

halacha - Chairs on Tishah B'Av

On Tishah B'Av, through Chatzos (Mincha) we sit on the floor (SA OC 559:3), like mourners (MB 559:10). If one can't sit on the floor, he may sit on a cushion or a chair close to the floor (ibid. 11).

Is this a rule about the height of the chair, that it must be close to the floor, or must it simply be uncomfortable, and so even a taller chair that's uncomfortable would be permissible.

Answer

It has to do with "being on the floor". The din is really to sit on the floor. Anywhere within 3 tefachim of the floor, (I think 12 inches) is considered part of the floor.

The gemora in many places speaks of a "mourners bed". Being that in that society all sitting and leaning were done on beds, the beds were higher, hence the need for a "mourners bed", one that is lower and close to the ground. Remember however, that this is still a "bed" and bound to be as comfortable as one.

I don't have exact sources, but regarding the mourners bed, the Artscroll Kinnos mentions it in the footnotes in relation to a kinnah that says everyone had to make their own mourners bed. In a regular society, the comforters would prepare the mourners bed for the mourners. However, by the churban EVERYONE was a mourner and therefore everyone had to prepare their own.

electrochemistry - How do I determine whether it is the *ferrous* or *ferric* ion that is implied in this displacement reaction?

I'm supposed to write a balanced equation for:

$$\ce{Iron(s) + copper(II) sulfate(aq) -> ?}$$

If I use Iron(II)/ferrous I get

$$\ce{Fe + CuSO4 -> FeSO4 + Cu}$$

and if I use Iron(III)/ferric,

$$\ce{Fe + CuSO4 -> Fe2(SO4)3 + Cu}$$

(Before balancing).

Is there a way to determine which one I am supposed to use?

hybridization - Hybridisation of ClO2

Find the hybridization as well identify the pπ-pπ as well as pπ-dπ bonds in $\ce{ClO2}$.

$\ce{ClO2}$ has 2 $\sigma$ bonds, 1 lone pair, 2π bonds and 1 odd electron.

Hybridisation is equal to number of $\sigma$ bonds + lone pairs. Since we consider odd electron a lone pair like in $\ce{NO2}$ therefore hybridisation is coming to be $\ce{sp^3}$. There will be no pπ-pπ bonding as all p orbitals are hybridised and there will be 3pπ-dπ bonds

But this is given wrong according to my textbook. What is my mistake?

Answer

I actually take issue with the question (which was asked of you not by you), as I think this oversimplifies a molecule, that still isn't well understood in the first place.

That is why I find this question incredibly difficult to answer and why I find that Nuclear Chemist's answer dangerous, because it propagates myths about bonding that have been disproved already.

But enough of the commentary, let's clear up some issues.

Find the hybridization as well identify the pπ-pπ as well as pπ-dπ bonds in $\ce{ClO2}$.

$\ce{ClO2}$ has two $\sigma$ bonds, one lone pair, two π bonds and one odd electron.

There comes a time, where you should realise that hybridisation is not always a useful concept to understand bonding. This time is now.

Your analysis of the bonding is not wrong, but maybe a bit too simple.

The reason for this is that the molecule has a very high symmetry, but it also has an unpaired electron. The problem here is that orbital symmetry cannot match with spacial symmetry, which means that hybridisation doesn't actually work here.
A bit more precise: The electron density of α-spin electrons is different from that of β-spin electrons. The hybridisation of the orbitals to produce either electron density need to also be different. In the very least you would have to consider two different hybridisation schemes at once.
All possible states (that is independent of any hybridisation model) then will be in superposition to form the actual ground state. This ground state will have a complicated bonding situation.

Of course you can use VSEPR theory to predict the shape of the molecule, that is a very good starting point. You will find out that the molecule is bent, and that matches the crystal structure. A bent molecule of the form $\ce{B-A-B}$ always has $C_\mathrm{2v}$ symmetry, it therefore always has π-orbitals. Whether those orbitals are essentially bonding or not, is an entirely different question.
It also does not tell you which atomic orbitals will be involved.

One obvious fault in the question is that there is no involvement of d-orbitals whatsoever in the molecules. The d-orbitals of chlorine are simply not accessible energetically; at least not in the way that it would form stable bonds. Anyone who is jibber-jabbering about 'octet-expansion' has stopped learning about chemistry about 20 years ago. (There are plentiful discussions about this on chemistry.se alone.)
As long as that last part of the question is not meant as a trap (which would be even more awful), it alone shows that the exercise is not well-thought about.

The π-orbitals will therefore be entirely composed out of p-orbitals of the involved elements.

If you look close enough you will realise, that writing a valid Lewis structure of the molecule is not that hard, and you don't even need π-bonds in the first place.
These are solely dictated by symmetry.

In principle that molecule is of a similar system like allyl-systems (with two extra electrons), or ozone (with one more electron). You will need a better than rudimentary grasp at molecular orbital theory to understand it.
Let's assume that things would be easier, and try tor roll with that for as long as possible. I have written a couple of times that terminal atoms can be (as a rule of thumb) regarded as having sp-orbitals. Therefore the two oxygen will use one sp-orbital to form a σ-bond towards chlorine, the other one is an in-plane-σ-lone-pair. That leaves for every oxygen one in-plane-p-lone-pair, which we will (in the spirit of the approximation) disregard as having any effect on bonding. There is one remaining out-of-plane-p-orbital per oxygen. These will, due to symmetry, participate in π-bonding.
From VSEPR-theory we know the molecule is bent. The approximate hybridisation of the orbitals of chlorine that match that would be sp². Let's just assume that this is the case. Two of these will be the counterpart for the σ-bonds. The remaining will be either a lone-pair, or singly occupied. Already in this very simplified view, the problems start here. Let's further assume, that because it has higher s-character, the orbital will be lower in energy and therefore be doubly occupied. That leaves the odd electron in an out-of-plane-p-orbital, which will participate in π-bonding.

In this simplified and assumption riddled thought-experiment, the π-bonding will form three molecular orbitals pictured below.

Essentially the stabilisation from the π-bonds itself should be small, and could be described as π-backbonding, or is similar to negative hyperconjugation; maybe negative π-backbonding (!?).

This all was deduced from a very reduced and simplified set of theory; the reality is probably by far more complicated. Some of the greatest minds of (theoretical) chemistry have been puzzled about $\bf\ce{ClO2}$, and we have not even started to discuss the three-electron bond they assumed in between. Let's just say that this is not an undergrad study problem.

I know this doesn't really answer your question, and this is not very satisfactory either, but this is science: It often gives you more questions than answers.

halacha - Can an adopted child call birth parents by first name?

Consider someone adopted by Jewish parents, whom he grew up calling 'mom' and 'dad'. After he reaches adulthood, he meets his biological parents. Can he call them by their first names, if 'mom' and 'dad' feel uncomfortable? I know in general one shouldn't call one's parents by their first names.

medicine - Where is the source not to walk over someone because it stops him growing?

I have been brought up with the belief not to walk over someone because it can stunt their growth. Can anyone else here say where they have also heard of this? If yeah, where is the source?

Answer

The Be'er Moshe 8:36 discusses this issue and says it is something that they used be makpid on not to step over a child and if they went over him they would ask the person to step over him the other way so he can grow to his full height.

The Be'er Moshe continues that this custom is considered among the custom of old women which the Rashba (Shu"t 1:69) wrote that we should not belittle even if we can not understand the reason, they are certainly established on "mountains of holliness".

choshen mishpat civil law - El Al Airfare error and Halachah

What are the Halachic implications of yesterday's El Al airfare snafu? In brief, El Al's air tickets were being sold online very cheap for a while; the price was later corrected, and El Al claimed the price had been due to a third party's error; and by law El Al must honor the low price for paid-for tickets.

Most of the issues I can think of are really variations on the same theme:

If you knew it was an error, could you buy the tickets?

If you did not know but assumed it was an error, could you buy the tickets?

If you thought it might possibly be an error, could you buy the tickets?

If you did not realize it was an error but your travel agent mentioned as much while booking your tickets, should you have stopped him from executing the transaction?

If you had no idea until after purchasing the tickets, do you have an obligation to offer to El Al to make amends (whether that means asking to cancel without penalty or offering the pay the difference or even canceling despite taking a penalty)?

Does the fact that El Al has virtually no way of forcing passengers to pay the difference or of canceling their tickets make any difference to my last question above?

In terms of application, I think this can be used as a perfect model for varying degrees of the same issue, that can arise in practically any business.

halacha - What is the shiur for anointing on Yom Kippur?

Is there a minimum shiur to be chayav (liable) for anointing on Yom Kippur, and, if so, what is it? The gemarah (Yoma 76b) seems to learn it out as a comparison to food consumption: would that mean it has the same shiurim?

discrete signals - Fast Hartley Transform Implementation in MATLAB

I want to implement Fast Hartley Transform (Specifically Discrete Hartley Transform) in a script file in MATLAB. Does anyone know have a reference implementation of this in MATLAB or another language so that a complete novice can understand it?

FIR filter design by the Fourier transform method

I am having some problems understanding how the Fourier transform method is used to determine the FIR filter.

As far as i have understood, you start by using the ideal impulse reponse for the specific filter design you want to have. Those are given in this table

As the the ideal impulse reponse contains infinite impulses, we truncate the infinite to finite a number by $m$, (which is confusing how this is done).

But my question is how do predetermine the order of the filter, without having to try randomly, using this method?

halacha theory - Why don't we just follow the shittah of Moshe Rabeinu?

My question can apply to virtually all mitzvos where there is a disagreement in the standard way to fulfill them.

If one reads the hakdama (introduction) to the Rambam's peirush mishnayos (commentary on the mishna) he explains the origin of machlokes (disagreement in halacha).

But if Moshe was the main Rebbe, why didn't everyone just follow Moshe?

For example, knowing what Teffilin Moshe wore should resolve the disagreement over what our Teffilin should be like. Why didn't everyone just follow his shittah and pass that tradition down to us?

Edit:I found in the Ben Ish Chai Shana Alef parshas vayeira 21 that from Moshe Rabbeinu until the Geonim people wore two pairs(Rashi and Rabbeinu Tam)

inorganic chemistry - Why do different elements form different types of carbides?

What property of the elements make them form different types of carbides like:

$\ce{Be}$ and $\ce{Al}$ - $\ce{Be2C}$ and $\ce{Al4C3}$ (Methanides) contains $\ce{C^4-}$ ion

$\ce{Na}$ and $\ce{Ca}$ - $\ce{Na2C2}$ and $\ce{CaC2}$ (acetylides) contains $\ce{C2^{2-}}$ ion

$\ce{Li}$ and $\ce{Mg}$ - $\ce{Li4C3}$ and $\ce{Mg2C3}$ (sesquicarbides) contains $\ce{C3^4-}$ ion.

Boron - $\ce{B4C}$ (covalent carbides)

Titanium and tungsten - $\ce{TiC}$ and $\ce{WC}$ (interstitial carbides)

Answer

According to wikipedia,

Carbides can be generally classified by chemical bonding type as follows:

1. salt-like carbides


2. covalent carbides


3. interstitial carbides


4. "intermediate" transition metal carbides.

This type of classification is based on the electronegativity of the element to which the carbon is bonded.

According to this site:-

The most electropositive metals form ionic or saltlike carbides, the transition metals in the middle of the periodic table tend to form what are called interstitial carbides, and the nonmetals of electronegativity similar to that of carbon form covalent or molecular carbides.

Actually credits goes to @jatin who gave me an important hint:-

You might wanna consider diagonal relationship which accounts for similarities between those particular metals.

As you can see that Li and Mg, Na and Ca and Be and Al all form diagonal element pairs. So, they are expected to have similar properties. So, considering their electronegativity, the diagonal element pairs have almost same value (though Li and Mg electronegativity is quite different). So they form similar type of carbide.

(original picture)

As for the intestitial carbides, @bon said that

Insterstitial carbides only form with large cations (Ti and W), as you might expect if the anion (very small) to fit in the spaces in the cation crystal structure.

halacha - Could a religious man be an anarchist?

Could a religious man be an anarchist?

Because by praying you becoming a slave to whatever you pray to.

But anarchism (except of some small branches) do not support master-slave relationships.

Could some people elaborate on that from a Jewish point of view (Torah point of view). If there was ever an anarchist there and why it's not allowed.

What does this lambda–sigma notation mean?

I am currently reading the CRC Handbook of Phosphorus-31 Nuclear Magnetic Resonance Data by John C. Tebby (CRC Press, 1991) and on several figures (ex. pages 9 to 14) there is a caption that reads along these lines

$\ce{^{31}P}$ NMR chemical shifts of three coordinate (λ3 σ3) phosphorus compounds. (Tables B to E.)

What does the (λ3 σ3) signify? I've not seen that notation before, and it is on the captions of some of the charts I need.

Answer

The notation refers to the valency (number of valence electrons involved in bonds, i.e., either 3 or 5) and coordination number (number of substituents attached) in organophosphorus compounds. For example, it could refer to the tautomeric forms of phosphonate esters:¹

So the λ³σ³ refers to a P with 3 bonding valence electrons (the lone pair doesn't count) and 3 substituents attached while λ⁵σ⁴ refers to a P with all five of its valence electrons involved in bonds and 4 substituents attached.

---

Reference

1. Kraszewski, A.; Stawinski, J. H-Phosphonates: Versatile synthetic precursors to biologically active phosphorus compounds. Pure Appl. Chem. 2009, 79 (12), 2217–2227. DOI: 10.1351/pac200779122217.

halacha - Is it forbidden for a noachide (Non-Jew) to be circumcised?

I heard Rabbi Immanuel Schochet bring this up in a lecture as an off hand comment, that circumcision is bodily mutilation, and thus the only reason why Jews can do it, is because it they are specifically commanded to do so. As such, Non-jews (Who fall under the 7 noachide laws) are not to be circumcised.

Is this his rhetoric, or is this discussed anywhere in Jewish literature?

everyday chemistry - C + O2 is equal to C + O, how is that possible

C + O = CO₂ . This is because carbon has valency of 4 while oxygen has valency of 2. When they react the valencies are criss crossed which means we will get C₂O₄ but this is simplified to CO₂.

But my textbook say that C + O₂ = CO₂.

So how is it possible that C + O₂ and C + O both get the same product of CO₂?

Also you can say that the reaction of C + O = CO₂ is not balanced but the balanced chemical reaction would be C + 2O = CO₂ not C + O₂ = CO₂ which is the reaction that my textbook says.

Answer

When thinking about chemical reactions it is very important to know which chemicals may react with each other. Jun-Goo Kwak already pointed out the nature of oxygen.

A quick reminder: The ground state of elementary oxygen is the triplet biradical $\ce{o2}$, which is a gas. This is what we have on the surface of the earth. Carbon however comes in many different forms in nature. The most popular and often is graphite. Other forms include diamond, fullerenes and graphene. At one point in your life you haw almost certainly come in contact with graphite: coal. As the principle repeating unit is carbon itself, its formula will be written as $\ce{C}$.

As for the binary combination of oxygen and carbon, there are also many different modifications. The most important of them are carbonmonooxide ($\ce{CO}$) and carbondioxide ($\ce{CO2}$). Like Uncle Al stated there are also suboxides known, which are usually byproducts of incomplete combustion (if not targeted explicitly).

Having said all that, if you burn coal, the following main reaction will happen (1):

$$\ce{C + O2 -> CO2}$$

However, given the right conditions (excess carbon) also carbonmonoxide may be formed (sum of reaction, 2):

$$\ce{2C + O2 -> 2CO}$$

The reaction itself will detour via the Boudouard reaction, which is very important in blast furnace processes. First forming carbondioxide via 2 and then convertin excess carbon to carbonmonoxide via 3: $$\ce{C + CO2 <=> 2CO}$$

electrochemistry - Can we separate positive ions from negative ions in a solution?

Can we make a solution containing only positive ions by using electrodialysis but instead of using 2 kinds of membrane (one blocks the positive ions and one blocks the negative ions) we can use only one kind (the one which blocks the positive ions) so the positive ions wont reach the electrode and wont be electrolysed while the negative ions will be electrolysed leaving the positive ions in the solution

agada stories legends - Whoever is greater than his friend has a greater inclination

Sukkah 52a has an interesting story with Abaye (translation from Sefaria.org)

כי הא דאביי שמעיה לההוא גברא דקאמר לההיא אתתא נקדים וניזיל באורחא אמר איזיל אפרשינהו מאיסורא אזל בתרייהו תלתא פרסי באגמא כי הוו פרשי מהדדי שמעינהו דקא אמרי אורחין רחיקא וצוותין בסימא

It is like this incident, as Abaye once heard a certain man say to a certain woman: Let us rise early and go on the road. Upon hearing this, Abaye said to himself: I will go and accompany them and prevent them from violating the prohibition that they certainly intend to violate. He went after them for a distance of three parasangs in a marsh among the reeds, while they walked on the road, and they did not engage in any wrongful activity. When they were taking leave of each other, he heard that they were saying: We traveled a long distance together, and the company was pleasant company.

אמר אביי אי מאן דסני לי הוה לא הוה מצי לאוקומיה נפשיה אזל תלא נפשיה בעיבורא דדשא ומצטער אתא ההוא סבא תנא ליה כל הגדול מחבירו יצרו גדול הימנו

Abaye said: In that situation, if instead of that man it had been one whom I hate (a euphemism for himself), he would not have been able to restrain himself from sinning. (After becoming aware of so great a shortcoming) he went and leaned against the doorpost, thinking and feeling regret. A certain Elder came and taught him: Anyone who is greater than another, his evil inclination is greater than his. (Therefore, Abaye should not feel regret)

What does this principle mean? It can't be understood literally, it defies logic. The more righteous a person is, the more lusts he feels for women and murder and stealing etc.? Usually we see the opposite...

I once heard an explanation that "greater" means more sophisticated. Instead of immature desires like food and pleasure the temptations are more refined. The problem is it doesn't fit the context of the story and Abaye's realization about himself

Answer

See the 6th chapter of Shemonah Ferakim in which Rambam mentions this aphorism, as part of his presentation of seemingly contradictory sources about whether it is better to have a negative urge and fight it, or to not have the urge at all. His conclusion is that the urge towards sins whose impropriety is generally intuitive is indicative of a character flaw with the person. Accordingly, it would be better to not have such an urge at all. The urge to commit sins which are not intuitive, however, is not indicative of a shortcoming and it is better to have them and overcome them.

In this scheme, the intent of the Gemara suggesting that greater people have greater urges towards sin, would be speaking specifically of sins which are not intuitive; commonly referred to as hukkim.

This category of hukkim includes forbidden sexual relationships, as is evident from his entire discussion there. For example, he cites a Tannaic teaching (Sifra Kedoshim 4:9:12) that a person shouldn't say that he doesn't yearn to commit various sins, including forbidden sexual relations, but rather that he yearns for them, but nevertheless resists and desists. Rambam explains this statement, as referring to hukkim in particular.

However, the passage does not, as you suggest, refer to murder and stealing, which Rambam specifically lists as sins which ought to be intuitive.

R. Ovadya Sforno seems to have a very different understanding in his commentary to Genesis (3:1). He equates the greater urge towards sin that the great have, with a greater capacity for imagination; picturing and fantasising about the act of sin. (Accordingly, presumably he understood the "great" in the sense of intellectual giftedness). Importantly, accordingly, it is not righteousness which leads to the urge to sin, as the question presumes, but rather intellectual and emotional gits.

Additionally, it seems likely that not every sort of sin would be included. For example, within the example of murder, the greater, i.e. more imaginative person would perhaps be more likely to become obsessed with a scenario in which involves killing someone, but not necessarily be any likelier (and perhaps even less likely) to commit a crime of passion, in the heat of the moment.