Thursday, January 31, 2019

Other meanings of でしょう besides "probably"



でしょう can usually be understood to mean "probably." But does it sometimes mean the same thing as ですね? What other meanings can it have? Can it mean "you know?"



Answer



Aside from the meaning of "probably", I've heard でしょう (だろう) used in the following manners:




  1. In polite speech, でしょうか can replace ですか. でしょうか sounds "softer" and a little less direct:



    この色【いろ】はいかがですか。 How about this color?


    この色【いろ】はいかがでしょうか。 How about this color? (slightly more polite)


    ちょっと分【わ】かりにくいですかね。 Do you suppose it's somewhat hard to follow?



    ちょっと分【わ】かりにくいでしょうかね。 Do you suppose it's somewhat hard to follow? (slightly more polite)





  2. でしょう and だろう can be used like ね to form tag questions, primarily when the speaker knows something to be true and is using it to prove a point to or convince the listener of some fact. This use of でしょう often has a rising intonation:



    で、帰【かえ】ったときに携帯【けいたい】はかばんに入【はい】ってなかっただろう? So when you got back, your cell wasn't in your bag, right?


    言【い】ったでしょう?明日【あした】、東京【とうきょう】に行【い】くって。 I told you, didn't I? That I'd be going to Tokyo tomorrow.



    The question particle か is omitted in this use. In my experience, you're more likely to find だろう being used by men and でしょう by women here, but the split is not well defined, as both are fairly gender-neutral.





matlab - Using Spreading spectral with Maximal likelihood


As asked here, HERE if we have the signal


x = 
[0.7 + 0.7i;

0.7 - 0.7i;
-0.7 + 0.7i;
-0.7 -0.7i];

Which was spread over code c and transmitted over channel H whose dimension is [4x4], so the convolution of signal after spreading will become:


r = reshape(H*reshape(x,4,[]),[],1);

comparing it with signal without spreading, it was


 r = H*x; 


That was explained well in the above link.


My question, suppose I am using Maximum likelihood estimation, in case if we didn't spread the signal, we will check the likelhood compared with the channel H, but what's about after using spreading ? how will become the channel ? It supposed to be a vector of [16x1], is that right ? but how will it be ?


thank you!



Answer



H was not reshaped, as you see in your command r = reshape(H*reshape(x,4,[]),[],1);, you reshaped the data itself.


In that case, you are going to add noise, then using ML estimation based on the received data. So that, H will be H without changing, what will be changed is the received data, you can reshape it similar to that way in the transmitter reshape(y,4,[]), where y is the received data, then reshape the results again into [16 x 1].


Good luck


halacha - Can one throw out a Menorah?


Is it an issue to discard a menorah that has been used for the mitzvah of Neros Chanuka?


What if the menorah is made from something not usually used for a menorah? For example,bottles, cans, potatoes, ice?



Answer



Mishna B'rura to 21:1 says that once a thing used for a mitzva is no longer usable for the mitzva, it can be discarded, but should not be discarded in a degrading manner or used for a degrading purpose. He considers deliberately throwing it onto the garbage heap as an example of discarding it in a degrading manner. [I've heard recommended that such an object be put in a separate bag and then in the garbage.] [However, see comments to this answer regarding whether a m'nora is included in this category.]


[As I wrote, he only says this about something used for a mitzva and no longer usable. I conjecture that his not considering a still-usable object is simply because such things aren't generally discarded at all, but that, if bal tashchis is not an issue, the same rule will apply.]


[As Double AA notes in his answer, this does not apply to things like m'zuzos and t'filin.]



As always, for practical matters, consult your rabbi rather than relying on what you read here.


purim torah in jest - What kind of horns did Moshe have?



Sh'mot 34:29 tells us that when Moshe came down from Har Sinai with the second set of tablets he did not know that קָרַן עוֹר פָּנָיו בְּדַבְּרוֹ אִתּוֹ -- horns of light were on his face from his speaking (with God). The gentile sculptor Michelangelo depicts them as short, knobby horns, similar to those that young goats have, if this city-dweller understands correctly. But that's not very stately, not the sort of thing you would expect as a divine symbol, and anyway we shouldn't trust the source to be familiar with our mesorah. Oh c'mon, the same guy painted God as a man, as if such a thing were possible! So surely this work has no hechsher (unless it's this one).


So the horns probably didn't look like this:



michelangelo


But what did they look like? Perhaps they looked like ram's horns, to remind us of the call of the shofar at Sinai even after the people moved on from there:


ram's horns


But that seems impractical if we assume that he needed to be able to lie down and sleep each night for the next forty years. So maybe the horns were more like this:


viking horns


But if so I can't determine what meaning we should take from it, nor have I found any source that might support it.


So maybe all of these are wrong. And anyway, it says on his face (panav), not on his head (rosho), and none of this reflects that.


What did Moshe's horns look like, and how do we know?







Answer



You translated "קָרַן עוֹר פָּנָיו בְּדַבְּרוֹ אִתּוֹ" (Ex. 34:29) as "horns of light were on his face from his speaking (with God)", but in fact it means "a horn was on the skin before him during His speaking with him". A few notes about this verse:



  • First and most obviously, Moses was speaking to God on a cell phone, and the cell phone had a skin.

  • The skin caused the cell phone to look like a horn — that is, a landline phone. You see, Moses didn't have his filter yet, so of course wasn't using the Internet on his phone, as it's completely forbidden without a filter. In order that people shouldn't think he was using the Internet, he dressed his cell phone up as a landline phone.

  • While Moses was speaking on the phone, it was "before him", i.e. not at his ear. This is because he was using his phone to videophone with God, as the verse says (Ex. 33:11) "וְדִבֶּר ה׳ אֶל מֹשֶׁה פָּנִים אֶל פָּנִים / God spoke to Moses face to face".

  • Rashi to 34:29 notes that this was Yom Kipur. How, you may ask, did Moses justify using his cell phone on Yom Kipur? Well, he figured it must be okay to use a cell phone, since, after all, God had asked him to bring the Jews two tablets.


calendar - Time Parameters of Mishenichnas Adar Marbin B'Simcha


Is "Mishenichnas Adar Marbin B'Simcha" just for the month of Adar, and then you take a step down in simcha for Nisan? Or are you supposed to raise your level of simcha and stay there until Av, when you're supposed to decrease your joy? If it's just for Adar, why? What about the other months in which we were saved in some way (Nisan, Kislev)?



Answer



According to the Michtav M'Eliyahu (Vol. 2 pg 125) on the essay titled "משנכנס אדר" he discusses how the command to be joyous when Adar enters is related to the joy of Purim.



He explains that the happiness we feel on Purim is a הכרת הטוב - recognizing the goodness - of the miracle of Purim, which is all about revenge. HaShem took revenge on Haman and ונהפוך הוא - turned the tables - and made Mordechai the Prime Minister in his stead.


The joy required to celebrate this הכרת הטוב efficiently requires work and preparation, continues the Michtav M'Eliyahu, and one needs to start this preparation as soon as Adar starts, in order to be in the right mood when Purim arrives.



ומתחילין כבר מראש חודש לגודל ההכנה הנדרשת, וממשיכים בעבודה זו מיום ליום



The Ramchal (Derech HaShem ח"ד פ"ח) says that the point of the joy of Purim is the קבלת התורה - celebrating the re-acceptance of the Torah.


So - using the reasoning of the Michtav M'Eliyahu - we would say that we need the 2 weeks to prepare for it; similar to the 49 days to prepare for Shavuoth.


So - back to the question - once Purim is over, one can wind down and get ready for entering the Pessach mood. Each Chag has its own mood and preparation period.


grammar - Making someone feel something




いちいち腹のたつことを、わざわざ言いにこないでよ
Don't come specially to say things which make me angry (my translation attempt)



I'm confused by 腹がたつ. It's my understanding that it means 'to get/become angry' rather than 'to make angry'. How can I understand what's going on here?


More generally, how do I say things like 'That person makes me angry' or 'Eating cake makes me happy. I include both examples because I suspect that people making you feel things is different from things making you feel things.



Answer



My gut feeling is that the cause of your confusion is the true transitivity of the idiomatic expression 「[腹]{はら}が[立]{た}つ」. You already seem to know it is intransitive in Japanese, but you rightly translated it as if it were transitive -- "things which make me angry".


Of course, you could have translated 「腹の立つこと」 as "things that I get angry over" or the like and the original transitivity would have been retained. In translation, however, whatever sounds better in the target language is the better translation.


You have achieved a good translation at the cost of a Japanese intransitive verb getting unduly treated like a bloody stupid transitive one. That kind of thing, however, happens all the time when translating between two unrelated languages.


At least, the above is what the average Japanese-speaker with a weird French username thinks is happening here.




"More generally, how do I say things like 'That person makes me angry' or 'Eating cake makes me happy. I include both examples because I suspect that people making you feel things is different from things making you feel things."



This is highly related to what I have ranted about above.


In natural settings, Japanese-speakers would not say the directly translated versions of "That person makes me angry." or "Eating cake makes me happy.", period.


The direct translations I am referring to would be:


「あの[人]{ひと}は[私]{わたし}を[怒]{おこ}らせる。」 and


「ケーキを[食]{た}べることは私を[幸]{しあわ}せにする。」, respectively.


Again, we would practically never say either of those in a natural setting. You would undoubtedly sound like a robot if you used those sentences in real life with a native speaker.


We do not use causative verb forms to express those feelings in Japanese. We would instead use sentences such as:



「(私は)あの人に[怒]{おこ}っている。」


「(私は)あの人に腹が立っている。」


「ケーキを[食]{た}べていると[幸]{しあわ}せな[気分]{きぶん}になれる。」


「ケーキを食べている[時]{とき}が[一番]{いちばん}幸せです。」


organic chemistry - Axial or planar chirality in spiro[3.3]hepta-1,5-diene


The two spirocyclic compounds drawn below are enantiomers. My question is, do they exhibit axial or planar chirality?


enter image description here


3D representations: enter image description here



Answer



Useful Definitions (from the IUPAC Gold Book)



  • chirality plane - "A planar unit connected to an adjacent part of the structure by a bond which results in restricted torsion so that the plane cannot lie in a symmetry plane. For example with (E)-cyclooctene the chiral plane includes the double bond carbon atoms and all four atoms attached to the double bond; with a monosubstituted paracyclophane the chiral plane includes the monosubstituted benzene ring with its three hydrogen atoms and the three other atoms linked to the ring (i.e. from the substituent and the two chains linking the two benzene rings)."

  • planar chirality - chirality resulting from a chirality plane.

  • chirality axis - "An axis about which a set of ligands is held so that it results in a spatial arrangement which is not superposable on its mirror image. For example with an allene abC=C=Ccd the chiral axis is defined by the C=C=C bonds; and with an ortho-substituted biphenyl the atoms C-1, C-1', C-4 and C-4' lie on the chiral axis."


  • axial chirality - chirality resulting from a chirality axis


Interpretation



  • According to the above definition, a chirality plane must involve restricted torsion (restricted rotation) about a bond.

  • A molecule can contain both a chirality plane and a chirality axis; an example would be an ortho-substituted biphenyl where the restricted rotation is responsible for chirality (atropisomers).


Conclusion



Axial or planar chirality in spiro[3.3]hepta-1,5-diene




There is no restricted rotation that brings about chirality in this molecule. Unlike trans-cyclooctene or a biphenyl, this molecule cannot be made to lie in a plane by torsional motion (at least not as long as we maintain the tetrahedral nature about the spiro carbon). Therefore, this molecule does not possess a chirality plane.


Rather, this molecule is analogous to the allenes. It does have a chirality axis passing through the $\ce{CH}$ group in each ring furthest from the spiro carbon along with the spiro carbon. The molecule can be said to possess axial chirality.


discrete signals - Higher order harmonics during sampling


I am studying about the sampling theorem in conjunction for ADC. I got little confused while reading about aliased frequencies. I see that as per the Nyquist theorem, the sampling frequency (fs) should be larger atleast twice the signal frequency (fsig=(2*fs)) to avoid aliasing, which would position all the aliases of the form: ((mfs)+fsig) and ((mfs)-fsig) above the nyquist frequency.


Since I see that the sampling is closely related with mixing operation (sort of modulation), like - its just a multiplication of two frequencies - what happens to the alias - ((mfs)+(nfsig)) and ((mfs)-(nfsig))?


Wouldn't that come below the nyquist frequency?


For example, if fs=100 MHz, fsig=50 MHz, (fs-(3*fin))=40 MHz - analogous to Third order intermodulation product.


Normally, when measuring the ADC output spectrum, it has signal power, some harmonics and quantization noise. the Dynamic range is the difference in signal power and highest harmonic content. So, these harmonics come from ((mfs)+(nfsig)) and ((mfs)-(nfsig))? Is this understanding correct?




Answer



The sampling is indeed analogous to mixing as to my understanding. In the sampling process, we multiply the time domain signal with an impulse train - the impulses in time are represented as impulses in frequency at integer multiples of the sampling rate. So instead of one or two (for a real sine wave) impulses in frequency, we have an infinite number but the process of multiplying in time is otherwise identical. The result you would get (which explains the aliasing well) is the same thing you would get if you had an infinite number of mixers and LO's, one for each harmonic of the sampling clock.


FT of Impulse Train


I have explained this with the additional graphics below to help those more familiar with RF mixing to understand sampling and aliasing, and then undersampling as well.


The reference to third order intermodulation product is not what would explain this aliasing, as that is specifically due to non-linearities in the signal chain. This can certainly occur for the same reason in ADC's causing intermodulation distortion but that is not what causes the aliasing. So when you see other spurious products in your spectrum, these certainly can be due to non-linear distortion (which can be confirmed by modifying the power level of your dominant signal to see if these products change), or can be caused by aliasing from other frequency bands due to insufficient front end filtering prior to ADC conversion (which means they would be present regardless of the presence of your input signal or not). Another source is spurs on the sampling clock itself, which too is explained well as a mixing process.


To understand the aliasing mechanism and how it is identical to mixing, first observe the sampling process for a 3 Hz Cosine Wave as demonstrated in the graphic below. Note that since we multiply in time the cosine wave with the time domain impulses, we convolve in frequency the 2 impulses representing the cosine wave as in the top portion of the graphic below with the impulses in frequency represented by teh middle portion of the graphic, resulting in the digital spectrum as given in the bottom graphic. In this case the signal was sampled at 20 Hz, so the output spectrum repeats every 20 Hz, so really only the spectrum from -10 Hz to +10 Hz needs to be given for the digital spectrum, as shaded in the graphic. (Or from 0 to 20 Hz, basically any 20 Hz will completely represent the output spectrum). However when working with mixed signal or multi-rate systems, I find that it often mentally helps to "un-roll" the digital spectrum and represent it out to $+/- \infty$ as I have done in this graphic.


samping 3 H Cosine


Note too that the output spectrum can be completely explained as a mixing process: The two impulses in the middle portion of the graphic at +20 Hz and -20 Hz do represent a real sinusoid at 20 Hz, while the two at +/- 40 Hz represent a sinusoid at 40 Hz, etc... Each of the outputs shown in the digital spectrum can be explained using the traditional "sum and difference" frequency outputs that you may be accustomed to when working with an RF mixer (as explained by the multiplication of two real sinusoids).


This explains aliasing quite well, as introduced in the undersampling example shown in the graphic below (Even though I explained the above with real signals and sinusoids, I prefer to work with complex frequencies such as $e^{j\omega t}$ recognizing that a cosine is $e^({j\omega t} + e^{-j\omega t})/2$ and from that we see that each impulse in these frequency domain plots is a single instance of $e^({j\omega t}$. Then instead of dealing with sums and differences, we just add the frequency terms. For example, the graphic below shows that the frequency component that is labeled "IF" results from the time domain multiplication of the input frequency component at "RF" with the specific frequency impulse in the impulse train that is labeled "-LO".


Analogy to Frequency Translation



With that view we can easily see how aliasing occurs (as explained by "mixing" operations!), and the next two graphics show the identical result between sampling in the 1st Nyquist Zone vs 3rd Nyquist zone with the first graphic colored to show which frequency components of the digital sampling spectrum are responsible for which outputs in the digital output spectrum.


1st Nyquist


3rd Nyqist


Error in using Kalman Filter for 2D Position Estimation in Python


This is my first question on DSP Stack exchange, so I apologise if it is poorly worded. I have some positioning data from a vehicle (GPX Format, collected through Strava) and want to use a Kalman filter as a first step to track the position of the car and determine the accuracy of the GPS measurement. However, the output estimate of the Kalman filter from my implementation seems completely wrong and absolutely does not match the position information and plot from the data. Can someone help me figure out what is wrong with this implementation and provide some methods to fix this problem? Appreciate all the help in advance. Thanks!



As a reference, I used the code given in the below link and correspondingly modified it based on my requirements: https://stackoverflow.com/questions/13901997/kalman-2d-filter-in-pythonn. Background: I only have a basic understanding of the working of the Kalman filter and am a new user to Python, but for this implementation, I've considered a constant velocity model with states as Position and Velocity, time step is assumed to be 1 (Considering GPS updates at 1Hz), the measurement matrix only considers the position information and the actual measurement gives the corresponding longitude and latitude values. The test GPX file was obtained from the following link: https://github.com/stevenvandorpe/testdata/blob/master/gps_coordinates/gpx/my_run_001.gpx


My implementation in Python:


import gpxpy
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

with open('test3.gpx') as fh:
gpx_file = gpxpy.parse(fh)
segment = gpx_file.tracks[0].segments[0]

coords = pd.DataFrame([
{'lat': p.latitude,
'lon': p.longitude,
'ele': p.elevation,
'time': p.time} for p in segment.points])
coords.head(3)
plt.plot(coords.lon[::36], coords.lat[::36], 'ro')
plt.show()

def kalman_xy(x, P, measurement, R,

Q = np.array(np.eye(4))):

return kalman(x, P, measurement, R, Q,
F=np.array([[1.0, 0.0, 1.0, 0.0],
[0.0, 1.0, 0.0, 1.0],
[0.0, 0.0, 1.0, 0.0],
[0.0, 0.0, 0.0, 1.0]]),
H=np.array([[1.0, 0.0, 0.0, 0.0],
[0.0, 1.0, 0.0, 0.0]]))


def kalman(x, P, measurement, R, Q, F, H):

y = np.array(measurement).T - np.dot(H,x)
S = H.dot(P).dot(H.T) + R # residual convariance
K = np.dot((P.dot(H.T)), np.linalg.pinv(S))
x = x + K.dot(y)
I = np.array(np.eye(F.shape[0])) # identity matrix
P = np.dot((I - np.dot(K,H)),P)

# PREDICT x, P

x = np.dot(F,x)
P = F.dot(P).dot(F.T) + Q

return x, P

def demo_kalman_xy():
x = np.array([[100.0, 0.0, 0.0, 100.0]]).T
P = np.array(np.eye(4))*1000 # initial uncertainty
plt.plot(coords.lon[::36], coords.lat[::36], 'ro')
result = []

R = 0.01**2
for meas in zip(coords.lon, coords.lat):
x, P = kalman_xy(x, P, meas, R)
result.append((x[:2]).tolist())
kalman_x, kalman_y = zip(*result)
plt.plot(kalman_x, kalman_y, 'g-')
plt.show()

demo_kalman_xy()

Answer




The main reason why your Kalman filter is not working is because you are not converting lat and lon values to kms. In the code below, I defined a new function called lat_lon_posx_posy which converts lat and lon values to px and py values in mts. You will need to make the following changes to your code.




  • Include the following function


    import utm

    def lat_log_posx_posy(coords):

    px, py = [], []
    for i in range(len(coords.lat)):

    dx = utm.from_latlon(coords.lat[i], coords.lon[i])
    px.append(dx[0])
    py.append(dx[1])
    return px, py


  • Change demo_kalman_xy() to the following:


    def demo_kalman_xy():

    px, py = lat_log_posx_posy(coords)

    plt.plot(px[::18], py[::18], 'ro')
    plt.show()

    x = np.array([px[0], py[0], 0.01, 0.01]).T
    P = np.array(np.eye(4))*1000 # initial uncertainty
    result = []
    R = 0.01**2
    for meas in zip(px, py):
    x, P = kalman_xy(x, P, meas, R)
    result.append((x[:2]).tolist())

    kalman_x, kalman_y = zip(*result)
    plt.plot(px[::18], py[::18], 'ro')
    plt.plot(kalman_x, kalman_y, 'g-')
    plt.show()


  • Final Plot:




enter image description here



Wednesday, January 30, 2019

halacha theory - What rules did Hamechaber set to himself before compiling the Shulchan Aruch?


Following Doniel's question, did R' Yosef Karo accept himself a set of fixed rules/guidelines by which he is going to compile the Shulchan Aruch?


For example, the order of Halochos, what he brings and what he omits from Tur, what authorities does he mention and what he doesn't, where he brings a Machlokes and where he Paskens.




Why is the Torah divided into five books?


When the Torah refers to itself, it refers to itself in the singular. There are numerous verses, notably in Devarim. One notable example Devarim 31:16 (Sefaria English translation:)



"לָקֹחַ אֵת סֵפֶר הַתּוֹרָה הַזֶּה וְשַׂמְתֶּם אֹתוֹ מִצַּד אֲרוֹן בְּרִית־ה' אֱלֹקיכֶם וְהָיָה־שָׁם בְּךָ לְעֵד׃"


Take this book of Teaching and place it beside the Ark of the Covenant of the LORD your God, and let it remain there as a witness against you.



Yet, we see that there are five sefarim (books) and on parchment, we denote the separate books by leaving several lines of spacing between the end of one book and the start of the next.


I notice that Rash"i as well as the Gemarah refer to some of the separate books by names such as "Torat Kohanim" (Vayikra) and "Mishneh Torah" (for Devarim).


When did the concept of separating the Torah into Five books begin? And, why was there a requirement to write a Torah into five books? Is that Misinai (from Sinai)? It doesn't appear to be this way from the Torah's verbage. Even it is Misnai, why separate it into five books?





solubility - Dissolving of non polar gases in water (liquid)


How does dissolving happen for non polar gases in water? Is it like being in the space between the water molecules or does there occur some kind of interaction occur between gas molecules and water molecules?


Also if the gases dissolve in water, how can their solubility be increased? I have also heard what's called Henry's law accounted for this?


Answers on molecular scale would be more appreciated.




thermodynamics - Why is N₂ stable but HCN and C₂H₂ unstable?


Compounds with triple bonds generally seem to be unstable. $\ce{HCN}$ and $\ce{C2H2}$ are high-energy, relatively short-lived molecules that will readily polymerise or react with other organic molecules. My naïve mental picture is that they don't really want to have a triple bond because the geometry makes it awkward, so they'll do anything to transfer an electron somewhere else and turn it into a double or a single bond instead.


But $\ce{N2}$ seems to be an exception. By my naïve reasoning, when an $\ce{N2}$ meets an organic molecule it should be eager to shrug off its triple bond and join the party. But in fact this doesn't happen, and nitrogen fixing organisms have to do quite a bit of work to get nitrogen to participate in organic molecules.


So my question is, what is it about $\ce{N2}$ that makes its triple bond so energetically favourable while $\ce{C#C}$ and $\ce{C#N}$ bonds are so unfavourable?


Note that this question isn't about reactivity with $\ce{O2}$ but rather with organic molecules. I'm interested in why it's so difficult for $\ce{N2}$ to react with organic molecules in general, given that other molecules with triple bonds seem to react with them very easily.


(Information to guide the scope of answers: I'm coming at this from a physics background, so thermodynamic concepts can be taken as understood, but I quickly get lost when it comes to electrons and orbitals and so on, hence the rather basic question.)




halacha - Is it permitted to use a pseudonym



Using a pen name or a pseudonym in writing letters to the editor or essays or a book might seem like lying.


Is it Halachically permissible?




gaussian - What is a $BT$ (Bandwidth-Time) product with reference to modulation?


I would like to know what does Bandwidth-Time product mean. I understand that Bandwidth ($B$) = 1/Symbol Time ($T$), hence $BT = 1$.



  • But how can it vary?

  • What is its significance?

  • e.g. When we say GFSK is GMSK when $BT = 0.5$, what does that mean exactly?



Answer




The $BT$ product is the bandwidth-symbol time product where $B$ is the $-3\textrm{ dB}$(half-power) bandwidth of the pulse/filter and $T$ is the symbol duration. For different applications you will find varying recommended values. In GSM telephony for instance, a $BT=0.3$ is recommended. In satellite communications with GMSK, for near-earth missions the CCSDS recommends a $BT = 0.25$ whilst for deep-space/interplanetary missions, the use $BT=0.5$ is recommended. You find more details in this CCSDS report on bandwidth-efficient modulations. See page 2-2 and page 2-3 for the mentioned recommended values.


What does that mean ? Let's say we have $1$ bit per symbol ($T$ then correspond to bit time). For a $BT = 1$, the pulse shaping the symbol spreads over one bit period duration. For $BT = 0.25$, the spread is over $4$ bit periods, for $BT = 0.3$ the spread is over approximately $3$ bit periods, and for $BT = 0.5$ the spread is over $2$ bit periods.


This means that a smaller $BT$ product results into higher ISI and a compact spectrum. Measures need to be taken for the introduced ISI in this case much more than in the case of a higher $BT$ product where less ISI is introduced and we have much less compact spectrum.


In GMSK, one of its properties is it maintains a constant envelope and that's because of the Gaussian pulse applied prior to modulation. The GMSK pulse can be defined as in equation $(1)$ below$^1$: $$ g(t) = \frac{1}{2T}\left[Q\left(2\pi B\cdot\frac{t-\frac T2}{\sqrt{\ln(2)}}\right)-Q\left(2\pi B\cdot\frac{t+\frac T2}{\sqrt{\ln(2)}}\right)\right]\tag{1} $$


Where $Q(t)$ is the complementary cumulative distribution function defined as: $$ Q(t)=\int_{t}^{\infty}\frac{1}{\sqrt{2\pi}}\exp\left(-\frac 12 x^2\right)dx\tag{2} $$ The figure below shows the pulse shapes for different values of the $BT$ product:


enter image description here


The spread of this pulse is inversely proportional to the $BT$ product and its peak amplitude directly proportional to the product. Again, this means that lower $BT$ results into a wider spread (over bit symbol period) and with lower peak amplitude and a high $BT$ results into a narrower spread with a higher peak amplitude. In conclusion, the pulse duration increases as the bandwidth of the pulse decreases.


Here they show a link between the $BT$ product, the filter’s $-3\textrm{ dB}$ cutoff frequency and the bit rate $R_b$ as: $$ BT = \frac{f_{-3\rm dB_{\rm cutoff}}}{R_b}\tag{3} $$ You can say that the $BT$ somehow determines the degree of filtering. More on fundamentals and properties of GMSK can be found in this paper $^2$ and this paper $^3$. In both papers discussions in relation to equation $(3)$ and the variations in the eye pattern as a result of $BT$ product values are given.


You can find extra stuff here, here, and here.





$[1]$: John G. Proakis, Digital Communications, 4th Edition, McGraw-Hill, 2000.


$[2]$: A. Linz and A. Hendrickson, "Efficient implementation of an I-Q GMSK modulator," in IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 43, no. 1, pp. 14-23, Jan 1996.


$[3]$: K. Murota and K. Hirade, "GMSK Modulation for Digital Mobile Radio Telephony," in IEEE Transactions on Communications, vol. 29, no. 7, pp. 1044-1050, Jul 1981.


kinetics - At equilibrium are the rates of the forward and backward reactions equal to zero?


At equilibrium, the concentrations do not change with time. So, is it true that the rates of the chemical reactions are zero at equilibrium? Wikipedia says that they are not zero. Why is this?



Answer



In equilibrium, the forward and backward rates are equal to each other. The net is zero, but the individual rates are not zero.


Consider something as simple as water — we know that the water molecule can dissociate in to an $\ce{OH-}$ and $\ce{H+}$, and the pH is a direct measure of the amount of $\ce{H+}$. Once equilibrium is achieved, it isn't like $\ce{H2O}$ stops splitting, or $\ce{H+}$ and $\ce{OH-}$ get back together — it is just at a macro level nothing changes.



Tuesday, January 29, 2019

halacha - Should the Chazzan say the pesukim of Kedusho loud?



In the repetition of the Amida, it seems (see Teshuvos Igros Moshe 3 (9), OC 104 (7), OC 125 Biur Halocho d.h. "elo shoskin ..") that the Chazzan should say the pesukim of Kedusho loud enough so that someone who has not yet finished his own Amida can hear them and thereby fulfill his obligation. But some Chazzanim do not, especially on Shabbos and Yom Tov. What sources do they have to rely on?



Answer



In Rambam's text of the siddur (printed after the various laws of prayer, blessings, and the like, in the back of his code), he writes:


Scanned text of Rambam's instructions



The chazan says each one calls the other, and the congregation answers holy holy holy ... the chazan says by David, your holy anointed one, and the congregation replies G-d shall reign forever. And all the parts that the congregation recites, he says along with them. He should not raise his voice while they answer with him.



halacha - When does טומאת הסגר begin?


When the Chumash speaks about a kohen's seeing some tzaraas on a person's body for the first time, it says the kohen "shall defile" (Vayikra 13:3, 13:11, 13:20, 13:25, 13:30, 13:44). Rashi (13:3) says that the kohen states to the other: "You are defiled." In some circumstances, though, the kohen does not declare person defiled; rather, he closes him in his house to await further evidence as to whether he has tzaraas (Rashi, 13:4). Nonetheless, during that closed-up period, the person is m'tame, i.e. he defiles things he comes in contact with (Rambam, Tum'as Tzaraas 10:12).


When it comes to tzaraas on clothing or a house, though, it is never full-blown tzaraas from the outset: The kohen, if he thinks it's tzaraas, closes it up to await further evidence (13:50, 14:38). During that closed-up period, the seeming tzaraas is m'tame (Rashi, 14:36; Rambam 13:13, 16:1).


From what point is the closed-up person, garment, or house m'tame? Specifically, is it from when the kohen sees the tzaraas (and knows it needs to be closed up) or from when he actually closes it up? If the latter, what exactly does the kohen do to effect the defilement? (For example, is it sufficient that he pronounces the house off-limits? Does he need to physically lock it up?)



Especially, does anyone address this question explicitly? Here's why I'm asking:




  • Yad Hachazaka never addresses the issue explicitly (as far as I see).




  • Rashi (14:36) writes about a house: "… the kohen will come and see the tzaraas, then it will need to be closed up and everything in it will be defiled". This is unclear: Rashi may mean that everything in it will be defiled when it's closed up, or he may mean everything in it will be defiled as soon as the kohen sees the tzaraas and the house needs to be closed up. The Maharal seems to resolve that ambiguity: "Meaning, when he sees the tzaraas, everything in it will be defiled immediately…." However, even this is not entirely clear, as he goes on to contrast this immediacy with a rule, not applicable here, about how long something can be in a tzaraas-afflicted house before becoming defiled. So he may mean "immediately" only in contrast with that and not as an indication of when the defilement begins. Nonetheless, his language does somewhat seem to me to imply that he holds the defilement begins immediately the kohen sees the tzaraas.




  • Rabenu Hilel ben Elyakim (commentary to Sifra to 14:36) writes about a house: "… For we didn't learn '[he's not defiled] until he remains [in the afflicted house] the time it takes to eat a half loaf' except about such items as he brings in [to the house]. But such as were there when the kohen arrived are all defiled immediately." Again, like the Maharal, this is ambiguous, but seems somewhat to imply the defilement begins on the kohen's arrival, not on his closing up the house.





  • Meshech Chochma to 14:36 says very clearly that the pasuk is teaching us there that the house is not defiled before the kohen comes. But he's not as clear about when it is defiled. He writes at the end: "…for at the time he sees the tzaraas, that is closing up, likewise everything in the house will be defiled". He may mean that seeing the tzaraas constitutes closing up, i.e. everything becomes defiled when the kohen sees it; but he may mean that the "seeing" referred to in Vayikra there is not literal seeing but an act of closing up the house.





Answer



You asked: From what point is the closed-up person, garment, or house m'tame?


Short snswer: When the Cohen makes a verbal declaration to that effect.




Details and sources:



The Rambam on the Mishna in נגעים 3:1 says יאמר לו הרי אתה מוסגר בנגע זה - The person becomes a Musgar (quarantined for 7 days) when the Cohen declares: "You are a Musgar regarding this discoloring"


The same procedure is used to create a Muchlat (full fledged Metzora): "שיאמר לו "הרי אתה מוחלט בנגע זה



ואמרו "מסגיר ופוטר" ענינו: שהוא בתחלה או בסוף שבוע יאמר לו הרי אתה מוסגר בנגע זה ופטור מזה וכן ג"כ שיאמר לו הרי אתה מוחלט בנגע זה ופטור מזה



Merely seeing the troublesome spot - even making a decision about it - is insufficient, as there are cases when the color - and hence the outcome - changes while the Cohen is busy looking at the discolorment before he makes the declarations. E.g.: Mishna 7:3



בַּהֶרֶת וְאֵין בָּהּ כְּלוּם, בַּתְּחִלָּה, בְּסוֹף שָׁבוּעַ רִאשׁוֹן, יַסְגִּיר . בְּסוֹף שָׁבוּעַ שֵׁנִי, לְאַחַר הַפְּטוּר, יִפְטֹר . עוֹדֵהוּ מַסְגִּירוֹ וּפוֹטֵר וְנוֹלְדוּ לוֹ סִימָנֵי טֻמְאָה, יַחְלִיט. בַּהֶרֶת וּבָהּ סִימָנֵי טֻמְאָה, יַחְלִיט. עוֹדֵהוּ מַחְלִיטוֹ וְהָלְכוּ לָהֶן סִימָנֵי טֻמְאָה, בַּתְּחִלָּה, בְּסוֹף שָׁבוּעַ רִאשׁוֹן, יַסְגִּיר. בְּסוֹף שָׁבוּעַ שֵׁנִי, לְאַחַר הַפְּטוּר, יִפְטֹר:‏
ר"ע מברטנורה בַּהֶרֶת. עוֹדֵהוּ מַסְגִּירוֹ. שֶׁהָיָה רוֹצֶה לְהַסְגִּירוֹ, בֵּין בַּתְּחִלָּה כְּשֶׁהוּבָא אֶל הַכֹּהֵן, בֵּין בְּסוֹף שָׁבוּעַ רִאשׁוֹן, וְלֹא הִסְפִּיק לְהַסְגִּירוֹ עַד שֶׁנּוֹלְדוּ סִימָנֵי טֻמְאָה, כְּגוֹן בַּתְּחִלָּה בְּשֵׂעָר לָבָן וּמִחְיָה, וּבְסוֹף שָׁבוּעַ רִאשׁוֹן בְּשֵׂעָר לָבָן וּמִחְיָה וּפִשְׂיוֹן, יַחְלִיט. אֲבָל מִשֶּׁהִסְגִּירוֹ, הָא תְנַן לְעֵיל בְּרֵישׁ פֶּרֶק ג', אֵין מַחְלִיטִין אֶת הַמֻּסְגָּר:‏




halacha - If a local store holds a "Christmas Sale" in the days leading up to Dec. 25th, may I shop there?




In mid-December, I received the weekly advertising flyer of a local store chain. At the top, the flyer said "Christmas Sale".


If a sale is advertised like this, with the name of a non-Jewish religious holiday explicitly in the title, is it permissible to shop at the sale, and to benefit from the sale?


Please base your answer upon sources, and please cite them.


[Note: Before following any answers that get posted here, ask your rabbi.]







  1. A question by DanF: "When a chain store adverises a 'Holiday' or 'End of Year' sale, may I buy their product?" DanF's question seems to be about stores which are less explicit in naming their sales.





  2. "Buying from non-Jews, or selling to non-Jews, within three days of their holidays".






halacha - Giving milk and meat to a baby


We have a one-year-old, BH. Is it OK to give him milk and then meat and vice versa without waiting in between?




organic chemistry - Can heteroatoms with lone pairs be chiral centres?


If a compound has a carbon atom with four different groups covalently bonded to it, it is called asymmetric and enantiomers of the compound can exist.


But imagine if one has a different central atom, such as a nitrogen or a sulfur where one of the four "groups" is an electron pair (see examples below).


An explosive chloramine and a sulfonium ion


Would such a thing still behave like a "normal" asymmetric carbon? If not, how else does it behave, i.e. are there enantiomers? Is my assumption that those will still have $\mathrm{sp^3}$ hybrid orbitals wrong? I would also enjoy pointers to literature, I was unable to find any.



Answer



Generally, amine nitrogens will not behave like a normal asymmetric carbon. Simple amines are roughly $\mathrm{sp^3}$ hybridiized and the molecules you use as examples do have 4 (we include the lone pair of electrons as a substituent) different substituents around the central nitrogen atom. So in principle me might consider it asymmetric or chiral. But simple amines can undergo a process called nitrogen inversion, which essentially coverts one enantiomer into the other.



enter image description here


enter image description here


(image source)


However, if one can find a way to slow down or eliminate the nitrogen inversion process, then chiral amines can be isolated. One way to achieve this is to incorporate the amine nitrogen into a 3-membered ring (an aziridine). Now to achieve the planar state necessary for nitrogen inversion requires the bond angle in the 3-membered ring to open from 60° to 120°, an impossible task. Aziridines containing a chiral nitrogen atom have been isolated and characterized.


halacha - What is a “halachic annulment” of a marriage and when is it employed?


I’m stunned that this question wasn’t previously asked.


The Gemara (Gittin 33a) discusses the concept of כל דמקדש אדעתא דרבנן מקדש - anyone who marries does so with the consent of the Rabbis. As discussed there, in very particular cases, they can uproot a marriage retroactively, and thereby permit her to remarry without a proper get (as she was retroactively never married to begin with). It also makes the point that if they did Kiddushin through intercourse, the Chachamim can decide retroactively that it was licentious and therefore did not accomplish Kiddushin.



  1. In what types of cases is this applied? Not every issue can be solved with this, clearly, as if it could, any agunah could go to her local orthodox Beis Din and get an annulment.

  2. Does this make them liable retroactively for...whatever prohibition is involved in a man sleeping with an unmarried woman?

  3. In the event that it’s possible for this to be applied when there are children involved, if their father was a Kohen, are they challalim?

  4. In the event that it’s possible for this to be applied such that a woman who ended up having children from a second husband can annul her first marriage, do those children lose their status of mamzeirus?




Answer



1. Where does the principle of halachic marriage annulment (afka'inhu) apply?


There are five Talmudic cases where this principle is invoked:




  1. A man betrothed (eirusin) a minor (rabinically) and was attempting to finalize the marriage (nissuin) once she reached majority. Before he did so, a second man seized her, and seemingly betrothed her on a biblical level. The second man's actions are invalid, because of afka'inhu (according to Rav Ashi). (Yevamot 110a)




  2. If a man coerces a woman to accept his betrothal, we invoke the principle of afka'inhu (according to Mar bar Rav Ashi) and the betrothal does not take effect. (Bava Batra 48b)





  3. A man divorces his wife on condition that he does not return, and he is prevented from returning unavoidably (b'oneis). Biblically, the divorce does not take effect, but the Rabbis applied afka'inhu to retroactively annul the marriage. (Ketubot 3a)




  4. A man sends an agent to divorce his wife, and then cancels the agency (under certain circumstances). Biblically, if the agent were to present his wife with the get she is not divorced, but the Rabbis applied afka'inhu to retroactively annul the marriage. (Gittin 33a)




  5. A man at death's door divorces his wife and then recovers. Biblically, she is not divorced, but (according to Rabbah and Rava) the Rabbis applied afka'inhu to retroactively annul the marriage. (Gittin 73a)





Can we apply it in other cases?


Rashba in Responsum 1185 writes that we cannot:



אין לך בכלל דברים אלו אלא מה שהתירו בהן בפירוש שאם כן אף אנו נאמר שכל שעשה שלא כהוגן בקידושיו לא ניחוש לקידושין


You only have in all these matters what they explicitly permitted. Otherwise, we could also say that in every case where one acts improperly in betrothal we can ignore it.



Chacham Tzvi makes the same point in Responsum 124, although he does note that Rivash in Responsum 399 thought that it may be possible for a community nowadays to legislate that any marriages performed against its own specific rules would be invalid.


(Parenthetically, the Rabbinical Assembly's Beit Din (Conservative Judaism) will annul marriages for reasons other than the Talmudic ones, normally in agunah cases where all other methods of resolution have failed - see e.g. here.)


2. Does afka'inhu make them liable for the prohibitions involved in engaging in sex outside of marriage?



This question is a little difficult to answer. There will certainly be no earthly consequences. Even Rambam who believes that there is a biblical prohibition couldn't prescribe any punishment here, as they were not 'warned' (hatra'ah) before the act.


Is G-d going to punish them? Presumably not, as they are now following Rabbinic legislation as they were commanded to, but (not being privy to G-d's point-scoring system) I don't say this with any great confidence.


3. What is the status of the children of an annulled marriage?


The children have the status of any other child born from unmarried parents i.e. they are completely normal Jews. They are not mamzerim, who are only formed from the product of adulterous or incestuous unions (Rambam, Hilchot Issurei Bi'ah 15:1). If he is a kohein, she does not become a zonah (Rambam, Hilchot Issurei Bi'ah 18:2), and thus the children are not challalim (Rambam, Hilchot Issurei Bi'ah 19:1).


4. Can afka'inhu revoke the status of a mamzer?


In theory, it appears that applying afka'inhu would allow a mamzer to lose his stigma.


However, R. Tam held that if it is obvious that someone is doing something in order to activate afka'inhu and thus 'purify' a mamzer, then the Rabbis would not apply afka'inhu in such a case. If, however, it's clear to us that such is not his intent, then applying afka'inhu would indeed 'purify' the mamzer. (Tosafot Gittin 33a s.v. ve'afka'inhu)


conditionals - What is the meaning of Noun + なら


So in my N4 textbook, I have the following explanation for a grammatical construct:



Noun + なら:
Use "〜なら" when you say that options are no good, but "〜" is possible, okay or not a problem.



The examples don't make a lot of sense, so I go and google なら. All I can find is stuff about how なら is a particle used to express conditionals, i.e. it's one of the ways of saying what 'if' says in English. This is a meaning of the なら particle that I'm familiar with. I can't find anything about any other meanings of なら.



Can someone explain what my book is on about? Is this related to なら's 'if' meaning, or is it an entirely different word/meaning completely?


The book examples are:



1) 日曜日なら時間が取れるから、いっしょに買い物にいこうよ。



I think this is supposed to mean - I have time on Sunday, let's go shopping together. The なら supposedly implying that days other than Sunday are no good.



2) A: 今度のパーティーでつうやくをしてもらえませんか。
  B: すみません。手紙のほんやくならできますが、つうやくはちょっと...。




So now it's lost me, I have no idea what this is supposed to mean, and what なら is doing here.



Answer



Just to add to xeta217's answer, なら is used when the speaker is making an assertion about what has just been said (or about a current state).


So 日曜日なら has a feeling of "If it's Sunday your talking about then..." Likewise 手紙のほんやくなら "If it's letter translating then...".


A) 店に行く


B) 店に行くなら、卵を買ってください。


A) I'm going to the shop. B) Well if it is the case that you're going to the shop then buy eggs please.


So when your book talks about an 'option being no good' it's not that なら has some special meaning in this context. It's just that this form of 'if' is most appropriate. The condition is an assumption about what has been said.


food - What Bracha did they make on the Mahn?



Did the Jews make a Bracha on eating the Mahn? Which Bracha did they make?



Answer



The sefer כמוצא שלל רב has several articles on it.


He quotes R' Yehuda Hechosid as specifying "HaMotzi Lechem Min HaShamayim" together with the Rama of Fano. Rav Tzvi Hirsch from Ziditschov quotes the mekubal R' Yisroel Dov that no brocho is to be made as mentioned anonymously in the Shut Torah Lishma 63.


Rav Aharon Levi from Reisha supports this view. The Bnei Yisoschor suggests that if it were not for the opinion of the Rama of Fano, he would have said no brocho on weekdays and "asher kideshonu bemitzvosov le'echol seudas Shabbos" on Shabbos.


Rabbi Chaim Pelagi (בספר נפש חיים מערכת מ' אות קו) from Izmir suggests "borei minei mezonos" because the mahn tasted like wafers with honey; but since they fixed their meal on it (not having any other "bread") the brocho was hamotzi.


Rabbi Eliezer Deutsch from Banihad (?) suggests that the brocho would depend on what food the eater intended. Rav Osher Weiss shlit"o points out that this depends on whether the mahn actually changed into the food imagined by the eater or just tasted like it.


There's much more in the sefer.


halacha - Are non-Orthodox marriages recognized by Orthodox rabbis?


Let's suppose a couple was married by a Reform rabbi in a standard reform ceremony (with egalitarian ketubah, and many other modifications to traditional kiddushin). If the couple later become baalei teshuvah, are they required to perform kiddushin again (or, I suppose, if the first wedding didn't count, for the first time)?


Is the case any different if the couple was married in a Conservative ceremony?


Related: Are civil divorces not recognized by Orthodox rabbis?



Answer



R' Yosef Eliyahu Henkin (פירושי אירבא סימן ד) held that it does not actually matter if the wedding was valid, as they are living together with intent to be married. Rav Henkin adopted the novel view that even if their intent to be married is not necessarily through Kiddushin, and even if they don't know that consumation of marriage can create Kiddushin, they are still married. According to this opinion, the question about the wedding itself really becomes moot.


However, most opinions did not accept the view of R' Henkin.


I was told that R' Elyashiv held that there is a problem with the normal procedure of a Reform and Conservative wedding which would invalidate the Kiddushin. Kiddushin is effected by the man giving something of value to the woman. R' Elyashiv understood that a two-ring ceremony is not a "gift" from one to the other, but is rather an exchange. The bride giving a ring to the groom in reciprocation to his giving a ring to her invalidates this as an act of Kiddushin. I was once at a Conservative wedding where the officiating Rabbi was sensitive to this issue - after the groom gave the ring to the bride, the Rabbi announced "The Kiddushin ceremony is now over. However, Cindy has indictated that she would also like to give a ring to Joel, which will be done now." I think this would obviate R' Elyashiv's concern, but it is atypical to your standard Reform or Conservative wedding.



tefilla - Silent Amidah when praying without a minyan


If one is davening b'yichidut (praying by oneself), without a minyan, do they need to say the amidah silently or can they say it out loud?



Phrased another way, what is the reason for praying the amidah silently when praying with a minyan? Is it so as not to disturb other people who are also praying, or is there another reason that would no longer apply when one is not praying with a minyan?



Answer



OC 101 (2) and MB s.k.5 and especially 6. MB: One reason not to raise the voice is not to disturb others. Other reasons are to be like the prayer of Channa; to avoid being one of those of little faith who do not believe that HaShem hears prayers uttered quietly and to avoid being like the false prophets who cry out loud to false gods. But the important thing is not to disturb others.


OC: If necessary to concentrate on the prayer and one is alone, it is permitted to raise one’s voice.


Rema: If one davens aloud to instruct one’s household, this is permitted.


organic chemistry - What's the difference between a nucleophile and a base?


Obviously it depends on the context whether you would call a particular species a nucleophile or a base but are the two terms largely synonymous or is there a difference?



Answer



The two are related, in that most nucleophiles are (Lewis) bases and vice versa. Some good nucleophiles are also strong bases, e.g. $\ce{HO-}$. However, a species can be a good nucleophile and a weak base, e.g. $\ce{I-}$; or a species can be a weak nucleophile and a strong base, e.g. $\ce{t-BuO-}$. How can we separate this behavior?



Nucleophilicity is a kinetic phenomenon.




Nucleophilicity is most often defined based on the relative rate of the reactions of nucleophiles with a standard substrate in a standard solvent.


For example, a standard reaction might look like:


$$\ce{CH3I ->[Nu-][H2O] CH3Nu}$$


The nucleophilicity will be related to the relative rate constant of reaction with the nucleophile (relative to the rate constant of the reaction with water $\equiv 1$).



Basicity is a thermodynamic phenomenon.



Basicity is based on the position of equilibrium:


$$\ce{B + HSol <=> BH+ + Sol-}$$



solubility - What is the Ksp of Al(OH)3?


Top hits on google are:


This site
Aluminum hydroxide $\ce{Al(OH)_3}$ >> $ 1.3×10^{–33}$


and


This site
Aluminum hydroxide $\ce{Al(OH)_3}$ >> $ 3×10^{–34}$


which is one order of magnitude different.


What can be the reason for this variation? Experimental conditions? Where can I get accurate or reliable results/data of $K_{\mathrm{sp}}$ in general?




word choice - What are the differences between「目的」and 「目標」?


Both「目的」and「目標」have a common meaning which is "goal", but what is the difference?
When can we use one but not the other?




Monday, January 28, 2019

word choice - Meaning of 「これはこれで」, and the difference between it and 「それはそれとして」



I came across the following lines.



・・・俺としては、下駄箱の中に手紙が入っているみたいなほうが好みだった。でもこれはこれで、少なくとも相手が積極的だってことはわかる。



I am wondering about the meaning of 「これはこれで」 here. As one might expect, it does not have any entries in the dictionaries that I use. However, it seems to me to mean something along the lines of "that aside".


If this is the case, what would be the difference between 「これはこれで」 and the 「それはそれとして」 below?



・・・まあ、それはそれとして、正解の答えがわかっても、どうすればあの「sprachgefühl」が身につけられるかという問題が残っています。



They both appear to have similar meanings.



Or would the sentence perhaps be better interpreted as such?



[これは] [これで少なくとも {相手が積極的だ} ってことはわかる]。




Answer



それはそれとして means "that aside, ..." "apart form that, ..."
Compare:
これはこれとして "that aside, ..." "setting this apart, ..." "apart from this, ..."


The これはこれ (≒ (これは)これなりに) here means "This (is good/okay, etc.) in its own way."
Compare:

それはそれで/(それは)それなりに = "That (is good/okay etc.) in its own way."
彼は彼で/(彼は)彼なりに = "He (is trying hard / doing his best, etc.) in his own way."


I would parse your sentence this way:



[これはこれで][少なくとも{「相手が積極的だ」ってことは}]わかる。



passover - Free sample of Chametz


What happens if a person recieves a free sample of chamets on peasach?




organic chemistry - Mechanism for reaction of Tollens' reagent with aldehydes


Upon treatment with Tollens' reagent (ammoniacal silver(I) nitrate), aldehydes are oxidised to carboxylic acid, and silver(I) is reduced to silver metal.


I am trying to find a mechanism for the this reaction online, but the only thing I can find is the balanced equation. Can someone propose or help me find the mechanism?



Answer



Here are the two half reactions:


$$\begin{align} \ce{[Ag(NH3)2]+ + e- &-> Ag^0 + 2NH3} \\ \ce{RCHO + 3OH- &-> RCO2- + 2H2O + 2e-} \end{align}$$



which together yield the overall reaction


$$\ce{2[Ag(NH3)2]+ + RCHO + 3OH- -> 2Ag^0 + RCO2- + 4NH3 + 2H2O}$$


Here is a diagram of the reaction mechanism. The carbonyl group is oxidized in the process and the $\ce{Ag^+}$ is reduced. The resultant oxidized aldehyde (now a radical cation) reacts with hydroxide to form a tetrahedral intermediate. A gem-diol like intermediate is formed via a hydrogen shift, which then continues on to the final carboxylate anion.


reaction mechanism


physical chemistry - What exactly is hydrogen bonding (and does it really need fluorine, oxygen, or nitrogen)?


I'm not satisfied with the rationale for the intermolecular attraction known as hydrogen bonding. In my book, it states that




Hydrogen bonding is a special type of intermolecular attraction between the hydrogen atom in a polar bond (particularly H ¬ F, H ¬ O, and H ¬ N) and non-bonding electron pair on a nearby small electronegative ion or atom usually F, O, or N (in another molecule).



It seems that chemists looked at the data and found they needed a 'fudge factor' to fit the higher boiling points of ammonia, water, and hydrogen fluoride.



Why doesn't hydrogen bonding apply to other atoms like Sulfur or Chlorine? They seem to be electronegative enough IMO. Is there an explanation that explains why this is, rather than saying that it's there? What makes Hydrogen so special?


Note: Chlorine is more electronegative than Nitrogen.



Answer



There are two main ways to look at hydrogen bonding. The first is electrostatic, where the electronegativity of the atoms is used to describe the interaction. Your argument about chlorine being more electronegative than nitrogen is a good one suggesting that the electrostatic argument is only part of the story, and there is at least one study that suggests that hydrogen bonding does occur with chlorine in polar molecules such as chloroform.


We can increase dramatically the number of atoms considered to undergo hydrogen bonding if we take a molecular orbital approach. My reasoning here is a summary of what can be found in Inorganic Chemistry by Miessler, Fischer and Tarr. They, in turn, rely heavily on a new definition of hydrogen bonding recommended by the IUPAC Physical and Biophysical Chemistry Division.


A hydrogen bond is formed when an $\ce{X-H}$ (where X is more electronegative than H) interacts with a donor atom, $\ce{B}$. The attraction $\ce{X-H...B}$ can be described as consisting of the following components:




  • An electrostatic contribution based on the polarity of $\ce{X-H}$

  • A partial covalent character which arises from the donor-acceptor nature of the interaction

  • Dispersion forces


The first bullet is typically the only phenomenon discussed in General Chemistry classes, and this is not unreasonable since the second bullet requires the introduction of Lewis Acid/Base concepts which may not have been covered.


It is important to note that the new definition includes what I like to call "the proof is in the pudding" where the existence of hydrogen bonding requires experimental evidence, which can be found using a number of methods:



  • The $\ce{X-H...B}$ bond angle: a bond angle of 180 degrees indicates strong hydrogen bonding and would be accompanied by shord $\ce{H...B}$ bond distances.

  • A red shift in the IR frequency upon formation of $\ce{X-H...B}$


  • Hydrogen bonding results in deshielding of the H atom, which can be observed in NMR spectroscopy.

  • Thermodynamic studies should indicate that $\Delta G$ for the formation of $\ce{X-H...B}$ should be larger than the thermal energy of the system.


While electrostatics is the dominant contributor to hydrogen bonding, an analysis of frontier orbitals can also be insightful. A thorough answer requires a fair amount of MO theory background, but for those interested, looking at the MO diagram of $\ce{FHF-}$ will be helpful. In brief, the base ($\ce{F-}$ in this case) has a filled $p_z$ orbital that gains access to a delocalized orbital with lower energy, thus validating the formation of a strong hydrogen bond.


minhag - Custom to light yahrzeit candle on Erev Shabbos before the yahrzeit


Has anyone heard of a custom to light a yahrzeit candle not on the eve of the actual yahrzeit, but on the eve of the preceding Shabbos? I know that there are other customs for the preceding Shabbos, such as saying kaddish, davening for the amud, possibly saying Kel Malei Rachamim, etc.--but is burning the memorial candle over that Shabbos also a tradition by anyone? (By whom?)


Motive: I am trying to find out if it could be my family's actual custom to do so, or if a relative instructed me to do this based on a misunderstanding.




Writing/buying Seforim rather than Sefer Torah


I've heard someone say that the mitzvah to write/buy a Sefer Torah in these days is actually to write/buy seforim that we use to learn Torah from. Do you know who the source of this opinion is?



Answer



This is the opinion of R. Asher b. Yehiel (Rosh) at the beginning of his Hilchot Sefer Torah:




וזהו בדורות הראשונים שהיו כותבים ס"ת ולומדים בו. אבל האידנא שכותבין ס"ת ומניחין אותו בבתי כנסיות לקרות בו ברבים מצות עשה היא על כל איש מישראל אשר ידו משגת לכתוב חומשי התורה ומשנה וגמרא ופירושי' להגות בהן הוא ובניו. כי מצות כתיבת התורה היא ללמוד בה כדכתיב ולמדה את בני ישראל שימה בפיהם. וע"י הגמרא והפי' ידע פי' המצות והדינים על בוריים לכן הם הם הספרים שאדם מצווה לכתבם וגם לא למכרם אם לא ללמוד תורה ולישא אשה:‏


This [commandment to write a Torah scroll] applied in earlier generations when they would write Torah scrolls and learn from them.


But today, when we write Torah scrolls and leave them in the synagogue in order to read from them publicly, the positive commandment incumbent upon all Jewish men who can afford to do so is to write humashim, mishnah and gemara and commentaries so that he and his children may meditate upon them.


For the commandment to write the Torah is [in order] to learn from it, as it writes, "And teach it to the Children of Israel, place it in their mouths."


And through the gemara and the commentaries one will thoroughly know the explanations of the commandments and the laws.


Therefore, they are the books that one is commanded to write, and also not to sell them (unless he needs the funds in order to learn Torah or to marry).



etymology - Why do days of the week use on-yomi kanji readings?



I would like to know if there is detailed information as to why days of the week use on-yomi readings, for example



月 in 月曜日 【げつようび】



Were these readings (as spoken) imported from the Chinese? And if so, is it known what days of the week were called prior to Chinese influence?



Answer



As for why they use on-yomi, it's just because they were lifted right out of Chinese by monks back in the Heian period. That's the easy part of this question, but interestingly it's really hard for me to find anything about what the days of the week were called before the introduction of 七曜. Apparently the naming of the days of the week based on the 7 visible planets came through an old Buddhist text, quite a mouthful, called 文殊師利菩薩及諸仙所説吉凶時日善悪宿曜経{もんじゅしりぼさつきゅうしょせんしょせつきっきょうじじつぜんあくすくようきょう} (or just 宿曜経 for short), with the 7 day system going as far back as ancient Babylonia.


Before this, however, I can't find anything too comprehensive. There is a system of days that also originated in China called the 六曜{ろくよう}, a system of a 6 day week where each month is divided up roughly into 5 segments. These 6 days are 先勝, 友引, 先負, 仏滅, 大安, 赤口, and they represent certain astrology-tyle 'lucky' qualities. The first is "lucky in the morning but not the afternoon." The next is good for lawsuits ad business. The third is unlucky in the morning. The fourth a very unlucky day (Buddha's death). The fifth is lucky, and the 6th is unlucky except at lunch time. According to wikipedia, though, this was actually introduced after the current system. So I guess the search continues.


There is another very old system of measuring time known as the 旬{じゅん}, but this also unfortunately does not refer to specific days. Rather it refers to groupings of 10 days, so in a month you have 上旬・中旬・下旬 to refer to the first, middle, and final 10 days of the month. This system of measuring time goes way back to the oldest writings in China, but you're not going to find your days of the week here.


With the above I guess it is possible that they used 十干{じっかん} to name days, but I'm not sure. The 10 are 甲・乙・丙・丁・戊・己・庚・辛・壬・癸, and they each apparently match up with one of the Chinese elements that were adopted into the names of days (look at the table on Wikipedia). Like I said, though, whether or not this naming convention was used in Japan I am not sure.



None of these is a really satisfactory answer to the question, but in all the searching I did I could not find any explicit information about the names of the days of the week in Japanese before this. However I did learn a lot about it otherwise so I wanted to write it out here anyway.


For further reading check out these sites:


http://www.cjvlang.com/Dow/dowjpn.html (English) http://ja.wikipedia.org/wiki/%E4%BA%8C%E5%8D%81%E5%85%AB%E5%AE%BF (another astrological grouping of 28 days from China) http://koyomi.vis.ne.jp/doc/mlwa/200611070.htm http://ja.wikipedia.org/wiki/%E4%B8%83%E6%9B%9C http://ja.wikipedia.org/wiki/%E6%9B%9C%E6%97%A5


kashrut kosher - Does bagged lettuce need a hechsher?


Does one need a hechsher on commercially available bagged lettuce? Or is the standard washing process used by the producers sufficient to remove all insects of halachic significance?


Anecdotally, I've noticed that a few Chabad Houses I am familiar with use bagged lettuce without a hechsher and do not check it themselves. When asked, they told me that their custom was not to be "machmir" about the issue of bugs. I assume that means they rely on the view of the Aruch HaShulchan YD 100:13 who provides a limmud zechus for "all the masses of Jews who are not careful (to check) and eat anything that comes into their hands as long as they don't see any obvious infestation, and Heaven forfend to say that all the Jews are stumbling in a great sin like this"



Are there sources for the leniency to rely specifically on commercial washing without a sampling-based hechsher? Or is the Aruch haShulchan really the primary basis for leniency? Are there contemporary poskim who are lenient?




talmud gemara - References for learning Aggada


I often run into aggadic passages in the Talmud, and would like to get a list of references beyond the standard 4 (Ein Yaakov, Maharsha, Benayahu/Ben Yehoyada and the Chiddushei Aggados of the Maharal).


Is there any other reference, which would interpret aggada, preferably not al-pi derech pshat?


Thank you very much.



Answer



Among Rishonim, the Meiri often explains aggadah, and the Rashba wrote a commentary specifically on aggadeta. The sefer Ein Eliyahu is a multi-volume commentary on aggadah. Many aggadeta are also discussed by the Chida in his פתח עינים. R. Moshe Tzuriel also collected many commentaries on aggadah in his Leket Peirushei Aggadah


See also this article, especially n. 10 .


electronic configuration - Is the half-full rule and full rule followed in the 6th and 7th periods?


Is the half-full rule and full rule followed in the 6th and 7th periods? (Note: Half-full rules is Hund's rule)


Example: What is the correct electron configuration? $$\ce{W = [Xe] 6s^2 4f^{14} 5d^4}$$ doesn't use half full rule, or $$\ce{W = [Xe] 6s^1 4f^{14} 5d^5}$$ uses half full rule.




Answer



Short answer: no! The first known exception to occur in the periodic table is in period 5: niobium’s ground state electronic configuration is



$\ce{Nb: [Kr] 5s^1 4d^4}$



which is not warranted by the “usual” rules for determining electronic configuration. So, the “half-full rule” is not sufficient in periods 5 and higher.




Let’s look at Wikipedia’s list of exceptions to Madelung’s rule. In period 4, the only exceptions are $\ce{Cr}$ and $\ce{Cu}$, which are accounted for by the “half-full rule”. (Don’t bother too much about the dispute for Ni.)


In period 5, the exceptions to Madelung’s rule are classified in three groups:




  • $\ce{Mo}$ and $\ce{Ag}$: they are the analogues of Cu and Cr

  • $\ce{Pd}$ is $\ce{5s^0 4d^10}$: a different type of application of the explanation that “fully filled shells are particularly stable”, because in this case two electrons from the s shell were pulled into the d shell. Not what you usually learn.

  • $\ce{Nb}$ is $\ce{5s^1 4d^4}$, and $\ce{Ru}$ is $\ce{5s^1 4d^7}$: these cannot be explained by simple rules, and one has to perform complex quantum chemistry calculations to understand these electronic configurations.


Period 6 contains further inconsistencies, because of the introduction of $\ce{f}$ orbitals into the mix.


Sunday, January 27, 2019

acid base - Why is potassium phosphate KH2PO4 in this reaction?


This is a continuation of this question because the first thing that came in my mind is that why potassium phosphate in this reaction is $\ce{KH2PO4}$ and not $\ce{K3PO4}$?


In the wikipedia article of phosphate ion ($\ce{PO4^3-}$), it is written that:




Aqueous phosphate exists in four forms. In strongly basic conditions, the phosphate ion ($\ce{PO4^3-}$) predominates, whereas in weakly basic conditions, the hydrogen phosphate ion ($\ce{HPO4^2-}$) is prevalent. In weakly acidic conditions, the dihydrogen phosphate ion ($\ce{H2PO4−}$) is most common. In strongly acidic conditions, trihydrogen phosphate ($\ce{H3PO4}$) is the main form.



So, $\ce{FeCl2}$ must somehow be acidic in aqueous solution so as to protonate potassium phosphate $\ce{K3PO4}$ to $\ce{KH2PO4}$. Is this statement true? This question throws some light on acidity of chromium chloride in aqueous solution but is it applicable to iron chloride as well?




In the previous question, the homework question was write the equation of reaction of Iron(II) chloride and potassium phosphate. So, students can assume the reaction to be $\ce{FeCl2 + K3PO4}$ to simply yield iron(III) phosphate or iron(II) phosphate and potassium chloride but why make the reaction complex by assuming potassium phosphate $\ce{KH2PO4}$.


Iron hydrogen phosphate are new in this world and has been recently synthesised and as not as stable as iron phosphates. So, can we just assume that reaction of Iron(II) chloride and potassium phosphate to yield iron (II or III) phosphate and potassium chloride?



Answer



I think that’s just another mistake the OP of the other question made. Potassium phosphate is $\ce{K3PO4}$ and any student using any hydrogenphosphate instead would lose marks if I were marking the exam.


If $\ce{KH2PO4}$ is meant to be added, use the correct term: potassium dihydrogenphosphate.



This nomenclature can be found in the current version of IUPAC’s Red Book, sections IR-8.2 and IR-8.4 and the anions in question are explicitly named in table IR-8.1 therein.


conversion to judaism - Were the converts mentioned in the Megillah actually Jews?


Esther 8:17 says that many people of the various lands מתיהדים which means, literally "Made themselves Jewish".


Does this mean that they were "valid" Jews, i.e. obligated in all the mitzvoth as other Jews such as those born Jewish or those who were already converts by other valid means (i.e. - prior to the Purim story?)


Why I believe not:





  • The term used here is מתיהדים as opposed to the term we would expect for converting which should be מתגיירים.




  • Acceptable converts must have done so of their own free will not because of fear or coercion. IN this case, the end of the verse says that they made themselves Jewish "...because the fear of the Jews fell upon them."




If either of these cases is correct, what does the term מתיהדים mean?



Answer




The Rambam writes in Hilchot Issurei Biah 13:15:



לְפִיכָךְ לֹא קִבְּלוּ בֵּית דִּין גֵּרִים כָּל יְמֵי דָּוִד וּשְׁלֹמֹה. בִּימֵי דָּוִד שֶׁמָּא מִן הַפַּחַד חָזְרוּ. וּבִימֵי שְׁלֹמֹה שֶׁמָּא בִּשְׁבִיל הַמַּלְכוּת וְהַטּוֹבָה וְהַגְּדֻלָּה שֶׁהָיוּ בָּהּ יִשְׂרָאֵל חָזְרוּ. שֶׁכָּל הַחוֹזֵר מִן הָעַכּוּ''ם בִּשְׁבִיל דָּבָר מֵהַבְלֵי הָעוֹלָם אֵינוֹ מִגֵּרֵי הַצֶּדֶק. וְאַף עַל פִּי כֵן הָיוּ גֵּרִים הַרְבֵּה מִתְגַּיְּרִים בִּימֵי דָּוִד וּשְׁלֹמֹה בִּפְנֵי הֶדְיוֹטוֹת. וְהָיוּ בֵּית דִּין הַגָּדוֹל חוֹשְׁשִׁין לָהֶם לֹא דּוֹחִין אוֹתָן אַחַר שֶׁטָּבְלוּ מִכָּל מָקוֹם וְלֹא מְקָרְבִין אוֹתָן עַד שֶׁתֵּרָאֶה אַחֲרִיתָם:


For this reason, the court did not accept converts throughout the reign of David and Solomon. In David's time, [they feared] that they sought to convert because of fear and in Solomon's time, [they feared] that they were motivated by the sovereignty, prosperity, and eminence which Israel enjoyed. [They refrained from accepting such converts, because] a gentile who seeks to convert because of the vanities of this [material] world is not a righteous convert.



Our verse, Esther 8:17, states:



וּבְכָל־מְדִינָ֨ה וּמְדִינָ֜ה וּבְכָל־עִ֣יר וָעִ֗יר מְקוֹם֙ אֲשֶׁ֨ר דְּבַר־הַמֶּ֤לֶךְ וְדָתוֹ֙ מַגִּ֔יעַ שִׂמְחָ֤ה וְשָׂשׂוֹן֙ לַיְּהוּדִ֔ים מִשְׁתֶּ֖ה וְי֣וֹם ט֑וֹב וְרַבִּ֞ים מֵֽעַמֵּ֤י הָאָ֙רֶץ֙ מִֽתְיַהֲדִ֔ים כִּֽי־נָפַ֥ל פַּֽחַד־הַיְּהוּדִ֖ים עֲלֵיהֶֽם׃


And in every province, and in every city, whithersoever the king’s commandment and his decree came, the Jews had gladness and joy, a feast and a good day. And many from among the peoples of the land became Jews; for the fear of the Jews was fallen upon them.




Thus, it seems unlikely that the מתיהדים actually converted. Although the Rambam does explain that a roundabout route of conversion was open, it was designed to weed out those who converted from external concerns-- like these people.


organic chemistry - Why does C=O have a larger dipole moment than C-O?


Why does $\ce{C=O}$ have a larger dipole moment than $\ce{C-O}$?


According to me, dipole moment directly depends upon bond length and electronegativity difference. In $\ce{C=O}$ and $\ce{C-O}$, (I guess, please clear if I am wrong) the EN difference is same, and bond length of $\ce{C=O}$ is less than $\ce{C-O}$. So, $\ce{C=O}$ must have less dipole moment than $\ce{C-O}$ but it is not so. Why?



Answer




According to Wikipedia, bond dipole moment depends on:



  1. Distance between atoms and

  2. Overall charge difference, not just electronegativity difference.


Resonance tells us that there is some amount of charge separation in $\ce{C=O}$ bonds because of the $\ce{C+-O-}$ contributor. This difference in charge, in addition to the electronegativity difference, is more significant than the decrease in distance between atoms, hence the larger dipole moment for $\ce{C=O}$.


Rashi's explanation that Noach did everything he was commanded


Bereishis 7:5 says:



וַיַּ֖עַשׂ נֹ֑חַ כְּכֹ֥ל אֲשֶׁר־צִוָּ֖הוּ יְהוָֽה׃


And Noah did just as the LORD commanded him.



Rashi there explains:




ויעש נח זֶה בִיאָתוֹ לַתֵּבָה:


And Noach Did- This is his coming to the Ark



However, verse 7 says:



וַיָּ֣בֹא נֹ֗חַ וּ֠בָנָיו וְאִשְׁתּ֧וֹ וּנְשֵֽׁי־בָנָ֛יו אִתּ֖וֹ אֶל־הַתֵּבָ֑ה מִפְּנֵ֖י מֵ֥י הַמַּבּֽוּל׃


Noah, with his sons, his wife, and his sons’ wives, went into the ark because of the waters of the Flood.



Rashi there explains Noach only went in because the flood forced him to


There's two ways to ask the question:




  1. If Noach only went in because he was forced, why is verse 5 praising him for listening to Hashem?

  2. If verse 7 (and 13) say explicitly that Noach went in the Ark, why does verse 5 need to tell me? (The Ohr Hachaim poses it this way)


The Gur Aryeh therefore explains the Rashi to verse 5 means Noach simply went to the ark, but didn't enter it. Verse 7 is where he enters it. The Levush HaOrah asks on this, that verse 5 says Noach did as he was commanded to by Hashem. Hashem told him to enter the Ark. By going to it and not entering it, how is that fulfilling Hashem's command?


At this point I don't understand how to reconcile the Rashi. How can his peirush be understood? (I understand there are other explanations for these verses, but I'm interested in understanding Rashi)




Dipole moment - calculation of percentage ionic character


Question: The dipole moment of $\ce{HBr}$ is $2.60 \times 10^{-30}$ and the interatomic spacing is $1.41$. What is the percentage ionic character of $\ce{HBr}$?


What I know is that the percentage ionic character is observed dipole moment divided by calculated dipole moment $\times\ 100$.


The calculated dipole moment is $\textrm{charge on electron} \times \textrm{radius of molecule}$.


However, how would I convert interatomic spacing into radius?




parshanut torah comment - Why didn't our forefathers buy land in the Holy land?


Our forefathers were freakishly rich, but they didn't invest in real estate in the Holy Land for their descendants besides two graveyards (for Sarah in Hebron and Yossef in Shechem).


It appears that they could buy a huge portion of the Land to inherit to Am Israel and significantly ease the future conquest.


EDIT 1: The [innumerous commentaries on the] story of Avraham buying the Cave of the Patriarchs shows the importance of appropriating the land in Israel by our forefathers, with no relations to the recognition by other nations. The Torah would certainly document the buys and we could have much better evidence than only the fact that G-d promised the land to the Israelites.


EDIT 2: Many commentaries say that G-d commanded Avraham to "acquire" the land by walking across, which clearly shows the need to acquire the land anyway.


Why didn't they do that?




digital communications - Understanding the Matched Filter

I have a question about matched filtering. Does the matched filter maximise the SNR at the moment of decision only? As far as I understand, ...