Notes

- November 27, 2018

Apparently the of last four, $\ce{Mg^2+}$ is closest in radius to $\ce{Li+}$. Is this true, and if so, why would a whole larger shell ($\ce{Mg^2+}$) be closer in radius to $\ce{Li+}$ than its isoelectronic neighbor ($\ce{Be^2+}$) with just one extra proton?

- November 27, 2018

I want to change $\ce{CO2}$ coming out of the tailpipe of a car to some other compound that is considerably less harmful to the environment with a filter of some sort.

What are some ways that this is possible?

$\ce{CO2}$ to carbon and oxygen?

- November 25, 2018

Say, you conducted two separate reactions; in one, you combined $\mathrm{50~mmol}$ saturated $\ce{KCl}$ solution with $\mathrm{10~mmol}$ 1-bromooctane (assume heating), and in the other you combined $\mathrm{10~mmol}$ saturated $\ce{KI}$ solution with $\mathrm{10~mmol}$ 1-bromoctane. In both cases $\mathrm{0.5~mmol}$ hexadecyltributylphosphonium bromide was used as a catalyst.

So, due to relative charge densities and the fact that the electrophillic carbon is primary, you would have a low yield of 1-chloroocatane vs starting material in reaction 1 and you would have a high yield of 1-iodooctane vs starting material in reaction 2, both cases obtained via SN2 reaction.

Now, suppose you would have repeated the same two reactions, only this time you would have reacted the $\ce{KCl}$ and $\ce{KI}$ with 2-bromo, 2-methyloctane, how exactly would the results differ from the results of the previous two reactions, or would they have been the same?

I know that the reaction would have no "choice" but to react via the SN1 (or perhaps E1) route, as the electrophillic carbon is tertiary and thus very sterically hindered. Also, I know that $\ce{I-}$ ions are good nucleophiles, but that doesn't matter in this case, does it?

Perhaps this reaction would go slower than the previous, owing to the fact that it requires the $\ce{Br-}$ to dissociate, and therefore there would be lower yields of both haloalkane products. But then again, wouldn't it go faster owing to the fact that it is in a polar protic solvent, and that the formed carbocation would be tertiary?

- November 25, 2018

Consider a simple case where two signals from two different sensors are cross-correlated, and the time-delay-of-arrival computed from the absissa of the peak of their cross-correlation function.

Now let us further assume that due to the dimensionality constraints of both antennas and the constraints on maximum possible sampling rate, the maximum attainable delay possible is $D$, corresponding to 10 samples.

The problem:

Because of those constraints, your computed delay may vary from any integer value between 0 and 10 samples, that is: $0 \le D \le 10$. This is problematic because what I really want is fractional-delay discrimination of the delay between the two signals impinging on my antennas, and changing the dimensions or the sampling rate are not an option.

Some thoughts:

Naturally, the first thing I think of for this case is upsampling the signals before performing a cross-correlation. However I think this is 'cheating' somehow, because I am not really adding any new information into the system.

I do not understand how upsampling is not 'cheating' in a sense. Yes, we are reconstructing our signal based on its currently observed frequency information, but how does this give one knowledge of where a signal truly started between, say, $D=7$ and $D=8$? Where was this information contained in the original signal that determined that the true fractional-delay start of the signal was actually at $D=7.751$?

The question(s):

Is this truly 'cheating'?
- If not, then where is this new 'information' coming from?
- If yes, then what other options are available for estimating fractional-delay times?

I am aware of upsampling the result of the cross-correlation, in an attempt to garner sub-sample answers to the delay, but is this too not also a form of 'cheating'? Why is it different from upsampling prior to the cross-correlation?

If indeed it is the case that the upsampling is not 'cheating', then why would we ever need to increase our sampling rate? (Isnt having a higher sampling rate always better in a sense than interpolating a low sampled signal?)

It would seem then that we could just sample at a very low rate and interpolate as much as we want. Would this then not make increasing the sample rate 'useless' in light of simply interpolating a signal to our heart's desire? I realize that interpolation takes computational time and simply starting with a higher sample rate would not, but is that then the only reason?

Thanks.

Answer

It's not cheating, and it's also not adding any new information. What you are doing is the same thing that any upsampling LPF is doing- adding zeros and then reconstructing the waveform with the already known frequency information. Thus, there is no new information, but there is still finer time resolution.

Upsampling the result is similar- no new information but finer time resolution. You can do something very similar through quadratic interpolation.

All of these methods- upsampling and polynomial interpolation- get their information on where the fractional peak is from both the peak itself and its neighbors. A quick pictorial example. Balanced Peak

The blue line in the picture above is my simulated cross-correlation data (though it could be any result, not just a cross-correlation). It is what I call a "balanced" peak because the neighbors are symmetric. As you might expect, the resulting quadratic interpolation (red line) indicates that the true peak is at zero.

The image below, on the other hand, shows an unbalanced peak. Please note that nothing has changed in the result except for the values of the two nearest neighbors. This causes the interpolator, though, to shift its estimate of the fractional peak. enter image description here

A nifty side benefit of these methods (polynomial interpolation and upsampling) is that it also gives you an estimate of the true peak value, though we are usually more interested in the location.

If indeed it is the case that the upsampling is not 'cheating', then why would we ever need to increase our sampling rate?

To satisfy the Nyquist criterion.

Isn't having a higher sampling rate always better in a sense than interpolating a low sampled signal?

No. From a theoretical standpoint, as long as the Nyquist criterion is satisfied it doesn't matter what the sample rate is. From a practical standpoint you generally go with as low a sample rate as you can get away with to reduce the storage requirements and computational load, which in turn reduces the resources that are needed and power consumption.

- November 25, 2018

I have read the description of the Kalman filter, but I am not clear on how it comes together in practice. It appears to be primarily targeted at mechanical or electrical systems since it wants linear state transitions and that it is not useful for anomaly detection or locating state transitions for the same reason (it wants linear state transitions), is that correct? In practice, how does one typically find the components that are expected to be known in advance to use a Kalman filter. I have listed the components, please correct me if my understanding of what needs to be known in advance is incorrect.

I believe these do not need to be known "in advance":

Process noise $\mathbf w$

Observation noise $\mathbf v$

Actual state $\mathbf x$ (this is what the Kalman filter tries to estimate)

I believe these need to be known "in advance" to use a Kalman filter:

The linear state transition model which we apply to $\mathbf x$ (we need to know this in advance, so our states must be governed by known laws, i.e. the Kalman filter is useful for correcting measurements when the transition from one state to another is well understood and deterministic up to a bit of noise - it is not an anomaly finder or a tool to find random state changes)

Control vector $\mathbf u$

Control input model which is applied to control vector $\mathbf u$ (we need to know this in advance, so to use a Kalman filter we also need to know in advance how our controls values affect the model, up to at most some gaussian noise, and the effect needs to be linear)

Covariance $\mathbf Q$ of the process noise (which appears to be time dependent in the wikipedia article, i.e. it depends on the time $k$) - it appears we need to know this in advance and over time, I assume in practice it is taken as being constant?

A (linear) observation model $\mathbf H$

Covariance $\mathbf R$ (which appears to also be time dependent in the wikipedia article) - similar issues to $\mathbf Q$

P.S. And yes I know many of these depend on time, I just dropped all the subscript clutter. Feel free to imagine small letter $k$ to the right and down from each variable name if you would like to.

Answer

For some context, let's go back to the Kalman Filter equations:

$\mathbf{x}(k+1) = \mathbf{F}(k) \mathbf{x}(k) + \mathbf{G}(k) \mathbf{u}(k) + \mathbf{w}(k) \\ \mathbf{z}(k) = \mathbf{H}(k) \mathbf{x}(k) + \mathbf{v}(k)$.

In short, for a plain vanilla KF:

$\mathbf{F}(k)$ must be fully defined. This comes straight from the differential equations of the system. If not, you have a dual estimation problem (i.e. estimate both the state and the system model). If you don't have differential equations of the system, then a KF isn't for you!

$\mathbf{x}(k)$ is, by definition, unknowable. After all, if you knew it, it wouldn't be an estimation problem!

The control vector $\mathbf{u}(k)$ must be fully defined. Without additional system modelling, the only uncertainty on the control vector may be AWGN, which may be incorporated into the process noise. Known matrix $\mathbf{G}(k)$ relates the control input to the states - for example, how aileron movement affects the roll of an aircraft. This is mathematically modelled as part of the KF development.

The system process noise $\mathbf{w}(k)$ is also, by definition, unknowable (since it is random noise!). However, the statistics of the noise must be known which, for a plain vanilla KF, must be zero mean AWGN with known covariance $\mathbf{Q}(k)$. Sometimes, the covariance of the noise may change between samples, but in many cases it is fixed and therefore $\mathbf{Q}$ is a constant. In some instances, this will be known, but in many instances, this will be "tuned" during system development.

Observations are a similar story. The matrix that relates your measurements to the states $\mathbf{H}(k)$ must be fully defined. Your measurements $\mathbf{z}(k)$ are also known because that's the reading from your sensors!

The sensor measurements, however, are corrupted by AWGN $\mathbf{v}(k)$, which, being random noise, is by definition unknown. The statistics of the noise must be known, which is zero mean with covariance $\mathbf{R}(k)$. Once again, the covariance may change with time, but for many applications, it is a fixed value. Often, your sensors will have known noise characteristics from the datasheet. Otherwise, it's not too hard to determine the mean and variance of your sensors that you need to use. Yes, this can also be "tuned" empirically.

There are a huge number of "tricks" that can be done to work around the restrictions in a plain vanilla KF, but these are far beyond the scope of this question.

Afterthought:

Whilst googling for "Kalman Filter" results in a million hits, there are a couple of things that I think are worth looking at. The wikipedia page is a too cluttered to learn from effectively :(

On AVR Freaks, there is an "equation free" intro to the Kalman Filter that I wrote some time ago to try to introduce where it is used for real.

If you're not afraid of maths, there are several books worth reading that are at the senior undergraduate/early postgraduate level. Try either Brown and Hwang which includes all the theory and plenty of example systems. The other that comes highly recommended but I have not read is Gelb, which has the distinct advantage of being cheap!

- November 25, 2018

Why does the starting compound not need an -OH group? I thought ozonolysis only produced carbonyls?

- November 24, 2018

Very rusty with chemistry and looking to review some basics. Came across the following:

Iron(II) chloride and potassium phosphate react. Write and balance the molecular, ionic, and net ionic equations.

What I have so far (guessing, basically):

$$\ce{FeCl2 + K(H2PO4) -> KCl + Fe(H2PO4)2}$$ [still need to balance but correct right hand side?]

I can't remember the exact rules for forming the right hand side. I just put this in place to match ion charges. What prevents me from writing the right hand side as something else entirely (not sure what but I'm asking, "well, couldn't I figure something out if I break everything apart and re-arrange into another option?").

EDIT: Additional Question Below

Ok, so assume the above reaction was balanced (it's not) and valid. Then, my question is does the reaction go both ways ($\ce{<-->}$)? If so, when/why/how? I'm trying to think back many years ago and it has something to do with "reactivity" and the row of the elements on the periodic table, correct? I'm going to look into it more myself but if someone has a quick "30 second" answer I'm sure it'd be of help to me!

[Assuming this is OK and valid in the forward direction. Again, needs to be balanced.]

$$\ce{FeCl2 + K(H2PO4) -> KCl + Fe(H2PO4)2}$$

[Is this ever ok/possible?]

$$\ce{KCl + Fe(H2PO4)2 -> FeCl2 + K(H2PO4)}$$

- November 24, 2018

I understand that for many people, this is almost impossible to do - as long as you go shopping anywhere outside a Jewish neighborhood, or if you turn on the television, you will be exposed to Christmas music. Similarly, if you work in an office and someone puts on the easy listening station for people to listen to, you will be exposed to a LOT of Christmas music.

Assuming you're able to avoid actively seeking out such music (for example, not shopping at Macy's Department Store during this time of the year), are there any other halachic things a person should be aware of if there is the potential for being exposed to Christmas music? For example, are we enjoined not to watch a television show if there is the possibility of some Christmas music being featured?

- November 24, 2018

Is anyone aware of any halakhic opinion regarding the playing of musical instruments, guitar for example, in shul on a weekday, not shabbo. Does it have the same religious stigma and opposition as having an organ in shul did at the beginning of the reform movement? Is it still seen as a move towards the practices of other religions?

- November 24, 2018

I've recently started playing with the Kalman filter for a simple 2D (x,y,dx,dy) tracking toy problem. But I seem to have some misunderstanding on what I can expect from the filter. I'm interested in plotting the uncertainty ellipse from the corrected covariance matrix but noticed a few observations:

The covariance decreases to a steady state regardless of how much error I introduce into the measurement.

The variance for x and y are exactly the same even though I introduce more measurement errors in y.

Staring at the maths for a bit it seems that this is how the vanilla Kalman Filter works. What I'm expecting is the opposite of the two points mentioned above. In the end I want to plot an uncertainty ellipse that reflects the error I'm observing. Is this possible at all? Do I have to do some post processing on the covariance matrix?

ANSWER:

It occurred to me what I needed was a Kalman Filter that has the ability to adapt its covariance. I found this paper that details a few different methods to do this.

http://www.gmat.unsw.edu.au/snap/publications/almagbile_etal2010a.pdf‎

- November 24, 2018

Link to exam

Which metal reacts most vigorously with water?

(A) Ca (B) K (C) Mg (D) Na

The given answer is B and the reasoning is that is is the most electropositive since it the furthest left and down according to periodic trends.

However, isn't $\ce{K}$ the conjugate acid from a strong base -- $\ce{KOH}$? So isn't the conjugate base of a strong acid quite weak? So why would $\ce{K}$ react strongly?

Answer

I might be wrong here, but I believe that the question asks about the metals in their atomic (non ionic) form.

In order for a $\ce{KOH}$ bond to form, the K must be ionized (since the $\ce{KOH}$ bond is ionic). This means that when $\ce{KOH}$ dissolves in water it'll form the $\ce{K}^+$ electrolyte, which is not the same thing as a pure $\ce{K}$ atom with its 19th electron.

A $\ce{K}$ atom, then, since it's the most electropositive of that list, is the one to react "more vigorously" (which I guess it refers to more speed/energy) with water (a polar molecule).

I hope this helped you. I'm sorry if I'm wrong!

- November 24, 2018

I know that activation energy for a reaction is the extra energy given to the reactants to reach the threshold energy so that they can collide and react. But then, why is it said that the activation energy does not depend on the temperature?

If the temperature is higher, the reactant molecules have a higher kinetic energy, and thus the energy difference between the threshold energy and the energy of the molecules will decrease, that is, the activation energy will decrease.

Answer

There is a simple (some might say simplistic) way to get an intuition about this and it involves thinking at the molecular or atomic level rather than about the bulk properties of the reaction (the thermodynamic view).

For a simple reaction where molecule A has to bang into molecule B to create molecule C, the reaction will only happen if the amount of energy involved in the collision is large enough. The amount of energy involved depends on the nature of the reaction which is determined by the electronic structures of A and B. Within limits, those electronic structures don't vary with temperature and a given reaction will only occur when there is enough energy in the collision for the reaction to happen.

What changes with temperature isn't the energy required for the reaction to occur, it is the number of molecules that have enough energy to overcome the barrier. At higher temperatures more molecules have that energy, but the amount of energy required doesn't change. The amount of energy require to initiate the reaction is roughly equivalent to the activation energy. It can be calculated by looking at the way the overall rate of the reaction changes with temperature. So the rate of reaction changes with temperature but not the barrier to the reaction happening.

This view is a little simplified but it gives the right intuition about the problem.

- November 23, 2018

The only secretion from the human body that I know to be kosher is human milk. I am curious to know which other bodily fluids are kosher.

For example, is it kosher to drink sweat or tears? What about mucus?

Assume that a person has only eaten pareve kosher food, and later vomits it out. Is this vomit kosher?

There's at least a dozen other related questions that come to mind, but I'll stop here to avoid being gratuitously gross. In general, which bodily fluids are kosher and which ones are not?

- November 23, 2018

This question spawns from the comments here.

I've heard that オタク could or could not be derogatory. During the times I've been in Japan and heard it used, I didn't think that it had any connotation of being an insulting term, but is this true?

I'm not sure about other countries, but in America as a borrowed word, many people are proud to be called an "オタク" depending on the circumstance. Is it not the same in Japan?

- November 23, 2018

There are many Jewish weekly or monthly publications (e.g. magazines) that offer the following deal:

Individual copies of the magazine are priced at say, $5 each. But, if you "subscribe" by paying in advance for the entire year, you get a discounted price which comes out to say, $3 each week.

It seems that this is a classic case of ribbis in the form of poskin al hapeiros we find in Bava Metzia. The only way out of it is either (1) the product has had a price setting in the form of yatza hashaar, which I do not think applies to most commercial products these days, or (2) the publisher already has the copies of all the magazines you are buying (yesh lo), which is clearly not the case here.

How are the publishers of these Jewsih publications and their subscribers not violating the prohibition of ribbis?

Answer

This issue is discussed here.

Summary: Magazine subscriptions to Jewish-owned publications are forbidden only where the discount is explicitly or obviously linked to the advance payment. In this case, the discount is usually linked to other factors, so most poskim permit it.

A little research online shows that the primary reasons that magazine publishers offer discounted (often severely discounted) prices for subscription is to raise advertising revenue (as advertisers pay more to be featured in magazines with more subscribers), and to be guaranteed the purchase for the whole year. This would then be permitted for Jewish publications.

However, if the subscription discount is advertised in a way that highlights the fact that the discount is for advance payment (e.g. "Subscription price is contingent on prepayment in full," or, "Pay for a year and save 45%") this would be problematic.

In the discussion here (note 43) though, an interesting problem is brought up:

If the price of the periodical increases during the subscription period, the subscribers could not be indemnified from the increase. In this case, a new subscriber who joins after the price increase is charged a higher price than the person who subscribed earlier. All of the outside motivations...apply to both subscribers. The only reason that those who subscribed earlier are protected from the increase is because they advanced funds at an earlier time. This benefit is prohibited.

The practical solution given there is that the publisher should offer the subscriber the option of paying the publisher itself or to place the money in escrow to be withdrawn by the publisher at the appropriate time. This eliminates the possibility that the discount is motivated by the advance payment. [It is also recommended that a heter iska klali be used.]

- November 23, 2018

It is written:

משנכנס אדר מרבין בשמחה (When Adar comes we increase in joy)

If a person started to get happy on Tu b'Shevat instead, is this permissible b'dieved (after the fact)? What if someone had an intention beforehand to increase joy before Adar and carried it out, for example, they told Purim Torah (offline) in Shevat?

- November 23, 2018

I have read in Ezechiel 29:12-15 that

"And I will make the land of Egypt desolate in the midst of the countries that are desolate, and her cities among the cities that are laid waste shall be desolate forty years; and I will scatter the Egyptians among the nations, and will disperse them through the countries. Yet thus saith the Lord GOD: At the end of forty years will I gather the Egyptians from the peoples whither they were scattered; and I will turn the captivity of Egypt, and will cause them to return into the land of Pathros, into the land of their origin; and they shall be there a lowly kingdom. It shall be the lowliest of the kingdoms; neither shall it any more lift itself up above the nations; and I will diminish them, that they shall no more rule over the nations."

Has this prophecy already been fulfilled? If yes, when and how?

Answer

According to Abarbanel, the several prophecies in Chapters 29-32 of Ezekiel are all concerning the future of Egypt (the future from Ezekiel's perspective), but they will not all happen at the same time. The first prophecies were realized during the reign of Nebuchadnezzar and his conquering Egypt, and the later prophecies will be realized before the coming of the Messiah.

The verses you quoted are from the first prophesy about Egypt, and thus Abarbanel interprets them as referring to when Nebuchadnezzar conquered Egypt, which is more clearly related in the subsequent (but connected) prophesy (29:19).

Nebuchadnezzar conquered Egypt and exiled its inhabitants such that they were "scattered among the nations" and Egypt "laid waste and was desolate" for 40 years. The calculation of 40 years is: 18 remaining years of Nebuchadnezzar's reign + 22 years of his son's reign.

After that began Belshazzar's reign, at the beginning of which Daniel's prophesy occurred, and then the Egyptians began to return to their homeland, fulfilling verse 13. However, the "new Egypt" was never again as powerful as it was originally, warranting a description as a "lowly kingdom" in verse 14, and even as "the lowliest of the kingdoms" in verse 15.

- November 23, 2018

I came across a sentence that ends with ひとつだけ in a book and searching on jisho gave me zero results (https://jisho.org/search/ひとつだけ); nor did searching for the individual parsing of what I remember from the audio of the VN (i.e. hitotsu--DakE) give me any helpful results that would make sense in context.

しかも、出入り口は錆の浮いた鉄扉がひとつだけ。

TDLR: What does the sentence end(?) ひとつだけ mean in the above context and does it have a general meaning when used at the end of a sentence as opposed to being used elsewhere in the sentence?

Edit:

Context: Narrator is describing a unfamiliar room he wakes up in. I think that ひとつだけ in the above context will not work as individual parsings as ひとつ most likely means either the "adverbial noun – just" or the numeric one in the above context that adverbially/numerically describes the 鉄扉 (iron door). The next bit, だけ most likely is a particle ("only") but I don't see how the "only" can affect the 鉄扉 as the ひとつ is already doing that to the "iron door". The only way I can see both affecting 鉄扉 is if ひとつだけ is a qualifier sentence (technically a qualifier phrase) being used in reverse-order.

- November 23, 2018

While reviewing my 漢字, I noticed that for "last", I have (at least) two words, either 最後{さいご} or 最終{さいしゅう}. I was wondering, is there any difference in usage, or can I use them equivalently?

Answer

最: most; extreme

後: later; latter

終: end

最後 is used as a noun or a の-adjective. (e.g. 列の最後, 最後の晩餐) In the form of Verb+が/たら+最後, it means once (e.g. 彼は外に出たが最後... Once he goes out...)

最終 is used as an adjective right before noun. (e.g. 最終列車, 最終的)

When they are adjectives, they are usually interchangeable. (e.g. 最後のバス is interchangeable with 最終バス)
However, while 最終 means to just happen after all other things, 最後 often implies that it is the end of things and that it will never happen again. For example, 最終試合 is just a last game of championships on which someone will be a champion; 最後の試合 is the final game for someone.

- November 23, 2018

We know that Israel was still in Goshen during their enslavement, because the text tells us that the plague of hail didn't affect Goshen "where b'nai Yisrael were" (Shemot 9:26). It sounds like they are still living apart from the Egyptians, else some Egyptians would have been spared by the hail (if they lived in Goshen too) or some of Israel would have been affected (if they lived outside of Goshen).

Right before the exodus, God instructs the people to borrow silver and gold from their neighbors (Shemot 11:1-3). "Neighbors" sounds like people who live nearby. In chapter 12 the Egyptians urge them to leave quickly, and that's when the borrowing occurs.

How isolated or how intermingled were Israel and the Egyptians at the time of the exodus? Did Israel have Egyptian neighbors, or did they actually borrow silver and gold from random Egyptians they encountered on the way out that night?

- November 23, 2018

I believe I understand what this piece of description is saying with regards to the subject but I'm confused by the last part and therefore not sure how to correctly parse it:

数年前の経歴も局長の立場から調べてあるが、何しろ冤罪によって部局を追放された身である為,

Is "身である為" the same as saying "身のためである" which means "for your own benefit"? In which case the sentence would probably go something like this - "he was evicted from the department anyway due to false accusations [for his own benefit]".

- November 23, 2018

I am quoting a line from a book regarding reactivity of alkali metals with liquid ammonia.

The blue colour of the solution is due to the ammoniated electron which absorbs energy in the visible region of light and thus imparts blue colour to the solution

Now my question is:

How does the independent electron get excited (without transitional levels)?

Why do salts of particular alkaline metal always have a fixed flame color if transitions of electrons can be from any energy level.

(I am asking this question based on my knowledge of school where we only studied transitions among hydrogen like species)

- November 23, 2018

On the topic on neigbouring group participation, it is mentioned in Carey & Sundberg (2007)^[1] that the effectiveness of the participation is dependent on on the ease with which the molecular geometry required for the participation can be attained. The example of the cyclization of ω-hydroxyalkyl halides was then given:

The rate of cyclization of ω-hydroxyalkyl halides, for example, shows a strong dependence on the length of the chain separating the two groups.

To prove the point, they showed the data for the solvolysis rates for ω-chloro alcohols with various chain lengths. Clearly, when a 5-membered ring is form, the rate of reaction is fastest. This is reasoned with the fact that a 5-membered ring has relatively little ring strain and thus, the rate of forming it would be relatively higher. However, this analysis does not seem to be convincing. If this reasoning was indeed correct, then wouldn't the next member in the series, with the capability of forming the 6-membered ring, have a higher solvolysis rate?

\begin{array}{|c|c|c|c|} \hline \text{Substrate} & k_\mathrm{rel}{}^\text{[2,3]} \\ \hline \ce{Cl(CH2)2OH} & 2000 \\ \hline \ce{Cl(CH2)3OH} & 1 \\ \hline \ce{Cl(CH2)4OH} & 5700 \\ \hline \ce{Cl(CH2)5OH} & 20 \\ \hline \end{array}

In general, why doesn't the rate increase as the alkyl chain increases in length, based on the reasoning using ring strain in the intermediate? We see that 3-chloropropanol is also another outlier.

Additional information

It seems that the relative solvolysis rates of ω-methoxyalkyl p-bromobenzenesulfonates also follow the same trend, with the rate peaking with the formation of the 5-membered ring.

\begin{array}{|c|c|c|c|} \hline \text{Substrate} & k_\mathrm{rel}{}^\text{[4]} \\ \hline \ce{CH3(CH2)2OSO2Ar^*} & 1 \\ \hline \ce{CH3O(CH2)2OSO2Ar} & 0.28 \\ \hline \ce{CH3O(CH2)3OSO2Ar} & 0.63 \\ \hline \ce{CH3O(CH2)4OSO2Ar} & 657 \\ \hline \ce{CH3O(CH2)5OSO2Ar} & 123 \\ \hline \ce{CH3O(CH2)6OSO2Ar} & 1.16 \\ \hline \end{array}

*The first entry shows the rate of solvolysis without any neighbouring group participation from the methoxy group.

References

Carey, F. A., & Sundberg, R. J. (2007). Advanced Organic Chemistry Part A. Structure and Mechanisms (5th ed.). Springer.

Capon, B. Neighbouring group participation. Q. Rev., Chem. Soc. 1964, 18 (1), 45–111. DOI: 10.1039/QR9641800045.

Richardson, W. H.; Golino, C. M.; Wachs, R. H.; Yelvington, M. B. Neighboring oxide ion and fragmentation reactions of 1,3-chlorohydrins. J. Org. Chem. 1971, 36 (7), 943–948. DOI: 10.1021/jo00806a019.

Winstein, S.; Allred, E.; Heck, R.; Glick, R. Neighboring methoxyl participation in solvolytic nucleophilic substitution. Tetrahedron 1958, 3 (1), 1–13. DOI: 10.1016/S0040-4020(01)82605-3.

- November 23, 2018

A question on Beer.SE asks why (according to the Kashrut Authority of Australia) beer from New Zealand must be presumed dairy. The question there asks what dairy could possibly be in beer.

My first thought was that, for whatever reason, the breweries in question are using dairy equipment and thus get a dairy hechsher. But the KAA web site lists the following in its key to designations:

D = Dairy
D-CY = Dairy/Chalav Yisrael
P = Pareve
P-DV = Pareve/Dairy Vessels

So if they have the P-DV designation (not all authorities distinguish this case but apparently they do), does this mean that it's always used when possible and New Zealand beer really does have dairy in it? Or are there cases where a kashrut supervisor might say "dairy" when it's instead an equipment issue?

My immediate question is about KAA, but if there are broader principles involved about how kashrut certifiers make these determinations, I'm interested in hearing htem.

Answer

I asked them and received the following reply from Rabbi Moshe D Gutnick (with permission to post here):

In NZ all ethanol is produced from whey and is Dairy. Therefore all ethanol based alcoholic beverages such as Vodka produced in NZ must be considered dairy. Beer was also included in that as a precaution. However it is now quite clear that none of the major breweries in NZ fortify their beers with ethanol and they are therefore Pareve .

- November 22, 2018

Does anyone know the German custom for the letter pey in Sta"m sofer? I know that the shape in Litvisch Bet Yosef is influenced by the Mekubalim of Tzfat (The Ari in particular) who said that the letter bet should appear within the pey. As the Germans were quite averse to most anything kabbalistic, would this apply to a sefer written by someone who follows German minhagim?

Answer

This is the picture from my sefer, which experts have identified as either German or Czech. As you can see, there is a beis visible inside the Peh but it made neither in the style of the old European Bet Yosef ksav nor the Mishna Berurah's modification. Peh, על כפו Yekke sefer torah

- November 22, 2018

What are some good resources for deciphering a Tosfos comment that I can't figure out?

Here is what I am looking for in a resource:

When Tosfos brings another gemoro this resource should provide an explanation of it without me having to look it up.

Unlike Artscroll, it shouldn't be just a summary of the Tosfos, but a full explanation of it.

And the most important it should be written by someone who really understands tosfos and gets it right.

- November 22, 2018

In the 2nd verse in Shelach, it says שלח לך (Shelach Lecha), which Rashi explains as " לדעתך, אני איני מצוה לך". Why don't we give the same explanation the other places in the Torah it says לך. E.g. in Parshas Lech Lecha, or by the Ketores (קח לך)?

Answer

It has to do with the fact that in this case, the same incident recorded later in the Torah, seems to tell us that it was Moshe's own decision (and the populace's initiative) to send the mission. We do not have such exceptional circumstances in the other cases you mentioned.

Edit: Actually, this only answers why Rash"i does comment here. The truth about why he doesn't comment elsewhere is probably just because a verb with a purposeful prepositional pronoun is a standard way to express a certain type of imperative in Tana"ch. See this interesting hirhurim post on the "polite imperative" as a description of this form.

- November 22, 2018

For an elementary chemistry class percent error is calculated as: [actual-experimental]/actual x 100% edit:bracket represents absolute value

So my question is if the experimental is close enough to the actual that the subtraction would give zero significant figures, would then the percent error then be zero?
EX: measured density of 0.997g/ml and actual density of 0.997171g/ml then, 0.997171-0.997=0.000171 which would be rounded to 0.000 due to sig. figs. -> there are no significant figures so this would mean the calculated 0.0171% error would be zero correct. If I remember my analytical correctly we will do away with sig. figs. and work with the propagation of error within each measurement but I have not thought about how this would work in a problem like this.

Thank you in advance.

- November 22, 2018

I am referring to the the following paper : Non-contact, automated cardiac pulse measurements using video imaging and blind source separation

In the above article, the authors are able to extract cardiac pulse signal out from RGB components. I try to visualize the process as follow.

R' = R + cardiac pulse
G' = G + cardiac pulse
B' = B + cardiac pulse

R', G' and B' are the colour components observed by camera. R, G, B are the colour components for a person, by assuming that he doesn't have any cardiac pulse.

It seems that we will be having 4 sources (R, G, B, Cardiac pulse). We are now trying to obtain 1 of the 4 sources (Cardiac pulse) from 3 mixture signals (R', G', B'), by using ICA.

Does it make sense? Am I missing some techniques? Or, am I making a wrong assumption on the process?

Answer

You might also want to consider Principal Component Analysis (PCA) or an extension of it known as Independent Subspace Analysis which is PCA followed by ICA. These techniques work very well for extracting pitch stationary signals from a single observation signal. I'm an audio specialist but have discussed biomedical signals with colleagues in the past and from recollection cardiac pulses from a single observation are pretty well characterised and thus would be suitable sources for extraction using ISA. I have used it to great avail to separate drums from full musical polyphonies.

- November 22, 2018

If 好き is a noun, then why does it take the な copula in things like 好きなこと? I thought that copula was reserved for adjectives, and I thought nouns took on the の copula.

- November 22, 2018

The meraglim (scouts) and their shevet (tribe) are listed in a strange order in Bemidbar 13:

Reuven

Shimon

Yehuda

Yissachar

Ephraim

Binyamin

Zevulun

(Of Yosef): Menashe

Dan

Asher

Naftali

Gad

As Ramban notes,

מנה הכתוב השבטים לא לדגליהם ולא לצבאותם ולא כתולדותם.‏

"Scriptures enumerates the tribes not according to their banners, nor their hosts, nor their order of birth."

Can we account for this order, other than with what Ramban suggests, that this was done based on their relative worth?

ונראה שראה למנותם הנה לפי מעלת השלוחים, כי היו ראשים ונשיאים בעם כאשר ספר, ואין מעלתם שווה אבל יש בהם גדול מחברו בחכמה (ובמניין): ובכבוד, והקדים הנכבד הקודם במעלה כי ממעלת עצמם מנאם לא למעלת השבט. וכן בנשיאים החולקים להם את ארץ כנען (להלן לד יז - כט): הזכירם כפי המעלה לא לתולדותם:‏

- November 22, 2018

I've always thought that Hebrew is the Lashon HaKodesh, the language G-d speaks, and the language of Judaism. And that Aramaic is also important but somewhat secondary.

But based on this answer, it seems that Aramaic may be as important as hebrew (or even more). How could Aramaic be the first language spoken? What's the importance of Aramaic in Judaism and how does it compare to Hebrew?

- November 22, 2018

Technically the word 微妙 means

as per WWWJDIC:

(adj-na,n) (1) delicate; subtle; sensitive; (2) difficult; delicate (situation); complicated; (3) doubtful; questionable; dicey;

However, last time I stayed in Tokyo ( about a year ago) most of my Japanese friends (about 25-30 years old) were using 微妙 to mean "kinda sucky" or "boring in an annoying way". I believe I remember a sentence like this:

海はどうだった？まあちょっと微妙。

How was the beach? Eh... it kinda sucked.

I also heard it used as an adverb with this meaning but I can't remember an example. When I asked my friends about it, they said they don't really use that word for positive things, though none of the numerous examples I saw on ALC had this slangy type of meaning. I guess the meaning of subtle mixed with dicey and then became "so either-or that it just sucks"? If anyone can explain the subtleties of this slang usage, I've been wondering for a while.

Answer

微妙{びみょう} has been going through an evolution during the time I've been in Japan. There was a time, maybe about a decade ago, when it seemed to be one of those popular words that people would over use. Similar to how there was a fad for a time, mostly with younger people, to add 超{ちょう}("ultra~") to almost everything for emphasis.

Being that slang is, by nature, fluid in its evolution and open to interpretation, I think you'll see a lot of variety in daily use, and the dictionaries, like ALC, might not be keeping up.

I don't think it means "kind of sucky," however. To me, "kind of sucky" is a clear judgment that something is "sucky", with the only question being to what degree, answered by appending "kind of." (Though I'll admit we might just be disagreeing on the definition of "sucky", which is itself slang, so I hope you can go along with the spirit of what I'm trying to convey if not the literal terms.)

微妙{びみょう} retains its lack of certainty even when it tends to the negative. So I would take your 「まあちょっと微妙{びみょう}」 to be just a little more vague. Something like "Meh, the beach didn't really do it for me." In other words, it wasn't that it was clearly bad, maybe there were some things that were okay, and maybe other people liked it, but me, I was nonplussed.

Used in its adjectival form, on example that I hear often is 「微妙{びみょう}に違{ちが}う」, which means something like "[it's] kind of off [somehow]". I think in this phrase, it's the 違{ちが}う that's doing more of the heavy lifting of conveying the negative than 微妙{びみょう}.

Just for comparison, similar terms are 中途半端{ちゅうとはんぱ}, which can go from "half done" to "half assed", or 今一{いまいち} which is literally "not quite" but can mean "almost but not actually good".

Hope that helps.

- November 21, 2018

I have seen people seemingly careful to sit down when beginning the paragraph of prayers that starts "Ashre yosh've vesecha" (Ps. 84:5). One such person told me that he was, in fact, careful to do so, and that this was so he be counted among those mentioned as fortunate in the verse ("Fortunate are those who dwell/sit in Your house…").

(Incidentally, this seems odd to me, because the verse seems to be referring to those who dwell, not those who sit, in God's house, and also because it's referring to sitting/dwelling in general, not specifically while reciting the verse itself. In any event…)

Is there a source that encourages sitting for "Ashre" (the paragraph, or its start)? or even a source that mentions the custom (perhaps even to indicate its baselessness)? Any information on the custom's provenance?

If so, any indication on whether the custom applies equally every time "Ashre" is recited (before shacharis, before mincha, before s'lichos, at the end of shacharis, or, heck, any time the verse is recited by someone saying T'hilim)?

- November 21, 2018

There is a common custom amongst many to recite the words

אל מלך נאמן

before Kriyas Shema when there is no minyan. However, in all Chabad siddurim I have davened from, this phrase is not there. Why is this?

Answer

The First Chabad Rebbe, known as the Alter Rebbe (and also known as "The Rav (Ba'al HaTanya)", the author of Shulchan Aruch Harav) writes in his Siddur:

יחיד המתפלל לעצמו יחזור תיבות אני ה' אלהיכם

An individual praying alone should repeat the words Ani Hashem Eloheichem

This is to exclude minhag ashkenaz (and what he writes in his Shulchan Aruch) that an individual says "אל מלך נאמן".

- November 21, 2018

I know that bond angle decreases in the order $\ce{H2O}$, $\ce{H2S}$ and $\ce{H2Se}$. I wish to know the reason for this. I think this is because of the lone pair repulsion but how?

Answer

Here are the $\ce{H-X-H}$ bond angles and the $\ce{H-X}$ bond lengths: \begin{array}{lcc} \text{molecule} & \text{bond angle}/^\circ & \text{bond length}/\pu{pm}\\ \hline \ce{H2O} & 104.5 & 96 \\ \ce{H2S} & 92.3 & 134 \\ \ce{H2Se}& 91.0 & 146 \\ \hline \end{array}

The traditional textbook explanation would argue that the orbitals in the water molecule is close to being $\ce{sp^3}$ hybridized, but due to lone pair - lone pair electron repulsions, the lone pair-X-lone pair angle opens up slightly in order to reduce these repulsions, thereby forcing the $\ce{H-X-H}$ angle to contract slightly. So instead of the $\ce{H-O-H}$ angle being the perfect tetrahedral angle ($109.5^\circ$) it is slightly reduced to $104.5^\circ$. On the other hand, both $\ce{H2S}$ and $\ce{H2Se}$ have no orbital hybridization. That is, The $\ce{S-H}$ and $\ce{Se-H}$ bonds use pure $\ce{p}$-orbitals from sulfur and selenium respectively. Two $\ce{p}$-orbitals are used, one for each of the two $\ce{X-H}$ bonds; this leaves another $\ce{p}$-orbital and an $\ce{s}$-orbital to hold the two lone pairs of electrons. If the $\ce{S-H}$ and $\ce{Se-H}$ bonds used pure $\ce{p}$-orbitals we would expect an $\ce{H-X-H}$ interorbital angle of $90^\circ$. We see from the above table that we are very close to the measured values. We could fine tune our answer by saying that in order to reduce repulsion between the bonding electrons in the two $\ce{X-H}$ bonds the angle opens up a bit wider. This explanation would be consistent with the $\ce{H-S-H}$ angle being slightly larger than the corresponding $\ce{H-Se-H}$ angle. Since the $\ce{H-Se}$ bond is longer then the $\ce{H-S}$ bond, the interorbital electron repulsions will be less in the $\ce{H2Se}$ case alleviating the need for the bond angle to open up as much as it did in the $\ce{H2S}$ case.

The only new twist on all of this that some universities are now teaching is that water is not really $\ce{sp^3}$ hybridized, the $\ce{sp^3}$ explanation does not fit with all of the experimentally observed data, most notably the photoelectron spectrum. The basic concept introduced is that "orbitals only hybridize in response to bonding." So in water, the orbitals in the two $\ce{O-H}$ bonds are roughly $\ce{sp^3}$ hybridized, but one lone pair resides in a nearly pure p-orbital and the other lone pair is in a roughly $\ce{sp}$ hybridized orbital.

- November 21, 2018

I'm reading a book on how to draw manga style characters, and I came across this sentence. It is part of a larger block explaining how to make a character look the same from all different angles.

同{おな}じ髪型{かみがた}といっても、どこから分けてあるか、どんな感{かん}じのカーブで、みけんならみけんのどこまでかかるのか、などに注意{ちゅうい}をはらって描{か}きます

I think I understand the general meaning of the whole sentence, but the part where it says みけんならみけん puzzles me a bit. I get that it's talking about where to draw the brow of the face and how far across it goes (「どこまでかかるのか」).

As I understand it, なら is something like "being the case that", so I translate みけんならみけん as "the brow as the brow", but that seems weird to me. How would the brow act as anything other than the brow when drawing a face? My translation must be wrong because it would be redundant to talk about the brow as the brow.

What is なら doing in this context?

Answer

"Even if it's the same hairdo, you draw keeping close attention on where to part it from, what sort of feeling of the curves, and [for/in the case of] the area between the eyebrows how far across to go of that area, etc."

みけんなら
=[for/in the case of] the area between the eyebrows

みけんのどこまでかかるのか
=how far across to go of the area between the eyebrows

- November 21, 2018

I was learning today's Tanya (יג תמוז, beginning of אגרת התשובה פרק ד)

I have a question based on the following part:

כשעבר עבירה שחייבים עליה כרת, הי׳ מת ממש קודם חמשים שנה

A violator of a sin punishable by excision would actually die before his fiftieth year.

ובמיתה בידי שמים, מת ממש קודם ששים שנה

In the case of death by divine agency he would actually die before sixty,

כחנניה בן עזור הנביא, בירמיהו

like the prophet Chananiah ben Azur in Jeremiah.

From here we see that כרת is dying before one turns fifty and that מיתה בידי שמים is dying before one turns sixty.

So, my question is what happens if someone does an aveirah for which the punishment is one of these after 50 or 60 (for כרת or מיתה בידי שמים respectively)? Do they die instantaneously?

- November 21, 2018

I would like to know how to compute the statistics of the discrete Fourier transform of a noise signal. To illustrate what I mean, I will first explain in detail a computation I have managed to do myself.

Suppose we have a discrete time series of values $x_n$ with $n$ from 0 to $N-1$. Each $x_n$ is a random variable, uncorrelated with the others, and Gaussian distributed with width $\sigma$. If I define the discrete Fourier transform

$$X_k = \frac{1}{N}\sum_{n=0}^{N-1} x_n e^{-2 \pi i n k / N}$$

then I find that $X_k$ is a complex random variable with real and imaginary parts Gaussian distributed with width $\sigma/\sqrt{2 N}$. I did the computation by using the fact that the distribution of a sum is the convolution of the distributions, etc.

Now I want to know how to do this computation in the case that $x_n$ are correlated. How does one approach this problem? I can make the assumption that the process is Markovian.

I had originally asked this on the Computation Science site, but I think here is a better fit.

Answer

After many weeks I give the answer to my own question.

There is a limit in which we can solve this problem in a reasonably simple way. Suppose we sum enough points in our DFT that the central limit theorem guarantees that the distribution of the sum's real and imaginary parts are Gaussian distributed. Then we only need to compute the variance. If we specialize the case of the variances of the real part of the DFT we can write

$$ \langle (\textrm{Re} X_k) (\textrm{Re} X_l) \rangle = \frac{1}{N^2}\sum_{n=0}^{N-1}\sum_{m=0}^{N-1}\langle x_n x_m \rangle \cos(2\pi n k / N)\cos(2 \pi m l / N) $$ The thing to note is that $\langle x_n x_m \rangle$ is just the correlation function of the time domain samples, which we can denote $\rho(n-m)$. Putting this in, we get

$$ \langle (\textrm{Re} X_k) (\textrm{Re} X_l) \rangle = \frac{1}{N^2}\sum_{n=0}^{N-1}\sum_{m=0}^{N-1} \rho(n-m) \cos(2\pi n k / N)\cos(2 \pi m l / N) $$

This form in terms of the correlation function is useful because the correlation function is frequently known; By the Wiener-Khinchin theorem the correlation function is the Fourier transform of the spectral density.

This sum can be computed numerically, or even analytically for some particular forms of $\rho$. To compute covariance with imaginary parts of $X$ just put $\sin$ instead of $\cos$.

I found the idea for this in J. Schoukens and J. Renneboog, IEEE Transactions on Instrumentation and Measurement, Vol. IM-35, No. 3, September (1986).

- November 21, 2018

We've just studied about the Wagner-Meerwein rearrangement in carbocations. Our teacher told us that it occurs in order to stabilize the carbocation intermediate.

Knowing the carbocation stability order,

$\mathrm{Tertiary > Secondary > Primary} > \ce{CH3+}$

I decided to test the "limits" of this particular rearrangement reaction.

I drew a primary carbocation (A):

Upon subjecting it to a Wagner-Meerwein hydrogen-shift (in my head), I obtained the secondary carbocation (B):

Which was all fine and dandy; well within what I've been taught.

But seeing the potential for additional stability another Wagner-Meerwein rearrangement could provide, I conducted a Wagner-Meerwein alky(methyl)-shift and ended up with the following tertiary carbocation (C):

I started with a primary carbocation, changed it to a secondary carbocation and finally ended up with a tertiary carbocation.

Now I showed this to my teacher, but he said that in this particular case the carbocation (B) won't convert to carbocation (C); i.e- carbocation (A) isn't going to undergo two Wagner-Meerwein rearrangements (1,2-anionotropic shifts), because in effect it'd be a 1,3-shift and not the 1,2-shift as the Wagner-Meerwein rearrangement calls for.

A few days later, I took a different sheet with carbocations (B) drawn on it and carried out a Wagner Meerwein alkyl(methyl)-shift to obtain carbocation (C) just as before [except that this time around, my starting molecule was B not A]. I showed this to my teacher again, but the rearrangement I carried out in this case doesn't seem to perturb him at all. His argument is that, since my starting intermediate is carbocation (B), to reach carbocation (C), it undergoes only one Wagner-Meerwein rearrangement which is perfectly fine, unlike my first case which involved two rearrangements.

Now my question is, if he's right, then how would carbocation (B) "know" whether it already underwent a Wagner-Meerwein rearrangement [from carbocation (A)] before considering rearranging itself to become the more stable, carbocation (C)? How does it "know" if it's the starting intermediate or not.

Answer

There is no reason why a sequence of two Wagner-Meerwein rearrangements wouldn’t happen — assuming low concentrations and thus the absence of directly capturing nucleophiles. In fact, a professor of mine once said:

The only secondary carbenium ion is the prop-2-yl ion; all others will rearrange to form tertiary carbenium ions.

(He did explicitly exclude carbenium ions stabilised by other means from that discussion; of course an oxocarbenium ion is well-known as is an allyl cation.)

A very well-known example of this is the biosynthesis of lanosterol, in which the enzyme lanosterol synthase takes squalene-epoxide, orders it in a boat-chair-boat conformation, catalyses a domino sequence of carbocations being captured by double bonds, followed by a sequence of four Wagner-Meerwein rearrangements and finally deprotonation to generate the backbone ring-structure of chloresterols. See the following scheme.

If nature can do it, it will happen in the lab at least to a minute extent.

- November 21, 2018

I am having a problem in finding the fundamental period of the signal $x(t)$ given below: \begin{align} x(t) &= 2\cos\left(\frac 45 \pi t\right)\sin^2\left(\frac{16}{3} t\right)\\ &= 2\cos\left(\frac 45 \pi t\right)\cdot \frac 12\left[1-\cos\left(\frac{32}{3}t\right)\right]\\ &= \cos\left(\frac 45 \pi t\right) - \cos\left(\frac 45 \pi t\right)\cos\left(\frac{32}{3} t\right)\\ & = \cos\left(\frac 45 \pi t\right)-\frac 12\bigg\{\cos\left[\left(\frac 45 \pi -\frac{32}{3}\right)t\right]+\cos\left[\left(\frac 45 \pi -\frac{32}{3}\right)t\right]\bigg\} \end{align}

- November 20, 2018

I was adopted at birth from a Jewish biological mother into a Jewish adoptive family. Should I observe mourning for my birth mother when she dies, and otherwise honor her as a parent? Thank you.

- November 20, 2018

I want to test for the presence of broadband noise in a snapshot 1000 complex baseband samples recorded by a software defined radio.

As a follow-up to this post, why was the $\chi^2$ test used? How many degrees of freedom should be used?

Also, how would one extend this approach to complex baseband data? I would assume that I and Q are iid Gaussian random variables. The magnitude of the complex data would then be Rayleigh distributed not Gaussian. Is there a generalization of the $\chi^2$ test for Rayleigh random variables? Or, would I just pick I or Q to operate on?

Update: I was able to find a paper: A test for whiteness. The author outlines a similar process.

- November 20, 2018

Consider the following two sentences,

仕{し}事{ごと}が早{はや}く終{お}わったら行きます。

仕{し}事{ごと}が早{はや}く終{お}われば行きます。

Is there any difference between them?

Answer

There are few chances you could sense the difference outside some edge cases but, yes, they have a little difference such as...

AたらB literally comes from "When A is over, then B", so it could imply that A has higher probability to be satisfied. A(れ)ばB, on the other hand, doesn't get along with an A happens as matter of course.

明日起きたら電話します。 (Fine.)

明日起きれば電話します。 (Won't you get up tomorrow!?)

AたらB can describe a one-off event, where AればB indicates general condition.

天国に行ったら何をしますか？ (Fine.)

天国に行けば何をしますか？ (Are you going to heaven every vacation!?)

(Note: judgements may vary among speakers, see the discussion below.)

As an aside, たら is not formal language. You should use -たならば in those settings.

- November 20, 2018

So how can I say "My TV was broken by you", which one is correct?

僕のテレビは君に壊れた

僕のテレビは君に壊れられた

Answer

This falls under the difference between transitive and intransitive verbs. You are using the intransitive verb, when you should be using the transitive verb.

Transitive verbs require an agent to do them. They do not happen on their own, and need someone/something to do them. For example:

I woke Brian up.

I opened the door

Intransitive verbs happen on their own naturally. In other words, they are done automatically, without your help. For example:

I woke up.

The door opened.

There is a transitive/intransitive pair for the verb break. The transitive form is 壊す｛こわす｝and it means "to break." Because it is a transitive verb, you need to do the breaking, it does not break on its own.

あなたは私のテレビを壊した。

You broke my TV.

The intransitive verb is 壊れる｛こわれる｝, and it means "to break, to be broken." This is a thing that happens on its own, and no one did anything to break it.

あのテレビは壊れた。

That TV is broken.

You are trying to say, "My TV was broken by you." This requires a passive voice, where the TV is the subject of the sentence. So you were on the right track when you used ～られる when you attempted this sentence. 壊す is a godan verb, so we won't use ～られる、but rather 「～base 1 + れる。」The conjugated form becomes 壊される。

私のテレビは君に壊された。

Hope it helps.

- November 20, 2018

I saw some sentences like this, but I couldn't understand them. What do they mean?

砂糖入りのお茶。

胡椒付きのサラダ。

Answer

砂糖[入り]{いり}のお茶 = 砂糖が入っているお茶

胡椒付きのサラダ = 胡椒が付いているサラダ

入り and 付き are suffixes derived from the verbs 入る and 付く. The forms 入り and 付き are the 連用形 renyōkei (masu-stem) of the verbs and behave much like nouns. This is why you see that 砂糖入り modifies お茶, a noun, with の.

For translation you could go for

tea containing sugar

salad with pepper

Many verbs do this, by the way. For example the suffix ～生まれ attaches to places and means "born in", e.g.

東京生まれの人
a person born in Tokyo

アメリカ生まれの日本人

a Japanese born in America

- November 20, 2018

Who knows two hundred seventy-two?

Please cite/link your sources, if possible.

At some undetermined point in the future, at least a day from now, I will:

Vote up all interesting, relevant answers.

Accept what I consider the "best" answer.

Move on to the next number.

In case this is the last entry before Rosh Hashanna: Shanna Tova!

Answer

Certain numbers in Hebrew are not written in the normal form. 15 would normally be written yud/hey, but because this spells a name of Hashem, it is customarily written tes/vav The same is true of tes/zayin, 16, instead of yud/vav.

The number 272 is also not written in the regular pattern, since the regular pattern would spell a word with a negative connotation. 272 would normally be spelled resh/ayin/bais which spells ra'av meaning "famine." Since the normal way to write this numbers spells a word with a negative connotation, it is written out of order.

- November 19, 2018

Avraham was extremely careful that Yitzchak not marry a Canaanite and as we know, he married Rivkah bas Besuel ben Nachor. Yitzchak was very careful that Ya'akov not marry a Canaanite and as we know he married Leah and Rachel bnos Lavan ben Besuel ben Nachor. The pasuk in VaYeishev specifically says that Yehudah married the daughter of Shua the Canaanite. VaYigash says that Shimon's youngest son Shaul was a son of a Canaanitess.

Sefer HaYashar to Parshas VaYeishev (Chapter 45) says as follows:

"Then Re'uven ben Ya'akov went towards Timnas and took Elioram bas Evi the Canaanite for a wife for himself and he came to her. She conceived and Elioram wife of Re'uven bore him Chanoch and Pallu and Chetzron and Karmi four sons. And Shimon his brother had taken Dinah his sister for a wife and she bore him Yemuel and Yamin and Ohad and Tzochar five sons. And after that, Shimon had come to Bonah the Canaanite that is Bonah who Shimon had captured from the city of Shechem. Bonah was before Dinah and she attended to her and Shimon came to her and she bore him Shaul. And Yehudah had gone at that time to Adulam and he turned to an Adullamite man and his name was Chirah. Then Yehudah saw there a daughter of a Canaanite man and her name was Eilis bas Shua and he took her and he came to her. Then Eilis bore to Yehudah Er and Onan and Shelah three sons."

The rest of the brothers do not marry Cana'anites, Levi and Yissachar marry two granddaughters of Yoktan ben Ever. Dan marries a Moabite. Gad and Naphtali marry two great-granddaughters of Nachor. Asher marries a Yishmaelite and then a granddaughter of Yoktan. Zevulun marries a Midianite (discussed here The wife of Zevulun (Sefer HaYashar)). Binyamin marries an Aram-Zovah-ite and a daughter of Zimran ben Avraham. Yehudah then Tamar bas Eilam ben Shem and Yoseph marries Osenas.

Why was Ya'akov not so careful that his sons not marry Canaanites?

In addition, I heard that Osenas was actually the daughter that Dinah had with Shechem, which would make Osenas a Canaanite as well.

Answer

According to Pesahim 50a, the very premise of the question; that Jacob's sons married Canaanite women is wrong. Indeed, the very notion is so inconceivable that that the Talmud interprets Genesis (38:2) as not implying that Judah married a Canaanite wife:

דכתיב וירא שם יהודה בת איש כנעני. מאי כנעני? אילימא כנעני ממש - אפשר בא אברהם והזהיר את יצחק, בא יצחק והזהיר את יעקב, ויהודה אזיל ונסיב? אלא אמר רבי שמעון בן לקיש: בת גברא תגרא

For it is written 'And there Judah saw the daughter of a Canaanite man'. What is meant by Canaanite? If you say an actual Canaanite, is it possible that Abraham warned Isaac, and Isaac warned Jacob [not to marry Canaanites] and Judah went and marries [one]? Rather Said R. Simon ben Lakish, [it means that] she was the daughter of a merchant.

According to R. Hayyim Paltiel (Genesis 37:35) even according to the opinion that the tribes married Canaanites, it is possible that they weren't ethnic Canaanites, but only resident there:

ר' יהודא אמר כנעניות היו. וצ"ע דסוף פרק אילו עוברין אמרינן בת איש כנעני אילימא בת כנעני ממש, אי אפשר, בא אברהם והזהיר בא יעקב והזהיר ויהודה נשא כנענית, ואילו הכא אמרינן השבטים נשאו כנעניות... ושמא י"ל דלא היו אלא מארץ כנען

Based on the above understanding the the brothers didnt marry Canaanites, Simon seems to be the exception that proves the rule. As Radak writes in Genesis (38:2):

בת איש כנעני ...וכנעני כתרגומו סוחר היה משאר האומות והתגורר שם, כי בני יעקב היו נזהרים מלהתחתן עם בנות כנען כמו האבות, כי שמעון שלקח אשה מבנות כנען זכרו לגנאי והפרידו מאחיו ואמר ושאול בן הכנענית:

The daughter of a Canaanite...And 'Canaanite' is identical in meaning to its Targumic explanation; that he was a merchant from a different nation [other than Canaan]. For Simon who took a wife from the daughters of Canaan, was mentioned negatively, and [listed] separately from his brothers, and it is said 'and Saul the son of the Canaanite'.

Carbonates

The quote from your text:

Carbonates of alkaline earth metals are insoluble in water and can be precipitated by addition of a sodium or ammonium carbonate solution to a solution of a soluble salt of these metals. The solubility of carbonates in water decreases as the atomic number of the metal ion increases. All the carbonates decompose on heating to give carbon dioxide and the oxide. Beryllium carbonate is unstable and can be kept only in the atmosphere of CO2. The thermal stability increases with increasing cationic size.

So the stability that you are referring to is thermal stability. This is an important detail. So what is thermal stability? It's how resistant a molecule is to decomposition at higher temperatures.

What's happening to cause thermal instability?

So, lets look at the carbonate ion here:

enter image description here

This is just an illustration, and in reality the negative charge we see on the two $\ce{O}$ atoms is localized due to resonance.

Below the illustration shows where the negative charge is likely to be concentrated (colored in red).

enter image description here

So, when we create a carbonate complex like the example below, the negative charge will be attracted to the positive ion.

enter image description here

Because of this polarization, the carbon dioxide will become more stable and energetically favorable.

How does going down a group play into this?

Well as you go down the group, the charged ion becomes larger. The larger the ion, we see a lower charge density. Charge density is basically the amount of charge in a given volume. So, if a small ion has the same charge as a larger ion, the charge density will be greater for that small ion. Greater charge density, means a greater pull on that carbonate ion, and a greater pull causes the delocalized ions, and a more stable $\ce{CO2}$ molecule. So, the larger the ion, the lower the charge density, the less polarizing of an effect, and reduced stability of a $\ce{CO2}$ molecule, favoring the $\ce{CO3}$.

Chloride and fluoride stability

Stability of fluorides, chlorides, and other halogens, are likewise related to thier size. The halogens, specifically fluouride, is known for their electronegativity. Electronegativity, is the tendency to attract electrons to itself. As you move up the group, you see an increase in electronegtivity. This results in the creation of polar bonds.

Illustrated below, you see that as charge of the positive ions increase, polarizability increases (left), and as the halogen ion increases, polarizability and electronegativity decrease (right). When the ions electron cloud, is less polarized, the bond is less strong, leading to a less stable molecule.

enter image description here

Information and illustrations on carbonate ions were sourced from here.

- November 19, 2018

I am doing the following question:

Calculate the pH of a $4.00\ \mathrm{mol\ L^{-1}}$ solution of citric acid. $\mathrm{pK_{a1}} = 3.09~~~~~ \mathrm{pK_{a2}} = 4.75~~~~~ \mathrm{pK_{a3}} = 6.40$

Usually for polyprotic acids, we can assume that the second, third and other dissociations of $\ce{H+}$ ions are negligible when compared to the first dissociation. However I believe that this is only valid when the pKa values are separated by around 4. So for citric acid, this would be an invalid assumption as the pKa values are pretty close to each other.

Now, I can find the pH of the solution by doing the long way by first finding the amount of $\ce{H+}$ ions formed by the first dissociation, then using that to find the amount of $\ce{H+}$ ions formed by the second dissociation and so on.

However the room that they have given for this question is pretty small and has only has enough room for a couple of lines of working out and I definitely wouldn't be able to fit all my working out in that box.

So am I missing some short cut method to finding the pH in cases like this, or is the above assumption that I have outline at the start still correct for citric acid?

Answer

The assumption that the second (and higher) deprotonation steps are negligible for the calculation of the pH of a polyprotic acid is valid for citric acid.

You can compare this by calculating the exact solution and then stepwise neglect deprotonation steps.

(For the sake of simplicity I write $c(\ce{H+})=x$ and $k_{a,n}=k_n$.)

Exact: $$x=\frac{k_W}{x}+c_0(\ce{H3A})\frac{x^2 k_1+2x k_1 k_2+3 k_1 k_2 k_3}{x^3+x^2 k_1+x k_1 k_2+k_1 k_2 k_3}$$ Neglecting $k_3$: $$x=\frac{k_W}{x}+c_0(\ce{H3A})\frac{x k_1+2 k_1 k_2}{x^2+x k_1+k_1 k_2}$$ Neglecting $k_2$ and $k_3$: $$x=\frac{k_W}{x}+c_0(\ce{H3A})\frac{k_1}{x+k_1}$$

Solving those equations give the following pH values (with super unrealistic high precision):

Exact: 1.2469291050971560

w/o $k_3$: 1.2469291065371300

w/o $k_2$ and $k_3$: 1.2470654318802320

As a pH can only be measured precisely within something like $\pm \left(10^{-2}\ldots10^{-3}\right)~\mathrm{pH}$, the calculated pH can be rounded to be 1.247 in every singly case. No matter which deprotonation step was neglected.

So for your case it is negligible. For more general cases I have to look it up and will add it to my answer within the next days.

- November 19, 2018

Inspired by this question:

If one receives a friend request on Facebook, especially from another Jew, is it permissible to reject them?

On the one hand, "חברים כל ישראל" - "All Jews are friends"; but on the other hand, it is non-beneficial to be socially connected to someone you don't know well.

This question is Purim Torah and is not intended to be taken completely seriously. See the Purim Torah policy.

Answer

In Pirkei Avos (1:15), we find clear instructions regarding this matter:

הוי מקבל את כל האדם בספר פנים

One should accept all persons on Facebook.

- November 19, 2018

There are many halakhoth that say you can't eat meat and dairy, nor prepare it, nor sell it/derive benefit from it. Does the same apply to Shaatnez? As a more specific example, if one does not personally wear it, can one buy a Shaatnez garment for another to wear at a special event?

- November 19, 2018

The decree of keeping two days of Yom Tov outside of Israel is because Rosh Chodesh used to be determined by Beis Din and its messengers couldn't reach all of exiles in time, thereby requiring people living outside the range to keep two days out of doubt. Therefore, nowadays we keep two days like out forefathers did.

My question is, why do we not put on tfillin on the second day of yom-tov (Rosh Hashana, Simchas Torah, 8th day of Pesach) out of sofek?

Answer

Today we don't treat the second day of yomtov as a "maybe it's yomtov"; it has been rabbinically enacted for us (non-Israel-dwellers) as a full-fledged yomtov.

The Talmud established long, long ago that rabbinic law has the power to order someone to be passive rather than fulfill a Torah obligation, e.g. not putting on tefilin on 2nd day yomtov (or not blowing Shofar if Rosh HaShanah is on shabbos).

I see your question is "the custom is done the way it was done then." Actually no; back then, a visitor to Israel would keep one day. While Rabbi Emden insists that should be the case today as well, Rabbi Feinstein says that when the practice was fixed its parameters changed; now you follow your hometown instead. Similarly, Ritva says that today, the borders of Israel with regards to 2nd day yomtov are the Biblical ones, even though back then it all had to do with where they could send messengers (much closer to the Talmudic borders).

- November 19, 2018

From 英語子音の攻略

次回は、これらの日本人にとって苦手とする発音をどのように訓練するのかということについて、ご紹介していきます。

My dictionary defines とする as:

そのように仮定する意を表す。

Does this definition apply to the sentence that I've found? Is the nuance in this context something along the lines of, "You think you're bad at it, but you don't have to be"?

Answer

No, this とする simply means "to regard". It's the second definition in this entry:

１ …と仮定する。「ここに川があるとする」
２ …と考える。…と判断する。「彼の意見をよしとする者」

So 日本人にとって苦手とする発音 means "the pronunciation which Japanese people regard as difficult."

But I feel this phrase is slightly clumsy. 日本人にとって苦手な発音 (using a na-adjective) or 日本人が苦手とする発音 (using a relative clause with a subject and a verb) would be better.

- November 19, 2018

I'm not quite sure I understand this. My question is:

Calcium chloride is a salt used widely to melt ice on sidewalks and roads. Explain why one mole of $\ce{CaCl2}$ would be more effective than one mole of $\ce{NaCl}$.

So from everything I've learned, $\ce{NaCl}$ would be more effective for the melting, because calcium chloride dissociates into three ions and sodium chloride dissociates into two, so that would make the boiling point of water with calcium chloride higher. Therefore, it shouldn't be used to melt ice over sodium chloride, as it would make the water have a higher boiling point so wouldn't melt it as well!

- November 19, 2018

The Nernst equation describes the relationship between cell potential and temperature. But why does temperature affect cell potential?

My understanding is that the collision model of kinetics is not relevant to electrochemical cells, plus an increase in temperature decreases cell potential. So why does the potential change?

Answer

Depending on how you write the Nernst equation the temperature might increase or decrease the potential of the cell. This depends more on the reaction quotient than on anything else.

The temperature comes in to the equation as a scaling factor where RT/nF has units Volt. This essentially defines how much the voltage changes per a decade change in the reaction quotient.

The temperature dependence here is just a matter of the scaling factor.

Going back to the collision model, that is more about kinetics than thermodynamics and it is not at play for the Nernst equation.

Nernst equation describes the thermodynamics of the electrochemical system.

The temperature dependence can be explained by the temperature dependence of work-functions.

Any electrochemical reaction by definition is an electron transfer. The electron goes from the highest occupied MO of one species to the lowest unoccupied MO of the other. Both these levels are temperature dependent.

- November 19, 2018

Under certain conditions, I know that uncontaminated (e.g. no insects / meat, etc) plant-based foods are prohibited (ie., non-kosher). Examples I can think of include:

Non-kosher wine

Chometz during Pesach and

Plants harvested on the sabbatical/shmita year

What other conditions would render uncontaminated plant-based foods non-kosher?

- November 19, 2018

Can you be buried in a Jewish Cemetery if you have a tattoo? I.e., is it just urban legend that you can't?

- November 19, 2018

In case I am talking with someone using the informal form but we are not close friends yet (perhaps a close acquaintance or someone I'm chatting with online) and I want to ask him a personal question (what is his occupation, something about his family ,etc.), should I proceed with the informal form or should I switch to polite (or even honorific) language to ask him the question?

Answer

This heavily depends on your character, your age, the relationship between you and him, and how personal the information you're trying to get is. In general, using honorific forms is probably an overkill, but temporarily switching to the です/ます style will not harm.

Personally, I am relatively slow to start dropping です/ます, and I am unlikely to talk with someone using the informal language if I don't even know his occupation.

- November 19, 2018

Sh'mos 3:15–18 reads:

‏15 וַיֹּאמֶר עוֹד אֱלֹהִים אֶל מֹשֶׁה…. 16 לֵךְ וְאָסַפְתָּ אֶת זִקְנֵי יִשְׂרָאֵל וְאָמַרְתָּ אֲלֵהֶם יהוה אֱלֹהֵי אֲבֹתֵיכֶם נִרְאָה אֵלַי… לֵאמֹר פָּקֹד פָּקַדְתִּי אֶתְכֶם וְאֶת הֶעָשׂוּי לָכֶם בְּמִצְרָיִם. 17 וָאֹמַר אַעֲלֶה אֶתְכֶם מֵעֳנִי מִצְרַיִם אֶל אֶרֶץ הַכְּנַעֲנִי וְהַחִתִּי וְהָאֱמֹרִי וְהַפְּרִזִּי וְהַחִוִּי וְהַיְבוּסִי אֶל אֶרֶץ זָבַת חָלָב וּדְבָשׁ. 18 וְשָׁמְעוּ לְקֹלֶךָ…‏

I'm unsure of how to read this. Specifically, the last part of pasuk 16 is Hashem quoting Moshe quoting Hashem. Is pasuk 17 the same, or is it just Hashem quoting Moshe? That is, do we read the passage as this —

God said further to Moses:

… Go gather the elders of Israel and tell them:

God, the god of your fathers, appeared to me… saying:

I paid attention to you and to what was done to you in Egypt. And I have said [or: say]:

I will raise you from the poverty of Egypt….

And they will heed your voice….

— or as this —

God said further to Moses:

… Go gather the elders of Israel and tell them:

God, the god of your fathers, appeared to me… saying:

I paid attention to you and to what was done to you in Egypt.

And I have said [or: say]:

I will raise you from the poverty of Egypt….

And they will heed your voice….

—?

- November 19, 2018

What are the specifications of Dina Dimalchusah? A more targeted question to answer would be: If I ripped off the label of my mattress — the label that says its removal is punishable by federal law — am I also doing a sin? If so, why; if not, why not?

Answer

As stated, in the mattress example, that tag is there to prevent mattress manufacturers from putting all sorts of awful stuff in their mattresses and consumers not knowing. Once you've read the "ingredients label" and have bought the mattress, you can do whatever you want with it. (Well if you go to sell it to someone else it gets tricky ...) So rip away!

The Gemara's discussions of dina d'malchusa apply to paying your taxes (pay them).

Rabbi Aharon Soloveichik was of the opinion that dina d'malchusa means halacha absolutely requires you to come to a full stop at every stop sign, even at 3AM when there's no one anywhere in a mile radius.

Other authorities say it's limited to things vital to the state (such as taxes), or things significant enough that the state would actually punish someone for.

- November 19, 2018

With an action verb, like 食べる, I can count 5 meanings of this sentence:

ジョンは納豆を食べている
"John is eating natto." (progressive)
"John is eating the natto." (progressive)
"John eats natto." (habitual)
? "John has eaten natto." (perfective: experience)
? "John has eaten the natto." (perfective: state of having eaten the natto)

To me, the last two readings are possible, but kind of odd.

However, you can completely force the experience reading:

ジョンは前に納豆を食べている
"John has eaten natto before." (perfective: experience)

And you can almost force reading 5:

ジョンは例の納豆を食べている

"John is eating that natto which we just saw." (progressive)
"John has eaten that natto which we just saw." (perfective: state of having eaten the natto)

Finally, if you use 〜ていない instead, I think all the readings are equally likely:

ジョンは納豆を食べていない
"John is not eating natto." (progressive)
"John is not eating the natto." (progressive)
"John does not eat natto." (habitual)
"John has not eaten natto." (perfective: experience)

"John has not eaten the natto." (perfective: state of not having eaten the natto)

In my opinion, the perfective readings here are equally or more likely than the other readings. They become even more likely if you insert まだ, for example.

(I guess, etymologically-speaking, it is not too surprising that 〜ている can have the perfective semantics, given that て was the 連用形 of the perfective auxiliary verb つ.)

Some of the meanings come from whether 納豆 is being talked about in general, or a specific serving of 納豆 is being discussed, but the reason why I included all of them is because the actual implications of the different perfective readings are entirely different for the two different cases (as in English).

Is what I've laid out here entirely correct? Are the perfective readings actually less likely for the simple 〜ている case like I think they are?

Answer

I am going to say just a couple of things regarding your first list of 5 meanings. I have been hesitating to do this because what I want to say might confuse the beginning students more than it could clarify things for them. 「Verb + ている」 is that subtle.

After mentioning it in the comment some days ago, I am still having difficulty understanding why you are using the word "experience". As a Japanese-speaker, I do know that 食べている, given the right context, COULD express one's experience of eating natto, but this usage is very rare in real life --- so rare that you will seldom hear it to mean it. Without saying 食べたことがある, we just rarely express experience.

Then again, it may be that it was your intention to include the rare usages in the first place. If so, I would have included the "future progressive" and "future perfective" as well. "I will be eating natto at (a certain time)" and "I will have eaten (the) natto by (a certain time)" are possible meanings of 食べている, too. In fact, I would say that those usages are a little more common than the "experience" usage.

If the distinction between "natto" and "the natto" is important to you, which it seems it is, I would include the "the natto" version under your "habitual" category because it is possible for one to habitually eat a particular brand/type of natto.

Tuesday, November 27, 2018

Sunday, November 25, 2018

Saturday, November 24, 2018

Friday, November 23, 2018

Thursday, November 22, 2018

Wednesday, November 21, 2018

Tuesday, November 20, 2018

Who knows two hundred seventy-two?

Monday, November 19, 2018

Carbonates

What's happening to cause thermal instability?

How does going down a group play into this?

Chloride and fluoride stability