physical chemistry - What is the pKa of the hydronium, or oxonium, ion (H3O+)?

Although the wikipedia page on Hydronium indicates a $\mathrm{p}K_\text{a}$ of −1.74, I noticed in the discussion of this page that the subject seems debated (cf. http://en.wikipedia.org/wiki/Talk:Hydronium#pKa.3F) since alternative (apparently more rigorous) reasoning leads to $\mathrm{p}K_\text{a} = 0$ for $\ce{H3O+}$.

Also, many demonstrations lead to $\mathrm{p}K_\text{a}$ and $\mathrm{p}K_\text{b}$ of 15.74 for $\ce{H2O}$ and thus, using $K_\text{w}=[\ce{H+}][\ce{OH-}]=10^{-14}$, give $\mathrm{p}K_\text{a}$ and $\mathrm{p}K_\text{b}$ of −1.74 for $\ce{H+}$ and $\ce{OH-}$ respectively. But those demonstrations seem to make use of the concentration $[\ce{H2O}]=55.56~\text{mol/L}$ instead of the activity $a_{\ce{H2O}}=1$ (for a solvent) in the equilibrium constant of the reactions.

So it seems to me that the $\mathrm{p}K_\text{a}$ of $\ce{H3O+}$ must be equal to $0$.

Is this question still debated?

PS1:
To add details about the question, the debate in the references mentioned in the discussion on the wikipedia page as well as in the link provided by Nicolau Saker Neto bellow seems to boil down to the coexistence of two different definitions for the equilibrium constant:
- one based on the activities of the compounds
- the other derived from the 'mass action law' and which thereby uses the molar fractions of the compounds

Reading through the Callen (Thermodynamics and an Introduction to Thermostatistics) gives me the impression that the derivation from the mass action law of an equilibrium constant involving molar fractions is based on the assumption of an ideal fluid. However, it is precisely the departure from ideality that seems to justify the use of activities instead of molar fractions. Is that correct?

PS2:
Another point, which I have not looked in details yet, seems to be a debate about the possibility to apply the definition for $K_\text{a}$ to the water molecules $\ce{H2O}$ considering that they are not a highly diluted solute since they constitute the solvent. Is this a valid issue and should then the acidity of $\ce{H3O+}/\ce{H2O}$ be determined in another solvent than $\ce{H2O}$ to be compared with the other acids?

Answer

The controversy surrounding the $\mathrm{p}K_\mathrm{a}$ of hydronium mostly arises from the definition of $K_\mathrm{a}$ or lack thereof.

There is no IUPAC definition of $\mathrm{p}K_\mathrm{a}$ or $K_\mathrm{a}$.

The closest IUPAC defined term is the standard equilibrium constant, which can be denoted as $K^\circ$ or just $K$.

Physical chemistry texts such as Levine and respected works such Bates's "Determination of pH — Theory and Practice" define $K^\circ_\mathrm{a}$ of an acid in water as:

$$\frac{a(\ce{A-})a(\ce{H3O+})}{a(\ce{HA})a(\ce{H2O})} \tag{1}$$

Where $a$ is activity.

Substituting that the acid is $\ce{H3O+}$:

$$\frac{a(\ce{H2O})a(\ce{H3O+})}{a(\ce{H3O+})a(\ce{H2O})} = 1 \tag{2}$$

and of course $-\log(1) = 0$.

The number $-1.74$ that some quote for the hydronium $\mathrm{p}K_\mathrm{a}$ comes from:

• omitting the activity of water from the denominator of the $K^\circ_\mathrm{a}$ definition (equation $(1)$); and


• taking the concentration of water (about $55.5~\mathrm{M}$) as the $K_\mathrm{a}$ of $\ce{H3O+}$.

With that, one obtains the $\mathrm{p}K_\mathrm{a}$ as $-\log (55.5) = -1.74$. For example, Levine even has the $-1.74$ value in a figure comparing the $\mathrm{p}K_\mathrm{a}$'s of various acids, but has a footnote explaining that the value for $\ce{H3O+}$ is based upon the alternative $\mathrm{p}K_\mathrm{a}$ definition.

However, revisiting the analysis that $K^\circ_\mathrm{a} =1$ is probably the most authoritative paper on this issue:

New point of view on the meaning and on the values of Ka(H3O+, H2O) and Kb(H2O, OH-) pairs in water, which insists that

$$\ce{H2O + H3O+ <=> H3O+ + H2O}$$

"does not correspond to an actual chemical process" and therefore "it is not legitimate" to extend the concept of $K^\circ_\mathrm{a}$ to $\ce{H3O+}$ in water.

The article goes on to say that only by studying the $K_\mathrm{a}$ of $\ce{H3O+}$ in another solvent such as ethanol can $\ce{H3O+}$ be compared to other acids.

The $\mathrm{p}K_\mathrm{a}$ of $\ce{H3O+}$ in ethanol is $0.3$ and $\mathrm{p}K_\mathrm{a}$ values are $1.0 \pm 0.3$ units lower in water than in ethanol, so the article suggests a $\mathrm{p}K_\mathrm{a}$ of $-0.7$ for $\ce{H3O+}$ in water, for the purpose of comparison to other acids.

titration - Potassium permanganate to analyze iron compounds

In my lab, I used potassium permanganate in order to analyze the amount of iron in a compound with iron in the +2 oxidation state using titration. My question is how would this analysis be different if we were analyzing iron in a different oxidation state like +3?

conjugations - Do 形容詞 have a 未然形 in Classical Japanese?

I was reading Eiríkr Útlendi's answer about -い vs. -き in 形容詞 and noticed that he identified -く as the 未然形 of 形容詞. When I studied classical Japanese, though, I was taught that 形容詞 lack a 未然形 (and also lack a 命令形, of course).

This jives with my (probably poor) intuition about how 形容詞 conjugate - you can't say *美しくず or *美しくぬ for the negative of 美し - you have to say 美しくあらず or 美しからぬ or something like that (i.e. using the 連用形, which is 美しく, adding an あり, and then tacking a negation 助動詞 onto the 未然形 of あり, which is あら).

Are there multiple schools of thought on whether or not 形容詞 have a 未然形? The textbook I used was 新編文語文法 by 大野晋, in case that helps.

---

UPDATE: I found my textbook; it states the following in the section on 形容詞の活用の種類 (p. 30): for the ク活用, we have two patterns of conjugation (未然・連用・終止・連体・已然・命令):

 1.　　 〇　　　　　―く　　　　　―し　　　　　―き　　　　　―けれ　　　　 〇
 2.　　―から　　　　―かり　　　（―かり）　　　―かる　　　（―かる）　　　―かれ

Likewise, we have two patterns of conjugation for シク活用:

 1.　　 〇　　　　　―しく　　　　―し　　　　　―しき　　　　―しけれ　　　 〇
 2.　　―しから　　　―しかり　　（―しかり） 　　―しかる　　（―しかる）　　―しかれ

The textbook does not specifically name the (2.) conjugations as the カリ活用 and シカリ活用, but does mention them. In any case, the textbook specifically claims that in their "bare" form (without あり), 形容詞 do not have a 未然形 (p. 31; emphasis added):

「ク活用」「シク活用」のいずれの場合も、本来の活用は「〇・く・し・き・けれ・〇」「〇・しく・し・しき・しけれ・〇」で、未然形・命令形がなかった。それでは助動詞に続かず不便なので、のちに、それを補うために、連用形のあとにラ変動詞「あり」をつけて、「高く＋あり→高かり」のように熟合させたのが[the (2.) conjugations]である。これによって未然形・命令形を補うと共に、助動詞との接続が自由になった。

は and が - Using は before 欲しい instead が

I was doing some exercises and the book that I'm using translated:

I don't want shoes

to

靴は欲しくないです

I answered using が particle instead は, since, as far as I know, I should use が before 欲しい. So why did the book use は this time?

I imagined that the reason is to make a contrast/comparison that は provide. Is that why?

Answer

"I want xxx." vs. "I do not want xxx."

When you want something, you will generally say:

「XXX + が + ほしい」

and when you do not want something, you will generally say:

「XXX + は + ほしくない」

The only times you can and must use 「XXX + が + ほしくない」 is when it is used in the if-clause or relative clause. Thus, it is correct to say:

Relative Clause:「靴{くつ} + が + 欲{ほ}しくない人は靴屋{くつや}へは行かない。」

"A person who does not want shoes would not go to a shoestore."

If-Clause:「靴 + が + 欲しくなければ、なんで靴屋に来たの？」

"If you do not want shoes, why did you come to a shoestore?"

Moving on...

The contrastive 「は」

This is essentially a different topic from what has been discussed above.

It is correct to say:

「靴 + は + 欲しくない。」

when you do not want shoes but want another thing. Thus, you can say:

「靴は欲しくないけど、ジーンズは欲しい。」

That is a pair of contrastive は's. "I don't want shoes, but I want some jeans."

I imagined that the reason is to make a contrast/comparison that は provides. Is that why?

No, as I stated above. We are talking about two different things. One is affirmative vs. negative. The other is contrastive.

kaddish - Women saying kadish

Why do some people hold a woman should not say kadish? She's not singing so it shouldn't be Kol Isha, and if she's behind a mechitza it shouldn't be a tzniut problem.

Answer

R' Brody discusses the issue on JPost's Ask the Rabbi. He cites many authorities, such as R.Y.D Soloveitchik and R.Y.Henkin, that permitted it and R.M. Feinstein who said it was common practice in Europe. However, he mentions some objections raised:

The permissive position was opposed by many decisors, who argued that (a) women could not participate in this part of the service (Minhat Yitzchak 4:30), (b) the classic mystical sources only spoke of men’s recitation (Mishpatei Uziel OC 3:13), (c) it was immodest in public settings (Aseh Lecha Rav 5:33), or (d) it would ultimately support antinomian trends found in the non- Orthodox movements (Yahel Yisrael 2:90).

It may be that in certain areas the Reform and Conservative movements cause an opposite reaction from Orthodox Jews.

shemos sacred names - Is reading the word "G-d" out loud from a secular text a violation of Shem Shamayim l'Vatalah?

For those who are careful not to say "G-d" in their casual conversation, would reading the name "G-d" aloud from a piece of non-religious text that one was asked to read aloud be a violation of this minhag? (or of this interpretation of Shem shamayim l'vatalah?)

Assume the content of the text is not otherwise special in any way (i.e., not idol worship nor a curse nor foreign praise of G-d that would be inadvisable for other reasons).

Also:

• 
  

  Would it be different if one were, say, declaiming "My G-d, she hangs upon the cheek of night" in a Shakespeare production, or perhaps singing "G-d bless America," than if one were reading a sample sentence including "G-d" in an explanation of English grammar?

  
  


• 
  

  What should one say instead?

  
  

Surprisingly, this situation is encountered a lot.

Answer

As not saying God or writing God are newly formed ideas that many consider to be from gentile sources, it should be considered a personal stringincy, and therefore the person who was taken on this additional stringincy should do what they feel is best. If they want to know what the majority of halakhists say regarding this manner, see the following:

We follow here the ruling of the Siftei Kohen, the great 17th-century commentator to the Shulchan Arukh: "The Name of God in Hebrew is properly considered a holy name. The Name of God written in any other language, however, is not a 'holy name' at all. You will understand this when you consider that it is permissible to erase a Name written in some other language, such as the word Gott in Yiddish or German" (to Yoreh De'ah 179, no. 11). For this reason, Rabbi Yosef Dov Soloveitchik used to say that "those who write the English word God in the form G-d do so out of 'total ignorance' (am-ha'aratzut gemurah)... since the English word God is not one of the formal Divine Names but merely a literary device that refers to the Holy One, Blessed be He"; R. Zvi Schachter, Nefesh Harav (Jerusalem: Reshit Yerushalayim, 1994), 161. True, there are authorities who dispute the Siftei Kohen (see R. Avraham Danzig, Chokhmat Adam 89:9) and who support the custom of writing the Divine Name as G-d (see R. Chaim Ozer Grodzinsky, 20th-century Lithuania, Resp. Achi`ezer 3:32). We, however, following Maimonides and the other scholars we have mentioned, regard that custom as an unnecessary stringency.

Source: https://ccarnet.org/responsa/rr21-no-5762-1/

Although the information is from Orthodox sources, the website is reform which apparently is problematic. Here are some other sources:

A. Opinion of the Mishnah Berurah. The Mishnah Berurah (85:10) rules that there are no limitations placed on the writing of God’s name in languages other than Hebrew. Indeed, this lenient view is strongly supported by the p’sak of the Shach (Yoreh Deah 179:11) and Achiezer (3:32). Furthermore, a paper that says “God” may be thrown away in the normal fashion. However, the Mishnah Berurah writes that the word “God” should not be uttered in the bathroom or other areas that are unclean and mentioning the word “God” may be a violation of saying God’s name in vain.

The Mishnah brerurah starts the trend of being more stringent on the name being spoken of in vain. However, it is mostly limited to bathrooms, and it "may" be saying God's name in vain.

B. Opinion of Rav Chaim Ozer Grozinski and Rav Akiva Eiger. Not only may the printed word “God” be written and thrown away normally, but the recital of the word “God” does not pose any halachic problem. After all, the status of the written word should be no different than the status of the spoken word.

However, if you really want to be stringent in the matter of not saying God's name, then maybe you should follow the talmudic dictum?

Shalom. The gemara (Shabbat 10b) rules that one may not greet his friend with the word “Shalom” in the bathhouse because “Shalom” is one of the names of God. Tosafot (Sota 10a) rules that for this reason one may not erase the word “Shalom”. Although God is also called a “Chanun V’rachum” all agree that these words may be erased because they are descriptions of God rather than the formal name of God. Rosh (Teshuvot Harash 3:15) disagrees with Tosafot and maintains that one may erase the name “Shalom” just as one may erase “Chanun V’rachum”. A. Writing Shalom. 1. The stringent approach. Rama (Yoreh Deah 276) cites those who are careful not to write the entire word “Shalom”, and instead merely omit the letter “mem” when writing “Shalom” in Hebrew.

Source:http://www.bknw.org/uploads/5/9/9/5/5995719/names_of_hashem.pdf

For sources from the Talmud i couldn't find them directly translated into English so here is a paraphrased from the Jewish Encyclopedia

Talmud (Shev. 35a) lay it down that it is forbidden to erase the name of God from a written document, and since any paper upon which that name appears might be discarded and thus "erased," it is forbidden to write the name explicitly. The Talmud gives an interesting historical note with regard to one aspect of this. Among the decrees of the Syrians during the persecutions of *Antiochus Epiphanes was one forbidding the mention of the name of God. When the *Hasmoneans gained the victory they not only naturally repealed the decree, but demonstratively ordained that the divine name be entered even in monetary bonds, the opening formula being "In such and such a year of Johanan, high priest to the Most High God." The rabbis, however, forbade this practice since "tomorrow a man will pay his debt and the bond (with the name of God) will be discarded on a dunghill" the day of the prohibition was actually made an annual festival (RH 18b). It is, however, specifically stated that this prohibition refers only to seven biblical names of God. They are ʾEl, ʾElohim (also with suffixes), "I am that I am" (Ex. 3:14), ʾAdonai, the Tetragrammaton, Shaddai, and Ẓeva'ot (R. Yose disagrees with this last, Shev. 35a–b). The passage states explicitly that all other names and descriptions of God by attributes may be written freely. Despite this, it became the accepted custom among Orthodox Jews to use variations of most of those names in speech, particularly ʾElokim for ʾElohim, and Ha-Shem ("the Name" and, for reasons of assonance, ʾAdoshem) for Adonai. The adoption of Ha-Shem is probably due to a misunderstanding of a passage in the liturgy of the Day of Atonement, the Avodah. It includes the formula of the confession of the high priest on that day. Since on that occasion he uttered the Ineffable Name, the text has "Oh, Ha-Shem, I have sinned," etc. The meaning is probably "O [here he mentioned the Ineffable Name] I have sinned," and from this developed the custom of using Ha-Shem for ʾAdonai, which is in itself a substitute for the Tetragrammaton (see also Allon, Mehkarim, 1 (1957), 194ff.; S. Lieberman, Tosefta ki-Feshutah (Mo ʾed), 4 (1962), 755). *Shabbetai b. Meir ha-Kohen (first half 17th century) states emphatically that the prohibition of erasure of the divine name applies only to the names in Hebrew but not the vernacular (Siftei Kohen to Sh. Ar., YD 179:8; cf. Pitḥei Teshuvah to YD 276:9), and this is repeated as late as the 19th century by R. Akiva Eger (novellae, ad loc.). Jehiel Michael Epstein, however, in his Arukh ha-Shulhan (ḤM 27:3) inveighs vehemently against the practice of writing the Divine Name even in vernacular in correspondence, calling it an "exceedingly grave offense." As a result the custom has become widespread among extremely particular Jews not to write the word God or any other name of God, even in the vernacular, in full.

Source: http://www.jewishencyclopedia.com/articles/11305-names-of-god

blessing - Why do you make a Bracha on seeing a monkey?

Why do you make the Bracha Mishaneh Habriyos on seeing a monkey?

Answer

The Mileches Shlomo on Kilayim (8:6) says the gemara in Sanhedrin says that the Dor HaMabul (generation of the flood) turned into monkeys and that is one of the reasons we make the bracha Mishaneh Habriyos translated- who changes the creations-on monkeys.

fourier transform - How do I convert a real baseband signal to a complex baseband signal?

I have radio telescope observations that have resulted in two real-valued signals (corresponding to the right- and left-handed circular polarizations).

The signals are sampled at rate $2B$, and provide a bandwidth of $B$.

I wish to get the full Stokes parameters from these signals, which requires me to convert these real signals into complex signals sampled at $B$ (half that of the real signals).

However, I don't know the procedure to do this. I just know that it is possible.

In general, how do I take a real-valued baseband signal and convert it to a complex-valued signal?

Answer

To convert a real signal sampled at rate $2B$ to its complex baseband representation (sampled at rate $B$), you want to map the frequency content in the range $[0, B)$ in the real signal to the range $[-\frac{B}{2}, \frac{B}{2})$ in the resulting complex signal. This can be done in a couple different ways:

1. 
   

   Design a linear filter to approximate a Hilbert transform. Run your real signal $r[n]$ through the filter to yield the transformed signal $\tilde{r}[n]$. Use this to form the analytic signal: $$r_a[n] = r[n] +j\tilde{r}[n]$$ $r_a[n]$ will contain only the positive frequency components of the original real signal $r[n]$; all of the negative frequencies will be zero (assuming a perfect Hilbert transformer; in practice, the effect will not be perfect). Thus, you have isolated the desired frequency band $[0, B)$.

   
   

   Multiply $r_a[n]$ by $e^{-j\frac{\pi}{2}n}$ to effect a frequency shift of $-\frac{B}{2}$, shifting the desired frequency content to the range $[-\frac{B}{2}, \frac{B}{2})$. Then, decimate the signal by 2 by discarding every other sample. The result is a complex baseband signal sampled at rate $B$.

   
   


2. 
   

   My preferred approach is a more straightforward implementation of the shift that you're looking for:

   
   
   
   
   • Multiply $r[n]$ by $e^{-j\frac{\pi}{2}n}$ to effect a frequency shift of $-\frac{B}{2}$, shifting the desired frequency content to the range $[-\frac{B}{2}, \frac{B}{2})$. The result is a complex signal that is centered in the appropriate place (the center of the band is at zero frequency).
   
   
   • Apply a lowpass filter to pass only the content in the range $[-\frac{B}{2}, \frac{B}{2})$ (to the extent required while meeting your application's antialiasing requirements).
   
   
   
   • Decimate the signal by 2 by discarding every other sample. The result is a complex signal sampled at rate $B$.
   
   
   
   

In practice, I always use some variant of strategy #2. You can make it even more computationally efficient by implementing the decimation as part of the lowpass filtering process, for instance with a polyphase filter.

everyday chemistry - Why does shaking a match put the fire out?

Move a match slowly and nothing happens but if you shake it violently the fire will extinguish. Oxygen makes fire grow so why does waving a flame through the oxygen rich air put the fire out? Does this primarily have to do with a decrease in temperature to the burning materials or is it something else?

Also what about forest fires, do high winds spread or kill the fire?

Answer

Combustion of small materials, such as a match or birthday candle, actually involve the release of volatile vapours, which themselves burn. It is not the solid material that burns. There needs to be a minimum amount of volatile material present in this combustion zone (just above the burning match) for the ignition to occur. As the combustion process continues, heat is given off, and more volatile materials are released, which in turn continues the combustion cycle. Now, if you shake a match or blow on a candle, you rapidly disperse these volatile fuels from the combustion zone, and there is no longer sufficient fuel to ignite. It is effectively removing the fuel component of the fire triangle, for just a brief moment.

Large fires can reignite because there is sufficient heat left in the fuel to further release volatile fuels, which can either self-ignite or ignite through the presence of embers.

Blowing gently on a small wood fire increase the oxygen content into the combustion zone, without dispersing the fuel. Similarly, if you experiment with a small enough wood fire, you will see that blowing on different parts of the fire will have a different outcome: blowing on the base of the fuels will increase oxygen content, and not affect volatile fuels. Blowing on the top of the fire (where the flame starts to burn) will probably put the fire out.

Will this put out a small paper fire? That will depend on the heat retained by the burning fuel. A single piece of A4 paper if shaken hard enough will extinguish. A ream of A4 paper that has burned half way down the page will be put out this way, but could easily reignite if the paper pages are pulled apart to allow oxygen into the released volatile fuels.

Generally, forest fires are accelerated by strong winds. Winds affect forest fires in a number of ways, and increase the rate of spread significantly. This is a topic for a whole other question.

photochemistry - Is a triplet state or singlet state more stable?

Is a triplet state or singlet state more stable? How can an atom have a long lifetime in a triplet state even though two electrons have the same spin?

organic chemistry - Which is the more stable enol form?

If I understand correctly, when we go from a keto to an enol form, we simply abstract an alpha proton and thereby create a double bond to a carbon-bearing the hydroxyl functional group.

When evaluating the stabilities of the two enol forms, it appears that the enol derivative of 2,4-pentadione is more stable because of intramolecular hydrogen bonding. Both have long-range conjugation, so that cannot be a factor. The only difference really is the hydrogen bonding ... and of course ring strain (a 5-membered ring with two double bonds can't be very stable).

Answer

Keto-enol equilibria reflect a delicate thermodynamic balance between the two forms.

The bonding differences between the keto and enol structures shown above are:

keto: C=O double bond, C-C single bond, C-H bond

enol: C=C double bond, C-O single bond, O-H bond

If we look up the bond energies for these bonds we find

keto: 745 + 347 + 413 = 1505 kJ/mol

enol: 614 + 358 + 467 = 1439 kJ/mol

This rough calculation tells us that, generally, the keto form will predominate. However, the energy difference between the two forms is only 66 kJ/mol, a relatively small number; so it is likely that small differences can cause a dramatic shift in the relative concentrations of the two species.

Some general guidelines for predicting shifts in keto-enol equilibria

Aromaticity and conjugation - The keto-enol equilibrium for phenol (I) lies entirely on the enol side due to thermodynamic stabilization provided by aromaticity. Compound III would be expected to have a higher enol content than compound II due to the extended conjugation present in the enol of III

Substitution - Replacing hydrogen with alkyl groups on a double bond stabilizes the double bond. Therefore, we would expect compound V to have a higher enol content than compound IV

Dipolar repulsion - The carbonyl dipoles in butane-2,3-dione (VI) can reduce their electrostatic repulsion by adopting the geometry pictured with the carbonyl groups oriented away from one another. Due to the constraints of the 5-membered ring, cyclopentane-1,2-dione (VII) cannot adopt a similar geometry. In this case, the dipolar repulsion is lessened by increasing the enol content in the equilibrium to a point where the enol predominates.

Hydrogen Bonding - Hydrogen bonding can stabilize the enol form. If the hydrogen bond is strong enough, and particularly if other factors also stabilize the enol form, the enol form can predominate. Your molecule, 2,4-pentanedione (IX), is a good example. There are two possible enol forms, VIII and X. X is by far the predominant enol as it has 1) extended conjugation and 2) substitution on the carbon-carbon double bond. In addition, X can form a very stable hydrogen bond involving a 6-membered structure between the two oxygen atoms.

Solvent Effects - Especially in cases where hydrogen bonding is involved in stabilizing the enol, the solvent can have a dramatic effect. In benzene, where intramolecular hydrogen bonding predominates, the IX:X ratio is approximately 5:95. In water, where the intramolecular hydrogen bond is replaced by hydrogen bonding to the solvent, the ratio is roughly reversed.

Answer to your question

Cyclopent-2-enone can form two different enols, XI and XIII. Neither enol has any features that would be expected to provide significant enol stabilization. There is no more conjugation than what is found in the ketone, there is no special hydrogen bonding, and no substitution of the carbon-carbon double bonds. Indeed, the proton nmr of cyclopentenone is just as expected, no evidence for a significant amount of enol. On the other hand, 2,4-pentanedione exists primarily as the enol form, at least in non-polar solvents, for the 3 reasons (conjugation, hydrogen bond, double bond substitution) discussed above.

As an aside, you mentioned that a 5-membered ring with two double bonds (a cyclopentadiene) might not be very stable; actually, they are quite stable and quite common, 2 double bonds in a 5-membered ring do not create a lot of strain.

grammar - Why is は appropriate for てはいけない?

Why does てはいけない use は? I know it's a construction, but where did it come from? て form verbs are not nouns, it doesn't make sense to me that は could be used with them.

noise - Optimal window function for amplitude estimation?

Assume you want to estimate the amplitude of a known frequency sinusoid in additive Gaussian (white or pink) noise. Also assume mainlobe width/sidelobe decay doesn't matter. Windows should be compared such that the time latency of the resulting amplitude estimate is equal. (I believe for all symmetric windows of a given period, their time latency will be equivalent -- specifically, equal to half of their period.) What is the optimal window in this case?

It seems this problem would simply reduce to what window has the smallest magnitude integral in the frequency domain (affects amount of noise smeared around) relative to its peak magnitude in the frequency domain (what will be used to estimate amplitude). However, given the presumably random phases of each noise frequency component, I am not sure it is as simple as just considering the magnitude of the window's fourier transform because there may be some 'destructive interference' among noise components of different phase.

The main two contenders I am aware of are: the rectangular window, which is said to have the minimum equivalent bandwidth noise for any window of its length (source); and the Gaussian window, which is said to minimize the 'time-frequency bandwidth product' (source). However, time-bandwidth product refers to the 'frequency duration' (sidelobe behavior) of a signal, which was stated to not matter in this case, so I don't think that optimality is useful here.

Therefore, I believe the goal would be to minimize the equivalent noise bandwidth of the window. If that is the case, how would one prove that the rectangular window does minimize ENBW, and that there is not some other obscure window in the function space that does 'better'? Here is an illustration of the 'optimality' in the ENBW-sense of the rectangular window (source):

Additionally, here are the corresponding time/frequency plots of rectangular and Gaussian windows, making it appear that the Gaussian window is much more spread out in frequency than the rectangular function and therefore does not have as high of a 'peak relative to frequency domain integral'. (Compare +/-5Hz, maybe +/-2.5Hz if window lengthened for Gaussian vs +/-1Hz for rectangular of same time duration.) (source_rect, source_Gauss):

---

Edit: I want to mention the possibility of a non-symmetric window function, since the goal is to optimize the amplitude estimate relative to a fixed measurement latency. My intuition is that it may be possible to use a 'ramp' window to more heavily weight the most recent samples, and allow the overall window size to be greater.

For instance, consider the following window of length $T$ with integral 1:

$$w(t) = \left \{\begin{array}{ll} \frac{2t}{T^2} & t\in (0,T] \\ 0 & t\not\in (0,T]\\ \end{array} \right.$$

E.g., for $T = 2$:

If we define the window latency as a linear weighting based on their time offset relative to the last sample taken, then for a window of length $T$:

$$weight_T(t) \triangleq T-t$$

As we would expect, a rectangular window $\frac{1}{T}rect\frac{t}{T}$ with integral 1 has latency:

$$\int_{0}^{T} \frac{1}{T}\cdot weight_T(t) dt = \frac{T}{2}$$

In the case of the ramp window, the latency is:

$$\int_{0}^{T} \frac{2t}{T^2}\cdot weight_T(t) dt = \frac{T}{3}$$

This implies that the ramp window can be 50% longer than the rectangular window and still have the same time latency.

Using the approach given in the answer below, which requires that the sum of the (discrete time) window coefficients = 1, we could for instance compare the total signal variance between a rectangular window of length 10 and a ramp window of length 15. Each rect window coefficient would = $\frac{1}{10}$, such that the total variance (assuming unit variance AWGN) would be:

$$\sigma^2_{rect} = (10)(\frac{1}{10})^2 = .1$$

The ramp window would have coefficients:

$$a_{ramp} = \{1,2,...,15\}\cdot (\frac{1}{120})$$

You can verify that the sum of these coefficients = 1. This would result in variance:

$$\sigma^2_{ramp} = \{1^2 + 2^2 + ... + 15^2\}\cdot (\frac{1}{120})^2 \approx .08611$$

Therefore, it would seem that the ramp window would perform better than a rect window in AWGN for a given amplitude measurement latency. The only practical caveat would be that the ramp window may suffer from larger discontinuities (i.e. if first sample does not have similar value to last sample).

Here's a comparison of the magnitude response for a ramp window of length 1.5 vs a rect window of length 1, and their difference:

It does seem that the rect window has a generally smaller magnitude response than the ramp function. However, maybe the complex components of the ramp Fourier transform result in destructive interference among the noise components?

Answer

Consider a window just three samples long, $[a, b, c]$. To enforce symmetry, we rewrite the window as $[a, b, a]$. As an estimate $A(\omega)$ of the amplitude of angular frequency $\omega$, we'd calculate:

$$A(\omega) = \left|\sum_{i=0}^2 e^{-i k\omega}[a, b, a]x[k]\right| = \Big|ax[0] + e^{-i\omega}bx[1] + e^{-i2\omega}ax[2]\Big|$$

I'm using zero-based indexing here. When noise is not present, the above will only work perfectly if $a+b+a = 1$, so we can rewrite the window as $[a, 1-2a, a]$. For simplicity, let's estimate the amplitude of frequency $\omega = 0$ by:

$$A(0) = \left|\sum_{i=0}^2 [a, 1-2a, a]x[k]\right| = \Big|ax[0] + (1-2a)x[1] + ax[2]\Big|$$

If $x[k]$ have additive white noise with zero mean and a variance of $1$ (I mean that the noise comes from such a distribution), then the windowed samples have errors with variances $[a^2, (1-2a)^2, a^2]$. Because the noise is white, the distributions of the errors are independent and their sum will have variance that is the sum of their variances, $a^2+(1-2a)^2+a^2$. Plotting that:

Figure 1. Variance $a^2+(1-2a)^2+a^2$ of the error as function of the window parameter $a.$

The potentially complex number $ax[0] + (1-2a)x[1] + ax[2]$ describes both phase and amplitude, the latter of which is extracted by taking the absolute value. The error due to noise in that number is zero-mean, so we may wish to minimize the variance of that error. The minimum variance $1/3$ is at $a = 1/3$, which means that the optimal window is $[1/3, 1/3, 1/3]$. That is not a proof but a pretty good indication that the rectangular window minimizes the error in phase and amplitude estimation in presence of additive zero-mean white noise.

Had we not imposed symmetry, the window would be $[a, 1-a-c, c],$ and the variance of the error to minimize would be $a^2 + (1 - a - c)^2 + c^2.$ Requiring the partial derivatives with respect to each of $a$ and $c$ to equal zero would give the same optimal window as before:

$$\cases{4a + 2c - 2 = 0\\ 2a + 4c - 2 = 0}\\ \begin{align} &\Rightarrow a = \frac{1}{3},\quad c = \frac{1}{3}\\ &\Rightarrow 1-a-c = \frac{1}{3}\end{align}$$

halacha - responsibility for passing on a virus (medical)

Would one be obligated to pay any of the five types of damages paid upon wounding someone, if they were to infect that someone with a viral/bacterial disease, whether through:

1. Peshia (negligence)?


2. Shemira Reuya (appropriate precautions)?


3. Ones (duress)?

words - はは or おかあさん what should be used?

What I've learnt is: when you talk about your mother you use はは、 when you talk about someone else's mother you use おかあさん。

But what happens when you talk to your mother? How should you address her?

In anime they usually say おかあさん, but isn't it too formal?

Answer

If you want to talk to your mother in Japanese, call her おかあさん. This is like calling your mother "mother". Small kids sometimes call their mother ママ ("mommy"), but since you're probably older than 10, you should stick to おかあさん. (And no, it's not too formal. Anime Japanese is not really known for being too formal...)

There are cutefied or colloquial variants on おかあさん, like おかあちゃん, かあちゃん, かあさん.

By the way, it's also possible to talk about your own mother using おかあさん, as in うちのお母さんが…

Just to be clear, 母 is not a form of address, but expresses the biological relationship "mother". Talking to your mother, you wouldn't address her with 母. You can use 母 in principle for talking about other mothers (太郎君の母を見ました), but this sound like "I saw Taro's biological mother".

In the olden days, 母上 was (and in Samurai circles still is) a formal way of addressing (and talking about) your own mother.

technology - Does texting count as speech?

For instance, say that I text someone "I promise I'll do X." Does that have the same status as if I said out loud the same thing?

The same question can be asked with respect to Shevuos (as in oaths, not the holiday). If someone says "Swear to me that X happened," for instance, and you text him "Amen" (this exchange is cited in the third perek of Maseches Shevuos as being a form of an oath), do I have to bring an Oleh v'Yoreid if it's false and meets the various criteria brought down in Shevuos?

One other possible nafka minah: one could ask regarding Hein Tzedek (BM 49a), the obligation to keep one's word, even if not phrased in terms of a neder.

Just to clear things up before anyone brings it up.

This question is not applicable to Lashon Hara, which just requires spreading the rumor, regardless of how it's done. At the moment I don't have the source for this claim, though I have heard it many times from my Rebbeim; if someone could provide a source, that would be great. I could make a chiluk between this and the above cases, though, where the issue is the speech, not the bad name.

This question is also dissimilar to halachos such as Virtual Kaddish or Answering Amein on the phone or even Havdalah on the phone in which the question is on the listener. My question is whether the texter has fulfilled any form of speech.

Also related, as this is about texting or emailing, this is not similar to התראה by phone which involves actual speech.

I'm also aware of this question about chat contracts, which is more of an issue of the legal status of the contract, not about whether it's a type of speech.

Finally, there is also this question about Hamapil which is highly related and I know someone's going to call duplicate. So I'd like to emphasize that my question is much, much broader. Maybe, for instance, that, which is only a d'Rabbanan, might be permissible, whereas by Nedarim, which is d'Oraisa, may require us to be stringent and force him to abide by his vow.

Is texting, essentially a written form of spoken conversation that hardly ever follows proper grammar (or spelling) considered speaking across Halacha, or in limited circumstance, or nowhere at all?

As a springboard, this discussion about whether digital text is considered written text l'halacha may be relevant.

avot patriarch fathers - Why did Avraham wait to have a bris?

Chazal tells us (Midrash Rabbah Bereishis 64:4 and 95:3; Yoma 28b, based on. Gen. 26:5; Kiddushin 82a) that the Patriarchs observed the mitzvahs before they were given. But Avraham did not circumcize himself or his male household members until specifically commanded. Why did he wait?

number - Chamishim Umeya?

Who knows one hundred fifty?

Please cite/link your sources, if possible. At some point at least twenty-four hours from now, I will:

• 
  

  Upvote all interesting answers.

  
  


• 
  

  Accept the best answer.

  
  


• 
  

  Go on to the next number.

  
  

Answer

150 perakim in Tehillim

concentration - Is 1 ppb equal to 1 μg/kg?

In an article I recently submitted, a reviewer asked that I provide a concentration in μg/kg instead of ppb (parts per billion), and mentions that the later is not correct. I am not a chemist, and I thought that 1 μg/kg = 1 ppb.

Is 1 ppb equal to 1 μg/kg ? What is a reason to consider ppb as incorrect ?

Answer

You are correct suggesting that 1 μg/kg implies 1 ppb, however the reverse is not true. For instance, 1 ppb can also be 1 nmol/mol, and the reader will never have a chance to deduce which one is it unless you explicitly define the usage of the "parts per something" in the text. This clutters the manuscript with redundant notes and causes overall confusion.

IUPAC also lists all similar symbols (ppm, ppt, ppb etc.) as deprecated; from IUPAC's “Green Book” [1, p. 98]:

Although ppm, ppb, ppt and alike are widely used in various applications of analytical and environmental chemistry, it is suggested to abandon completely their use because of the ambiguities involved. These units are unnecessary and can be easily replaced by SI-compatible quantities such as pmol/mol (picomole per mole), which are unambiguous. The last column contains suggested replacements (similar replacements can be formulated as mg/g, μg/g, pg/g etc.).

$$\begin{array}{lllll} \hline \text{Name} & \text{Symbol} & \text{Value} & \text{Examples} & \text{Replacement} \\ \hline \ldots & & & & \\ \text{part per billion} & \text{ppb} & 10^{-9} & \text{The air quality standard for ozone is a} & \pu{nmol/mol} \\ & & & \text{volume fraction of}~\varphi = 120~\text{ppb} & \\ \ldots & & & & \\ \hline \end{array}$$

References

1. IUPAC “Green Book” Quantities, Units, and Symbols in Physical Chemistry, 3rd ed.; Cohen, R. E., Mills, I., Eds.; IUPAC Recommendations; RSC Pub: Cambridge, UK, 2007. (PDF)

grammar - How do I express "this made me laugh"?

This is the kind of simple question I'm often too embarrassed to ask, because I should probably know this by now. But here goes...

I was ordering something at a cafe, and I noticed some slightly awkward English on the menu something that made me laugh. It wasn't super funny or anything, it just caught me a little off guard. The cashier noticed me laugh and looked puzzled. So I pointed at the text and said:

これを笑{わら}わせた。

This happens all the time where I speak off the cuff, and then after the moment has passed, I realize I almost certainly said it wrong. Unfortunately, unlike other cultures, in Japan people rarely call you out. The cashier didn't look at me like "what the hell did you just say?", she just smiled. Leaving me unsure if I basically spoke complete nonsense and she was being nice, or that maybe I was close enough and she couldn't be bothered to offer any adjustments.

Passive and causative verb forms and the right particles to go with them have always been a source of trouble for me.

I think I should have said:

僕{ぼく}を笑{わら}わせた

I am the thing being made to laugh, so it's acting on me, so I take the particle を. However, I want to make the thing I'm pointing at the focus of my sentence, not me. So, maybe I should have said:

これで笑{わら}わせた

In a sense, I was made to laugh by this thing I'm pointing at. It's a shortened form of:

(僕{ぼく}に)これで笑{わら}わせた。

I often turn out to be totally wrong, so, am I wrong again? What would be the best way for me to express, while pointing at the text on the menu, "this made me laugh"?

---

Also see this question and answer about the causative and passive forms of 笑 for related information. A joke is an interesting edge case, because, as explained in answers below, a thing has no animacy, so it doesn't "make" people laugh, but a joke is the result of actions between people, so in a sense, the joke us a proxy that can be said to "make" people laugh.

Answer

笑わせた(笑わせる) is the causative form of 笑う(笑った), so

これを笑わせた。

means "(I) made it laugh."

僕を笑わせた。

means "(Something) made me laugh", so logically speaking this statement would be correct in your situation.

これで笑わせた。

would mean "(I) made (someone) laugh with this." (I think the で works as an instrumental/具格 case here)

(僕に)これで笑わせた。

doesn't make much sense. Probably you meant to type:

(僕を)これで笑わせた。

? But this is more like "(Someone) made me laugh with this."
"This made me laugh" literally translates to:

これが僕を笑わせた。

However, normally you don't say it this way in Japanese, because the Japanese language tends to avoid using 無生物主語(inanimate subject) (as user4092's post states), especially in verbal/casual communication. So I think you should say it more like this:

(僕は)これで笑ったんですよ。/笑ってしまったんですよ。(I) laughed because of this.
(僕は)これにorこれを笑ったんですよ。/笑ってしまったんですよ。(I) laughed at this.
これが(ちょっと)おかしかったので、(僕は)笑ってしまいました。/笑ってしまったんですよ。 etc.

... using 僕 as the subject. (The 僕は is normally left out.)

---

To sound even more natural, you could just say like 「(いや、)(ちょっと)これがおかしかったんで・・・」「(あぁ、いやぁ、)この英語が(ちょっと)おかしかったんで・・・」etc., as @Haruo says.

halacha - Humming during shmoneh esre

On shabbat for shacharit and mussaf, I am usually still davening shmoneh esre by the time the chazzan gets to kedusha. In this situation, can I hum to the tune of kedusha?

This essentially boils down to: At what point does use of your voice for something other than shmoneh esre in the middle of shmoneh esre become a hefsek?

Is saying "oyoyoy" in places where you're not allowed to speak (e.g. Shemoneh Esreh) a hefsek (interruption)? Does it make a difference that it doesn't have any consonant sounds (in which case "oyoyoy" would be permitted and "aididididi" forbidden)?

Answer

Shu"t Shevet haLevi (V:16) divides this into 3 parts:

1. If the singing is done together with the words of tefilla, this is considered part of tefilla and a kiyum of lezamer leshimcha elyon.


2. Other times, music is considered separate from the tefilla. For example, the nigun is separated from the words and is "too long" or it's not for the davener's tefilla enhancement, but to get the congregation "into it".


3. In all cases, a nigun without dibur is not considered a hefsek to have to repeat shemona esre.

To sum up: While the chazzan may sing during recitation of the kedusha (and may be a good thing as well), one who isn't davening should not hum. B'd'eved, though it's not a hefsek.

sources mekorot - Connecting Shas and Halacha

What resources are available to trace the connections from the Gemara to the Halachic codifications and the reverse? For example, how can someone learning Daf Yomi find the related Halachic rulings in the Shulchan Aruch that were based on that particular page of Talmud, and how would someone studying Mishneh Torah find the source in the Gemara?

Answer

The Be'er HaGolah (printed next to the Shulchan Aruch) gives all the sources as listed in Tur/BY. The Biur HaGra gives more thorough sources than the Be'er HaGolah, so you should probably use that one.

There is also, of course, the Ein Mishpat, if you want to go the other way around (Gemara to poskim). It's found at the top of the outer margin of each daf, and it's referenced by k'tav ashurit letters throughout the text of the Gemara.

purim torah in jest - "Peyshar Davar"?

Who knows what the meaning of "a thing" is?

פשר דבר - מי יודע?‏

Kohelet 8:1 expresses uncertainty about the meaning of "a thing":

... וּמִ֥י יוֹדֵ֖עַ פֵּ֣שֶׁר דָּבָ֑ר ...

... and who knows the meaning of "a thing"? ...

Is there a traditional Jewish answer to this apparently age-old question?

If so, it could have been very useful in a recent US Supreme Court case, Yates v. United States, in which some of the brightest legal minds in the United States argued about whether a fish is a thing or not and concluded, by a narrow vote, that a fish is not a thing. Justice Elana "Einekle?" Kagan, apparently lacking any Torah sources, was reduced to trying to argue against the prevailing opinion by citing One Fish, Two Fish, Red Fish, Blue Fish, by Dr. Seuss.

Please address both the general question and the more specific question raised by this case and by the alternative reading of Kohelet uncovered by Yates:

... and who knows "a fisher-thing"? ...

---

Answer

The verse in Bamidbar 20:19 is fairly explicit:

רק אין-דבר

There just isn't a thing

Apparently, a thing isn't.

A fish, also, is clearly not a thing, as follows: Nechemia 13:16 says

והצורים ישבו בה, מביאים דג וכל-מכר; ומוכרים בשבת

And the Tzurites ... brought fish... and sold them on Shabbos

and we all know that אין אדם מקנה דבר שלא בא לעולם, you cannot sell something which doesn't exist eternally (Kiddushin 62b). Now, these fish, being sold on Shabbos, were clearly going to be consumed shortly afterwards for the Shabbos meal. So, in order to sell them, they must not be things.

In terms of fisher things, they are actually quite nice, as the Targum to Bereishis 40:17 says:

וַחֲזָא רַב נַחְתּוֹמֵי, אֲרֵי יָאוּת פַּשַּׁר

And the Head Baker saw that Fishers are lovely.

words - What is the function of "Eloheinu" in blessings?

Many blessings open with the familiar formula:

ברוך אתה יהוה אלהינו מלך העולם

In additions, many blessings close with the familiar shorter formula:

ברוך אתה יהוה

Now, we know (Berakhot 40b, Rambam Berakhot 1:5, ShA OC 214) that a proper blessing needs to contain mention of both God's name and His kingship (Shem uMalkhut). Clearly "יהוה" is a part of the former of those requirements and "מלך העולם" is a part of the latter. Where does "אלהינו" fit in?

On the one hand, אלהינו is a name of God which cannot be erased (Rambam Yesodei 7:2, ShA YD 276:9) so it seems to be part of the "Shem" part of the formulation. Mishna Berura (214 sk 4) rules that אלהינו alone can function as the Shem in a blessing. Indeed the combo "יהוה אלהינו" appears quite frequently in Tanakh (with conjunctive Trop on the first word), and, even when unwarranted, people automatically run them together.

On the other hand, in the shorter closing formulation of longer blessings the chosen name of God to use is not "יהוה אלהינו" but just "יהוה". I can accept that Malkhut need not be mentioned again at the conclusion, but why should only part of the Shem be left out? It's worth noting that the name אלהינו has associations with Divine Judgement which in a certain sense fits more with Malkhut than Shem.

I note that in many prayer books there are Trop marks on the blessing preceding the Haftarah, opening with בר֨וך את֤ה יהוה֙ אלהינו֙ מ֣לך העול֔ם which, by putting the primary division on יהוה, indicates אלהינו is part of the latter phrase. However, these notes are of unknown origin and clearly do not conform to the regular rules of Trop (you can't have two Pashtas in a row unless they follow a Revi'i; I suspect the notes were just lifted from Chronicles 1:29:10 without much thought to context). Hence, I don't think this should be taken as conclusive evidence.

I note as well that in my experience, those who say "Barukh Hu Uvarukh Shemo" when hearing God's name in a blessing (cf. OC 124:5) do so after hearing the word יהוה but before the word אלהינו (eg. during the Chazzan's recitation of the morning blessings), indicating a separation in the blessing. As before though, this could be a carryover from, for example, the repetition of the Shemoneh Esrei where that phrase is regularly used in the context of the shorter closing formulae of blessings.

So which side is it? Is "אלהינו" in a standard blessing part of the Shem or part of the Malkhut? If part of the Shem, then why leave it off in the closing formula and pause between the two halves of the Shem? Proofs from earlier sources (≥Rishonim) are especially sought.

nomenclature - Hyphenation of chemical names

When a word has to be split broken into multiple lines, it is almost always hyphenated. Chemical names can be considered words, or at least they consist of words. So the hyphenation should apply to them as well. However, hyphens often are integral parts of systematic chemical names. Therefore confusion might arise, whether such a hyphen emerged from hyphenation or if it is "mandatory". Are there any official rules for the (possible) hyphenation of the chemical names? I could not find any, yet. I am sure some journals could have it mentioned in their style manuals, but I am primarily interested whether this topic is mentioned by IUPAC.

In fact, I am undecided whether to represent inserted optional breaks in long chemical names (that have to fit into some fixed-width infobox) HTML(5) representation as ­ or , which however means hyphenation, and non-hyphenation, respectively.

Answer

IUPAC project 2014-003-2-800 addresses this issue. However there seems to be no officially released recommendation to date.

terminology - When can the impulse response become zero?

The article Efficient Use Of Sparse Adaptive Filters (Proc. Asilomar Conference, Khong et al., 2006) introduces adaptive filters for the estimation of channels or systems having a sparse impulse response. Assuming that the channel is modeled by an FIR model, then the output of the channel will be given by $$y[n] = \sum_{i=0}^{p-1} h[i] x[n-i] \tag{1}$$ where $x$ is the input to the model and $h$ is the MA coefficients. As an example, consider an MA(3) model of order p=3 having coefficients h = [1,0.2,0.5,0.6]

I can expand the equation to write as $y[n] = x[n] + 0.2*x[n-1] + 0.5*x[n-2] + 0.6*x[n-3]$

My problems are:

1. From a time series or statistics point of view, FIR filter = Moving Average and IIR = Autoregressive model. I cannot understand how to relate the delays, 1,2,3 denoted by the order to the lags terminology often used in statistics. The impulse are known as the coefficients of the model and how to relate the impulse to the coefficients?


2. Why or rather what is the intuitive meaning of the coefficients becoming zero?


3. When does that happen/some real life examples of applications?

Answer

The notion of sparsity entails that an object, living for instance in an $n$-dimensional space, can be described (in the suitable basis/frame) by a number $k$ of meaningful components (each above a threshold, or whose combination is close enough to the signal) "much smaller" than $n$.

When talking about filter identification (adaptive or not), the filter is, at the beginning, unknown. To avoid looking inside an infinity of possibilities, one first restricts the space of solutions to the subspace of length-$n$ or order-$n$ filters. Either for true physical reasons, out of wishful thinking or heuristic motivations, or because the optimisation problem is not directly tractable (non-smooth, non-convex), one may call for Ockham's razor, or the law of parsimony, one may want to restrict the solution (not the real object) to be $k$-sparse.

Your example could be sparse per se, if initially the space of solutions could have up to 100 taps. Additionally, it could perhaps be approximated (in practice) by a sparser filter: $$y[n] = x[n] + 0.6*x[n-3]$$ discarding the two smallest coefficients.

With this introduction, let us go back to your questions:

1. I would disagree with "FIR filter = Moving Average and IIR = Autoregressive model": an IIR can be AR/MA, some FIR can be rewritten in an AR fashion. The rest of the question is unclear to me: if the model is linear, the impulse response would be some sparse approximation of the actual coefficients.


2. The actual coefficients are not becoming zero. But, either they form a filter short enough to be qualified as sparse, or their estimate has very few non-zero taps


3. It may happen in some echo cancellation problems: either in a room or on delay lines, one expect that the source bounces after some travelling back and forth. If at each bouncing the reflection is scarce, and there is some attenuation, the "global" echo filter could look like (two bounces) $$y[n] = x[n] - 0.25*x[n-99]+ 0.5*x[n-100]+ 0.25*x[n-101] + 0.125*x[n-199]+ 0.25*x[n-200]+ 0.125*x[n-201]$$ hence a sparse filter, even with order 201. Outside speech processing, we used such priors in seismic processing of remove multiples, approximate models of bouncing waves, assuming that the filters were sparse at boundaries between rock layers, see A primal-dual proximal algorithm for sparse template-based adaptive filtering: Application to seismic multiple removal, 2014, IEEE Transactions on Signal Processing:

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured “noises”. As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data.

Note that parsimony, usually resorting to an $\ell_0$ count measure, is not easy to optimize, as non-differentiable, non-convex, etc.

solutions - Why is the maximal percent concentration of acids similar to their molar mass

Why is the usual percent concentration of a concentrated acid's solution similar to its molar mass?

For example:

                FW (amu)     mass %
sulfuric        98.08        98%
nitric          63.00        68%
hydrochloric    36.46        36%

Is there some reason for this similarity or is it coincidence?

Answer

Because of its solubility. More concentrated solutions of, for example, nitric acid or hydrochloric acid, will result in fuming solutions where acid concentration evaporate out until the solution reaches an equilibrium. Do not get confused. You can actually dissolve more than 370g of hydrochloirc acid in 630 mL of water. In effect:

Solubility in water (Wikipedia)

823 g/L (0 °C)

720 g/L (20 °C)

561 g/L (60 °C)

But if we talk about a commercial solution, which should stay at the same concentration in time, you need to find a compromise between most quantity of acid possible in solution and less lose of acid due to vaporization.

Remember that pure hydrogen chloride is a gas at room temperature. If you continue increasing its concentration, you end up with man equilibrium shifted towards gas phase.

Also, as you can see, if you increase the temperature, solubility decreases, so if you heat a 50% aqueous solution of hydrochloric acid, you would end up not knowing what quantity of the reactant are you actually using.

Nitric acid is less volatile, and sulphuric acid is much less volatile, so you can have the latter almost in a pure form (98% is not an aqueous solution anymore! is just sulphuric acid with some water and other trace compounds)

nuances - How is 「ように」 different to just 「よう」?

When writing or reading a sentence in Japanese, does the word 「よう」 have a nuance any different to using 「ように」?

For example, sentences using 「ように」:

好きなように踊ってよろしい。

落第しないように一生懸命勉強しなさい。

君の将来が幸せでありますように。

ちょっと怒ったようにきこえた。

For example, sentences using 「よう」:

まるでボスのような話し方をする。

君は自分のためになるような書物を読べきだ。

ここには、誰もいないだよ。

映画を見たようです。

学生のようだ。

physical chemistry - Why are sigma bonds stronger than pi bonds?

Why are sigma bonds stronger than pi bonds?

Answer

The reason behind this is the orientation of the overlapped orbitals. Sigma bonds result from head-on(co-axial) overlapping while pi bonds are outcome of lateral(para-axial) overlapping. Here is a pictorial representation of ethene(sp² hybridized C atoms) :

The greater the extent of overlapping, the higher the probability of finding the valence electrons in between the nuclei and hence the bond will be stronger & shorter.

In MOT, this can be explained using Overlap Integral. This is how Atkins depicts it :

In simple terms, after forming a sigma-bond (a pre-requisite for pi-bonds), the two atoms get locked along the inter-nuclear axis. As a result, the orbitals available for pi-bonding can only partially overlap, thus forming a weaker bond.

homework - Determining if reaction is endothermic or exothermic using equilbrium constant

For the following reaction: $$\ce{W_{(s)} + 4 Br_{(g)} <=> WBr4_{(g)}}$$

At 900 K, $K_\mathrm{p}=100$ and at 2800 K, $K_\mathrm{p}=5$.

At higher temperatures, the equilibrium has shifted towards the reactants since $K_\mathrm{p}$ is significantly smaller. However, how do we determine if a reaction is endothermic or exothermic from this information? Here are my thoughts, If the reaction was endothermic, an increase in temperature would push the equilibrium to products to counteract the increase in heat. However, the equilibrium has been pushed to the reactants thus signifying the reaction is exothermic. But this assertion is on the assumption that the forward reaction is exothermic. Any thoughts?

Answer

Think about it this way. In an exothermic reaction that is at equilibrium the forward reaction has a lower activation energy. So, if you increase T the forward reaction rate increases but the reverse rate increases even more. That's because the rates of reactions with higher activation energy are more sensitive to temperature. With the reverse rate higher more reactants will be made until the concentration reactants reaches a point where the rate of the forward reaction equals the reverse rate.

In an endothermic reaction increasing T increases the forward rate more than the reverse, producing more product until the increased product concentration causes the reverse rate to equal the forward rate.

The equilibrium constant can be thought of as a ratio of products to reactants needed to equalize the rates of two reactions with different activation energies.

orthography - Distinguishing certain characters in handwriting and print (Similar-looking Kana and Kanji)

Japanese has some sets of characters which look very similar or even identical. Obviously, context is usually more than enough to distinguish which character is intended, but I'm wondering if there are subtle differences which can be used to disambiguate. It's easy enough to compare characters in computer fonts, so my question is really more about handwriting.

• 
  

  ー (katakana), 一 (kanji) and — (em dash)

  
  
  

  The first two can be distinguished from the last one in Minchō-type fonts, and usually it is possible to distinguish between all three. In vertical writing the katakana bō and the em dash are oriented vertically so is easily distinguished from the kanji ichi.

  
  

  What about in handwriting or Gothic-type fonts? I suspect they are indistinguishable then, but counterexamples are welcome.

  
  


• 
  

  ロ (katakana) and 口 (kanji)

  
  

  In print, katakana ro is usually printed a little bit smaller than kanji kuchi. In some of the fonts I have the final stroke of katakana ro protrudes to the right, while the penultimate stroke of kanji kuchi protrudes downwards.

  
  


• 
  

  カ (katakana) and 力 (kanji)

  
  

  Like the above, katakana ka is usually printed a little bit smaller than kanji chikara; but I've also noticed that the little hook is subtly different for katakana ka, and that in some fonts katakana ka has a bit of a rightward slant or curvature.

  
  
  


• 
  

  ニ (katakana) and 二 (kanji)

  
  


• エ (katakana) and 工 (kanji)


• タ (katakana) and 夕 (kanji)


• 
  

  ト (katakana) and 卜 (kanji)

  
  

  Other than size, it seems like the only way to distinguish these pairs in Minchō-type fonts is to rely on the tendency for katakana to have more brush-like strokes than the kanji.

  
  



• 
  

  ハ (katakana) and 八 (kanji)

  
  

  These are usually easy to distinguish in print, even in brush-type fonts, since the last stroke of katakana ha is of a different type from the last stroke of kanji hachi. What about in handwriting?

  
  


• 
  

  え (hiragana) and 之 (kanji)

  
  

  These are easily distinguished in print and good handwriting, but I have trouble making them distinct in my handwriting.

  
  


• 
  

  へ (hiragana) and ヘ (katakana)

  
  
  

  Is there any difference between these two? They are identical in Hiragino Mincho, for instance...

  
  

avodah zarah - Does the Jewish tradition command Jews to love Christians?

Does the Jewish tradition command Jews to love Christians, who believe in a triune (trinity) God and believe that Jesus is God or a part of the triune God? If so does this extend to fringe minority Christian groups like Mormons, Unitarians, etc. who don’t believe Jesus to be God?

parshanut torah comment - Why didn't Yaakov and Yosef spend much time together?

It seems that Yaakov and Yosef did not spend much time together in Egypt. After the emotional reunion is there any other mention of them together? Why not?

Answer

פסיקתא רבתי‎ 3:45 has it that it was engineered by Yosef as such, so Yaakov would never say "by the way Yosef, how exactly did you um, get lost when you went looking for your brothers, and wind up in Egypt?"

minhag - Dropping a phone siddur or chumash

If you have a siddur or chumash on your phone and you drop it, do you kiss it if...

• the siddur is not open


• the siddur is open, but shem hashem is not showing


• the siddur is open and shem Hashem is showing

Answer

Thankfully, there are currently no smartphones that are made with e-paper.

Because of that, all smartphones today don't have the halachic status of writing, so you are allowed to switch screens from views which have Hashem's name on them, and it is not considered erasing the name. Even if they were made out of e-paper, I assume they would be given a halachic status of writing with sand, but the issue hasn't come up yet.

The reason we kiss books when they fall on the floor is out of respect to the book and the name which is in it. So while the name does not exist in written form in the phone, I can't see any harm with treating the phone with respect while the siddur app is open, or while you consider your phone a special place in which your siddur or Torah learning originates.

halacha - How does one become a Min?

What is a min (heretic)? And how does one become a min?

And what are the Halachic Ramification about a min? Some Examples: Can't talk to a min. No matter what reject min's teshuva. etc.

Thank You.

(Some help tagging)

Answer

There are many instances where this is discussed, so for simplicity's sake I'll just quote a few passages from the Rambam.

The Rambam defines the terms 'min', 'apikores', and 'kofer' in Hilchos Teshuva 3:6-8

The following have no share in the world to come, but are cut off, and perish, and receive their punishment for all time for their great sin: the minim, the apikoresim, the kofrim (deniers) of Torah, the kofrim (deniers) of Resurrection of the dead, the apostates, they that lead many to sin, they that turn away from the ways of the [Jewish] community, etc.

Five are called 'minim': (1) he who says there is no God and the world has no leader; (2) he who says the world has more than one leader; (3) he who ascribes to the Lord of the Universe a body and a figure; (4) he who says that God was not alone and Creator of all things at the world's beginning; (5) he who worships some star or constellation as an intermediate power between himself and the Lord of the World.

Three are called apikorsim: (1) one who says that there is no prophecy at all, and that there is no knowledge that comes from the Creator to the hearts of men (2) one who denies the prophecy of Moses (3) and one who says that the Creator doesn't know of the actions of man.

In addition, while it isn't listed here, the Rambam also requires that one believe in Divine retribution in order to not be considered a heretic of some kind (Commentary to the Mishna, intro to Sanhedrin 10:1)

Regarding practical ramificatins, there seems to be no difference between a 'min', a 'kofer', and an 'apikores' - all of them lose their share in the world to come, and are in general excluded from being considered a part of the Jewish people (Source: Rambam Hilchos Avodah Zarah 2:5) Therefore, any law that requires a Jew, such as returing their lost object (Hilchos Gezailah V'aveida 11:2), writing of Sifrei Kodesh (Yesodei HaTorah 6:8, Tefillin 1:13), or testifying in court (Eidus 11:10) cannot be done by any of these categories of people, who from now on I will refer to as heretics.

In addition, one is not allowed to speak to such people, or respond to their claims (Hilchos Avodah Zara 2:5). In fact, the Rambam writes, based on the Gemara (Avodah Zara daf 26) there is a 'great thing' to kill them, either publically, if the socio-political climate will allow such things, or privately arrange for his death (Hilchos Rotzeach 4:10). However, the Chazon Ish (Yoreh Deah, Hilchos Shechita 2:16) wrote that this last halakha is not applicable today, and many great poskim have followed his view. (To clarify, I am NOT advocating the murder of anyone, just quoting the Rambam)

However, a person of such status can still do teshuvah (Rambam Hil. Teshuva 3:14)

minhag - Is there any source for not sharing a baby's name before the bris?

For some reason, I have it ingrained in me that a baby boy's name before the bris is a secret and should not be shared. Are there any sources for this, or is it something made up?

usage - When do you use the "な" version of the copula?

As I understand it, the copula "だ" turns into "な" in some situations. The most obvious one is after な-adjectives, but it often appears after nouns too, like in this sentence: "スミスさんは、将来日本の会社で働くのが夢なんだって".

Are there any rules for when だ turns into な? It seems to me that if the copula shows up at the end of a sentence it's "だ" and elsewhere it's "な", but I have no idea if it's that simple.

Answer

when does the copula become "な"?

Simply, だ turns into な when it modifies the following noun, which is の/ん in this case. な is the attributive form of the copula だ. So-called na-adjectives and ordinary nouns are technically both nouns, so they share the similar grammar pattern.

This の/ん is a tiny special noun commonly referred to as explanatory-no. This の/ん is a big topic in Japanese, so please read these first:

So, 夢なのだ/夢なんだ has an added nuance as compared to simple 夢だ. "スミスさんは将来日本の会社で働くのが夢なんだって" may be used in the following situations:

1. When this sentence works as an explanation/clarification of the previous context.
   

   
   

   スミスさんは毎日、日本語を一生懸命勉強してるよ。将来日本の会社で働くのが夢なんだって。

   
   

   
   


2. When this sentence works as a preliminary remark (i.e., background information).
   
   

   
   

   スミスさんは将来日本の会社で働くのが夢なんだって。お勧めの会社を知ってたら紹介してくれない？

   
   

   
   


3. When you just realized this fact.
   

   
   

   ねえ、今本人から聞いたんだけど、スミスさんは将来日本の会社で働くのが夢なんだって!

   
   

   
   

organic chemistry - Reaction of secondary alcohol with ammoniacal silver nitrate (Tollens' reagent)

What are the products of the reaction of 2-butanol with silver nitrate?

For the moment, I am a bit stumped as I only have $\ce{AgNO3}$ as an oxidizing agent to form a carboxylic acid from an aldehyde. Additionally, the lack of $\ce{H2O}$ indicates that this is not the reaction I should be looking for. The only reaction that seems feasible to me is an S_N2 mechanism where the nitrate anion acts a nucleophile and the hydroxide ion as the leaving group.

Here is my proposed mechanism much in the style of Tollen's reaction with an aldehyde.

image processing - Feature Detection on a Circular Metal Surface for Character Recognition

Hello I'm trying to recognize characters on the circular metal surface.

Without any preprocessing I could match cropped features with original image. I've actually cropped 2 characters together to increase interested points on a template.

however on different locations of the conveyor belt and with different illumination angle and perspective SURF matching fails.

I will definately crop the ROI from conveyor belt but still I am not sure whether I have to create a database of images to increase accuracy or some kind of preprocessing (I've read that for feature detection there is no require preprocessing on images)

I am open to new suggestions for this problem. Maybe a different algorithm or method that can help me out.

thanks in advance.

Answer

Do not struggle forming a database of images to match via descriptors. This would be too computationally cumbersome and would require immerse amount of training. Such a scalable solution doesn't exist out of the box yet. I would rather rely on Neural Networks or SVMs to train the possible appearances of characters.

Of course using a classifier relies on the assumption that the images appear more or less in a controlled fashion and you can segment the characters. To meet these criteria, you need to stabilize your illumination conditions. You can do this with the appropriate choice of LED lighting. After the illumination is more or less uniform and robust, the character segmentation is straightforward. You can simply threshold the image through local techniques (which posses certain illumination treatment) and apply blob analysis. You can also put all the constraints you have in this stage. Don't forget to unwarp your images prior to segmentation as described in this post.

To train your classifier do not use plain intensity values. This would be very noisy. Instead exploit the gradient information (or normalized gradients). This is proven to be robust in many works such as this one. Also, don't even use the gradients directly. It is better to quantize them (Remember canny?). Robustness of LINEMOD is also a good example of this.

I would suggest further reading on machine vision as this is a practically involved topic. Many techniques on machine vision differ substantially from the methods in computer vision. You can think of this as a practice-theory duality. Refer to this book for instance.

When should I calculate PSD instead of plain FFT magnitude spectrum?

I have a thirty-second speech signal that was sampled at 44.1 kHz. Now, I would like to show what frequencies the speech has. However, I'm not sure what would be the best way to do that. It seems sometimes one calculates the absolute value of a Fourier transform, and sometimes power spectral density. If I understand correctly, the latter works so that I divide my signal into parts, do FFT part-by-part and somehow sum these. Window functions are somehow involved. Can you clarify this a bit for me? I'm new to DSP.

Answer

Now, I would like to show what frequencies the speech has. However, I'm not sure what would be the best way to do that. It seems sometimes one calculates the absolute value of a Fourier transform, and sometimes power spectral density.

If you want to attach physical meaning to your analysis, then go with the power spectral density, (PSD). This is because this will simply give you the power of your signal, in each frequency band. On the other hand if you do not want/care about a physical meaning, but want to know how the fourier amplitudes of each band vary relative to each other, you can stick to absolute magnitude.

In practice, you can compute the PSD as simply the absolute magnitude of the fourier transform squared. For example, if your signal is $x[n]$, and its DFT is $X(f)$, then the absolute magnitude of the DFT is $|X(f)|$, while the PSD is $|X(f)|^2$.

If I understand correctly, the latter works so that I divide my signal into parts, do FFT part-by-part and somehow sum these. Window functions are somehow involved. Can you clarify this a bit for me? I'm new to DSP.

No, this is not true. What you are talking about here refers to the Short Time Fourier Transform, (STFT). This is simply chopping up your time domain signal, widowing it, and then taking the fourier trnasform. At the end of the day though, you will still have a complex matrix. If you choose to take its absolute magnitude, you will have an absolute magnitude fourier transform matrix. If you take its absolute magnitude squared, you will have a power spectral density matrix.

purim torah in jest - Why do we shake four heretics on Sukkot?

On Sukkot, we shake the Arba Minim. But

ארבע = four

מינים = heretics

Why do we shake four heretics on Sukkot? And furthermore, what heretics are you supposed to shake? Sadducees and Cuthites? This has really been on my mind recently.

Answer

This is in fulfillment of numerous Biblical verses that imply that the wicked will be shaken.

For example, Job (38:12)

לֶאֱחֹז, בְּכַנְפוֹת הָאָרֶץ; וְיִנָּעֲרוּ רְשָׁעִים מִמֶּנָּה

That it might take hold of the ends of the earth, and the wicked be shaken out of it.

Furthermore, Psalms (112:5-6) states that specifically the righteous shall not be shaken; implying that the wicked will be shaken.

טוֹב-אִישׁ, חוֹנֵן וּמַלְוֶה; יְכַלְכֵּל דְּבָרָיו בְּמִשְׁפָּט: כִּי-לְעוֹלָם לֹא-יִמּוֹט

Well is it with the man that dealeth graciously and lendeth, that ordereth his affairs rightfully. For he shall never be shaken. (Trans. Mechon Mamre).

In a similar vein, see Proverbs (10:30).

Additionally, Isaiah (13:13) states that God will shake the heavens and the Earth as punishment:

עַל-כֵּן שָׁמַיִם אַרְגִּיז, וְתִרְעַשׁ הָאָרֶץ מִמְּקוֹמָהּ--בְּעֶבְרַת ה' צְבָאוֹת, וּבְיוֹם חֲרוֹן אַפּוֹ.

Therefore I will make the heavens to tremble, and the earth shall be shaken out of her place, for the wrath of the LORD of hosts, and for the day of His fierce anger.

From context (ibid 9), it appears that these punishments are specifically for the wicked:

וְחַטָּאֶיהָ יַשְׁמִיד מִמֶּנָּה

And to destroy the sinners thereof out of it.

See also Radak thereon.

---

So we see that we shake the wicked just as God shakes the wicked. However, the question remains, which heretics are considered the wicked who must be punished. It appears that these are the people about whom we are commanded to "lower [to their doom] and not save" (Avodah Zara 26b). This appears to refer particularly to those who betray their fellow Jews to gentile authorities (cf. Hilkhot Hovel UMazik 8:10) and to idolaters and those who sin to anger God (cf. Hilkhot Rotseah 4:14).

equilibrium - Pressure and LeChatelier's Principle

We know that if a system's equilibrium is exposed to a stress, the system shifts to relieve that stress. According to my teacher, certain kinds of pressures are stresses and others are not.

Normally, if we just say that the total pressure of a container with a reaction occuring inside is increased, the reaction shifts toward the side with a small sum of the mole ratios (i.e. $\rm 2A +3B \longleftrightarrow C + D$, if increasing pressure reaction shifts to the right to decrease pressure). I understood this formerly, but another case erases this understanding.

My teacher also said that if we add a noble gas to the container in which this reaction is occurring, although the pressure increases because of a new gas, the equilibrium does not shift to counteract this pressure increase. She says it has to do with the partial pressures of the reactants and products of only the particles In the reaction, but not in the total balloon. But this makes no sense to me because by increasing the total pressure of the system as described before, how does this cause an equilibrial stress and this case doesn't? How does increasing total pressure even cause an equilibrium shift? By increasing total pressure we have a proportional increase in the collision rates of all particles involved, do we not? If this is true, then why wouldn't the reaction rates both be doubled, and hence cause the equilibrium to not shift?

If I'm missing some fundamental principle, please let me know.

Thanks!

halacha - Can a Jewish, non-observant parent cook for his Orthodox child?

Can a Jew who understands the laws of Kashrut but is not personally observant cook for a Kosher-observant Jew? For example, can a Jewish but non-observant parent cook for his Orthodox child?

halacha - How to say Tefilas HaDerech while on the road alone

My question applies to circumstances in which one is driving an extended distance by oneself. They also apply primarily--though not exclusively--to people who do not have the Tefilos HaDerech memorized, or whose minhag is to daven in front of a text at all times (i.e., Chabad).

One is supposed to say Tefilos haDerech while on the road. (Source: http://www.chaburas.org/derech.html). Presumably, attempting to say the prayer while actually driving would be prohibited for reasons of pikuach nefesh and kavana. The other options are to pull over, and say the prayer while stopped on the shoulder (i.e., of the highway), or to leave the highway and say the prayer at a rest stop or somewhere off an exit. However, both these options would seem to have problems. The first (stopping on the shoulder) seems like it could still be quite dangerous, especially for visibility reasons at night, or in bad weather conditions. The second is not always practical, and I am not 100% sure whether it would fall under the halacha of literally being on the road.

So, how, when, and where should one say this prayer?

Answer

If you have a mechanism (such as Bluetooth) for safely talking on a cellphone in your car:

There's a service I once heard of (in the United States) that is provided for precisely this purpose. In short, call 212-DRIVING (+1-212-374-8464) and a man will dictate the Tefillah. He even pauses after each phrase to let you repeat it as he's saying it.

Similarly, you can call a friend and ask him to dictate the Tefillah to you.

Otherwise:

Take the next exit / rest area, pull over, and then say it.

The second is not always practical, and I am not 100% sure whether it would fall under the halacha of literally being on the road.

I'm not sure where you get the halacha that you literally need to be on the road. The tefillah is for travelling. It needs to be said after a certain minimum distance has been traveled outside the city limits, but does not need to be said while actually traveling. As long as you have a certain minimum distance left for the travel, you can still say it.

As for the practicality of it: barring emergencies, I really cannot imagine a highway or road system that does not have stopping areas along the way...