physical chemistry - Why are complex basis functions not used in electronic structure calculations?

I've noticed while reading about Hartree-Fock in Modern Quantum Chemistry (Szabo and Ostlund) that most basis sets use only real basis functions. What I'm wondering is why aren't complex basis functions used? I might be mistaken, but from my experience it seems as though integration on the complex plane would have a lot of convenient properties that would make computations easier. Put another way, are complex basis functions not used because of some difficultly in implementation or is it because of difficulty in interpretation of properties like the molecular orbitals?

Answer

The basic answer is rather simple: In the non-relativistic limit it is just not necessary. There is no complex operator and hence nothing which could change the complex component of your basis functions. Using complex basis functions would only double the required work (i.e., computer time). There are very efficient schemes in order to calculate the standard integrals (McMurchie-Davidson, Obara-Saika, ...). I don't think that the representability of MOs is a reason for using real basis functions, since, strictly speaking, you can interprete only the square of the MOs and not their amplitude.

However, there are situations, where your MOs can be complex. This can happen when you have a complex operator in your equation. An example are the Pauli spin matrices of which $\sigma_y$ has only an imaginary compound. They occur, e.g., the Dirac equation (see here one formulation where they explicitly state the incorporation of the Pauli matrices). Complex MOs can be obtained either by using complex basis functions and real MO coefficients or by using real basis functions with complex coefficients. Starting from a non-relativistic implementation it might be simpler just to keep your basis functions real and to choose the MO coefficients complex.

sources mekorot - Waiting after meat as a minhag

I was once told in the name of R' Hamburger שליט”א that the practice of waiting between meat and milk is, for Ashkenazim, a minhag. I was told that nonetheless, as we are accustomed to wait and following his understanding of מנהג אבותינו תורה היא (The custom of our fathers is Torah) we must continue to wait.

Regardless, does a source exist amongst the Ashkenazi rishonim which agrees with what I've said above?

grammar - When going somewhere, is there any difference between e (へ) and ni (に)?

Can you use へ and に interchangeably, as in:

北海道へ行く

and

北海道に行く ?

Are there any subtle differences in the use of these two?

Answer

• に emphasizes the location


• へ emphasizes the direction


• まで emphasizes the process or journey

sources mekorot - Game theory in the Tanaim

I read an article a while back (maybe over a year ago?) in the Mishpacha English Magazine (I'm pretty sure, although it may have been in the Ami) that discussed a certain machlokes Tanaim about how to divide some disputed amount of money among different parties (that is all I remember of the case). There was a discussion if two people claim it, or three or more. Perhaps it was a discussion if someone stole something but doesn't know from who and there are several claimants it was them (but I'm not sure of that).

One of the opinions is very difficult to understand the theoretical basis behind, and the article quoted a Rishon as saying it is incomprehensible. The Halacha, of course, is paskened according to other opinions on how to do the division.

Then the article went on to say that that according to modern game theory this incomprehensible opinion was in fact comprehensible and consistent with this theory. I distinctly remember the specifics of the game theory not being discussed.

So which Machlokes Tanaim is this? What is the case, and the source? (The statement that one of the opinions is incomprehensible is probably enough to recognize it, but I have a feeling I'll recognize the case if I see it again).

Bonus points: What idea in Game theory helps explain the hard-to-understand opinion?

Answer

The discussion is indeed Dr. Aumann's discussion on Kesuvos 93a regarding the man who dies with insufficient funds to pay for his three wives' Kesubos. He claims to be the first to come up with this theory, but I think Rashi figured it out first. He theorizes as follows: First, award equally amongst all parties until one receives half of his claim. Then award equally among all other parties. Repeat until only one is left. Then continue awarding money to him until the difference between his claim and the amount he's getting equals the difference between his claim and the next guy's claim. Then award to the top two claimants equally. Repeat until all parties are receiving money again. Continue awarding money equally until everyone receives their claim.

As for the math behind it. I went over to the Math.SE to see what I could find out about this part. A fellow named Holger I Meinhardt answered the call here. (I tried copying it over, but apparently Mi Yodeya doesn't support MathJax.)

matlab - Generalized Cross Correlation

What is the definition of Generalized Cross Correlation?

I need it for estimating the delay (time offset) between two audio signals. The time offset between the two signals might be as large as 500ms.

Answer

Cross-correlation implies that you have 2 signals, and there is a delay between them. A 'basic' frequency domain cross-correlator does an FFT on each signal, conjugates one of them, multiplies one versus the other, then inverse transforms. A peak in the result indicates a time delay.

There are a lot of problems with this simple approach. For instance: you want a linear cross-correlation instead of a circular one; you may have strong sinusoidal interference which will generates multiple peaks; you may have very low SNR; the noise may not be what you expect it to be, etc.

A 'generalized' cross-correlation adds a windowing (or filtering) function prior to the inverse transform. It's purpose is to improve the estimation of the time delay, depending on the specific characteristics of the signals and noise (broadband/narrowband/interference signals, Gaussian noise, etc.). Since there are many different types of signals and noise, there are many different window functions (eg.: SCOT, Ekhart, etc.) Each one is designed for specific problems. Understanding these differences is not trivial, nor is proper calculation of the window function. They are typically dealt with in graduate-level time delay estimation or sonar/radar courses.

Some references for generalized cross-correlation are:

J. C. Hassab, R. E. Boucher, “Optimum Estimation of Time Delay by a Generalized Correlator,” IEEE T-ASSP, vol. 27, no. 4, Aug. 1979, pp. 373-380 (discusses various window types).

J. C. Hassab, R. E. Boucher, “Performance of the Generalized Cross Correlator in the Presence of a Strong Spectral Peak in the Signal,” IEEE T-ASSP, vol. 29, no. 3, June 1981, pp. 549-555.

J. C. Hassab, R. E. Boucher, “An Experimental Comparison of Optimum and Sub-Optimum Filters’ Effectiveness in the Generalized Correlator,” J. Sound and Vibration, 1981, pp. 4+ (12 pages total)(Fig. 1 contains a block diagram of a generalized cross-correlator).

There are many others.

organic chemistry - Does acetic acid give a positive result with the iodoform test?

Acetic acid contains a $\ce{-COMe}$ group, so theoretically, it should give a positive result in the iodoform test (i.e. a yellow precipitate of $\ce{CHI3}$ being formed).

But apparently the iodoform test is used to distinguish between acetic acid and other compounds with a $\ce{-COMe}$ group. So, logically, acetic acid must not give a positive result. Why is this so?

Answer

The iodoform reaction proceeds by the mechanism shown below. (The final proton transfer need not occur between the two partners, any other hydroxide could abstract the acid’s proton and any water molecule can protonate iodoform.)

This can fail for carboxylic acids or esters in one of two ways:

1. 
   

   The first step. The $\mathrm{p}K_\mathrm{a}$ value of the proton being abstracted is $26.5$ for acetone and $29.5$ for ethyl acetate according to the Bordwell $\mathrm{p}K_\mathrm{a}$ table. This can be attributed to the second oxygen of an ester donating electron density into the carbonyl group and thus lowering the tendency to form the enol(ate). But we can still argue that enough ester will be deprotonated for the iodination to occur. (Note that this fails entirely for a free acid, since the molecule is already charged. A second deprotonation to produce the endioldiate is very unfavourable.)

   
   


2. 
   

   The final fragmentation step. In esters, $\ce{R}$ also contains an oxygen atom, so there are a total of three pathways by which the tetrahedral intermediate can fragment (one being redissociation of the hydroxide). In the ketone’s case, only one is productive, namely the formation of iodoform which precipitates and drives the equilibrium towards its formation. The ester can fragment under displacement of the alcoholate (productive, gives an acid) which is much more favourable than displacing a $\ce{CI3-}$ group due to the $\mathrm{p}K_\mathrm{a}$ value of both’s conjugate acids.

   
   
   

   The resulting acid is merely deprotonated. The attack of a nucleophilic (hydroxide) species to the resulting anion is strongly disfavoured.

   
   

It is also to be noted that an ester can always be hydrolysed to the corresponding acid under basic aquaeous conditions. Thus, at any intermediate an acetate anion could generate inhibiting any further reactions.

halacha theory - Why did Sanhedrin deal with who has a share in Olam Habah?

The Gemmorah (Sanhedrin 104b) describes that the members of the Great Assembly dealt with the question of who does or does not deserve a share in the World to Come.

As they demonstratively disagreed with Heaven (Bat Kol), it is assumed that they didn't have an existing tradition but tried to judge the persons themselves (at least part of it).

As it seemingly has no practical Halachic value, no mentioning that the question is out of their powers anyway, why would they deal with such a question in the first place?

particles - Using both と and を with the verb 言う？

I've recently been reading Tobira and there was a sentence that I was really having trouble finding exactly what was going on in it.

そして、「どこに住んでるの？」と「い」を言わなかったり、「どこ、住んでるの？」と「に」を落として言ったりすると、もっとくだけた感じになります。

I think I figured out the meaning which I would interpret as

"Not saying the 「い」 in 「どこに住んでるの？」 and saying 「どこ、住んでるの？」 while dropping the 「に」 gives a more relaxed impression."

But my issue is specifically with そして、「どこに住んでるの？」と「い」を言わなかったり,

Normally, from my interpretation when a phrase marked with と followed by the verb 言う in this manner it would be quoting what was said/will be said. However, what's being said in this case seems to be marked with the を? Intuitively, I initially thought 「どこに住んでるの？」と「い」を言わなかったり carried the meaning of "Not saying 「どこに住んでるの？」 and 「い」".

My logic behind this being that the 言わなかったり is of course in the negative form. If someone could breakdown the grammar for this example (especially regarding using both particles in a single sentence with 言う) I would be super appreciative!

I've seen the particle を with 言う a lot recently but haven't considered the differences between と and を with 言う until now. What exactly is the difference between using を or と with 言う and what are some cases one would be chosen over the other?

Thanks!

Note: The question this was claimed to be a duplicate of does not have an answer that addresses the concurrent use of both particles within a single sentence.

verbs - Which form is はじめまして?

So I've learned that はじめまして is used in first meetings and that it stems from the verb はじめる (to start; to begin). But what form is it? It's apparently not the polite past form, which has a -た at the end (はじめました). Is it a proper verb form of はじめる anyway or should it simply be seen as a set expression?

Answer

To break it down, はじめまして is the て form of はじめます, and はじめます is the polite form of はじめる.

はじめまして is a fixed expression.

You'll see ～～まして in some fixed expressions such as:

• あけましておめでとうございます。-- Happy new year.


• どういたしまして。-- You are welcome.

as well as in polite/formal speech or writing such as:

• ご来店くださいまして、誠にありがとうございます。
  
  -- Thank you for visiting our store.


• ご迷惑をおかけしまして、申し訳ございません。
  -- We are sorry to have troubled you.

choshen mishpat civil law - Is an ex-employee allowed to work with the customers of his former employer?

Shimon works for Business A, he has access to the contact information of all the clients and is responsible for interacting with them. Moreover, he knows how much each client is paying for Business A's products and services, as well.

Shimon leaves Business A and opens his own Business B that operates in the same field. Shimon wants to use all the information he collected on his former clients to attract those clients to his business.

Can this behavior be considered a"steal" Halachicly?

If yes, can he be sued in Beis Din and what can be the verdict?

orthography - Why are points used where furigana would be normally?

Sometimes in mangas there are points where you would expect normally furigana. What meaning is it supposed to have?

Answer

The dots, called 傍点【ぼうてん】 (or 圏点【けんてん】), function like italics or underline with the Latin alphabet. They are for emphasis.

To see the effect in rōmaji:

futatabi kanojo jishin no kuchi kara kiku koto ni naru to wa

Update. To answer the question in the comments, 傍点 and ふりがな may be combined (although ふりがな may also be omitted, as in the snippet in the question body). ONE PIECE isn't exactly a case study of minimalist typography (I'm counting at least 7 text fonts), but for completeness here is an example of 傍点 on top of (or rather, to the side of) ふりがな:

inorganic chemistry - Is ClH7 possible?

Chlorine can be $sp^3d^3$ hybridized.

If so, it can form $\ce{ClH_7}$ and then chlorine, being more electronegative, will have (-7) as its oxidation number. But we know that the oxidation number of $\ce{Cl}$ lies between (-1) and (+7).

Thoughts?

halacha - Learning laws of aveilut when your parents are alive?

Is it appropriate to learn the laws of aveilut when both your parents are alive? Or is there a superstition that it could be dangerous to them?

shabbat songs - Is it okay to sing Zemirot for Shabbas day on Shabbas night?

I know there are zemirot that are generally for Shabbas night, and others that are for Shabbas day, but is it okay to sing them whenever on shabbas?

Is there any significance to why they are traditionally sung on Friday night or Shabbas day?

grammar - What does the に do in 表情から察するに?

その表情から察するに魔剣を所持している人は少ないみたいだ。

I'm having trouble figuring out what に does here. Does it have the same meaning as と?

Answer

That's right. This kind of に won't always be replaceable with と, but in your case it basically is.

From デジタル大辞泉:

［接助］活用語の連体形に付く。
１ あとの叙述の前置きとして続ける意を表す。…と。…ところ。
「考えてみるに庶民のための政治は当分望めそうにない」

The に marks a lead-in to the main point which follows.

• その表情から察するに〜 Judging from the expression…


• 私が思うに〜 The way I think of it…


• 彼が言うに〜 According to him…

organic chemistry - Effect of reduction potential on particle size of chemically precipitated silver particles

Is there no mathematical relationship between redox potential and particle size saying that an $X$ potential should yield a $Y$ particle size? Right now its general that large redox potential results in smaller particles, but I want to know if, for example, for silver particles I use $\ce{AgNO3}$ with glucose reducing agent and say the redox potential is $\pu{0.33V}$, what the ballpark for the particle size should be based on that potential (assuming $\mathrm{pH}$ does not change)?

everyday chemistry - Why does superglue ignite cotton?

Cotton is mostly cellulose, a plant saccharide. Superglue refers to a class of cyanoacrylates. What is it about the two that causes ignition?

I'd imagine that the cellulose in cotton is in its linear form and not in its ring form since the ring-linear form interconversion only occurs in solution. Is it that the cellulose attacks the cyanoacrylate?

The three hydroxyl groups, one primary and two secondary, in each repeating cellobiose unit of cellulose are chemically reactive

So, do the hydroxyl groups attack the carbonyl group in superglue?

Answer

Cyanoacrylates include methyl 2-cyanoacrylatecommonly sold under the trade names "Super Glue".In general, cyanoacrylate (consists of monomers of cyanoacrylate molecules) is an acrylic resin that rapidly polymerises in the presence of water (specifically hydroxide ions), forming long, strong chains, joining the bonded surfaces together. Because the presence of moisture causes the glue to set, exposure to normal levels of humidity in the air causes a thin skin to start to form within seconds, which very greatly slows the reaction. Because of this cyanoacrylate is applied thinly, to ensure that the reaction proceeds rapidly and a strong bond is formed within a reasonable time.

So to sum up, in order to start the reaction off some water is normally needed.. damp things stick better/quicker than dry ones and the glue goes hard faster on a humid day.

In cotton wool, which is made of cellulose, a polymer of sugar molecules, there are lots and lots of hydroxy (-OH or alcohol groups), which can start the reaction in the same way as the water does, only because there are lots of them they can start many more reactions at once.

Since the reaction gives out heat, the cotton bud therefore gets hot (and as it becomes hotter so the reaction goes faster etc), and it may get hot enough to catch fire.

verbs - How to parse ～なくたって?

I've been running into verbs such as 言わなくたって recently. I found these sentences using a sample sentence search and it seems to be a stronger form of ～なくても

見てなくたっていいよ。 You don't have to stand over me.

そんなトゲトゲしい言い方しなくたっていいだろう。 You don't have to use such a harsh tone with me.

Where can I find this in a dictionary? It doesn't seem to be [達て]{たって}, nor the たって in 雨が降ったって出掛けるよ

Answer

This たって is the same as たって (≒even if, even though) in 雨が降ったって出掛けるよ. The difference is that なく (te-form of ない) is inserted between the main verb (=言う) and たって. (And of course 言う is in its nai-form before ない)

• 言わなくたって分かるよ。 Even if you don't say it, (I/he) can understand.


• 言ったって分からないよ。 Even if you say it, (I/he) can't understand.

The literal translation of 見てなくたって would be "Even if you are not seeing, (it's) okay." The opposite is 見てたっていいよ, which is the contracted form of 見ていたっていいよ.

And the negated version of 雨が降ったって is 雨が降らなくたって.

雨が降らなくたって傘を持っていくよ。

acid base - How sure can we be about the structure of purine?

While answering the question Basicities of nitrogen atoms in purine, I noticed, that there might be a rapid interchange of the hydrogen bonded to the nitrogen atoms.
I have found a crystal structure in D. G. Watson, R. M. Sweet and R. E. Marsh, Acta Cryst. 1965, 19, 573-580. (DOI: 10.1107/S0365110X65003900, CCDCID: 1239746, 1239747), that resolves it as 1. However, at least in solution I would assume that there should be a distribution of structures according to the scheme below. In all cases the aromaticity is retained.

I am not an expert on crystal structures, and I don't know how to read the .cif file correctly. I remember from my course on crystallography, that the positions of hydrogen are notoriously hard to confirm.
Can we therefore really be sure about this structure? Is there evidence in the crystallography data for a large disordering?

To provide a bit more context, I am asking this, because it is likely to change part of the answer I have given to the linked question. If there exists an equilibrium between the above protomers, then that would certainly make it even harder to find the most basic nitrogen in purine.

halacha - Does Down Syndrome make one a Shoteh?

I had a very strange experience and I would like to know what halacha thinks.

I was in shul on Shabbos, and an adult with Down Syndrome ripped by opening the box of tissues. I was not going to say anything, but I guess he noticed my disapproval of what he had done. Now I remind you I said nothing. He looks at me with a straight face and says, "Don't worry; I am a Shoteh." Now, I want you realize that he was intelligent enough to read my face and understand what I thought he did was wrong, yet I still want to know: Is he actually correct?

calendar - Why is Rosh Hashana two days in Jerusalem?

Rosh Hashana is the only festival celebrated for two days even in Jerusalem, since there was a possibility that witnesses for the new moon would come in the middle of the day and the Beis Din would declare it Rosh Hashana (retroactively). If the witnesses didn't come, Rosh Hashana would (biblically) automatically be deferred to the next day, but Melacha would continue being prohibited due to the fear that people would Mezalzel the first day of Rosh Hashana the next year.

Nowadays, Rosh Hashana always falls out on the 1st and 2nd. So the calendar is programmed "as if" the witnesses came the first day.

Why do we have a second day?

covalent compounds - Structures for NO+ (Nitrosonium)

There are two possible structures for Nitrosonium :

• In the first structure, there is a +1 Formal charge on Oxygen, whereas,


• In the second structure, there is a +1 Formal charge on Nitrogen.

Q. Which is a better lewis structure?

Q. Are they resonating structures of NO+?

Wikipedia gives the first structure only, so i think that is the only correct structure.

I think structure in which less electronegative atom has a positive formal charge is better, so the first structure is better.

Q. Is the above reasoning correct?

Answer

Which is a better Lewis structure?

There is no such thing as a better or a worse Lewis structure. They should be properly referred to as major or minor resonance contributors/forms.

I looked up a textbook to check the rules of determining which resonance structure contributes more. The order is:

1. Structures that satisfy the octet rule are greater contributors than structures which do not satisfy the octet rule.


2. As long as the octet rule is not exceeded for second-row elements, the contributing structure with the greater number of covalent bonds contributes more.


3. When two or more structures satisfy the octet rule with the same number of covalent bonds, the major contributor is the one with the smallest separation of oppositely charged atoms.


4. Among structural formulas that satisfy the octet rule with the same number of covalent bonds, and in which one or more atoms bear a formal charge, the major contributor is the one in which the negative charge resides on the most electronegative atom.

In the first structure, all atoms possess a complete octet. But in the second structure, nitrogen only has six electrons around it: consequently, by rule 1, the first resonance structure is the major contributor.

Are they resonating structures of $\ce{NO+}$?

Not exactly.

The actual structure of the nitrosonium cation is somewhere in between the two forms. This means that the N–O bond is somewhere between a triple bond and a double bond. However, since we have established that the first form contributes more to the actual structure, it is going to be closer to a triple bond than a double bond. You could think of it as a 2.9-bond. Molecular orbital theory tells us that the actual bond order in $\ce{NO+}$ is 3, but that's an entirely separate story for another day.

The cation does not resonate between two distinct structures. Let me cite another example. Benzene also has two different resonance structures, both of which contribute equally (since they are identical to each other). Does that mean that the C-C bonds flip between being a single bond and being a double bond? No. All the C-C bonds in benzene are 1.5-bonds, at all times. The common usage of alternating single and double bonds (the Kekule structure) is just us being lazy since many mechanisms are easier to draw that way. Similarly, the $\ce{NO+}$ cation does not flip between the two resonance structures, which represent two extreme ends of a spectrum of possible structures. The actual structure is always in the middle of the spectrum. Which side the actual structure leans towards, is determined by which resonance form contributes more.

At risk of sounding like a broken record - The actual structure is somewhere in between the two resonance forms. It does not oscillate between two different resonance forms. This is a very important concept to understand!

I think the structure in which the less electronegative atom has a positive formal charge is better, so the first structure is better. Is the above reasoning correct?

Yes and no. There are several methods of measuring electronegativity, and in all of them, nitrogen is less electronegative than oxygen. By your reasoning, this means it would be more favourable to place the positive formal charge on nitrogen, i.e. resonance form 2. So your reasoning is a little bit off there.

On the other hand, you would be correct if there wasn't a difference in the number of bonds between the two resonance forms. As I mentioned at the top of the post, the number of bonds takes precedence over the electronegativity issue.

purim torah in jest - Why is it okay to give more than half a shuckle?

In Shemot 30:11-16, it says we should give half a shuckle when giving an offering to G-d. The posuk is very clear that we cannot give more or less than exactly one half-shuckle. So why do some people give many full shuckles when they are saying prayers, our modern korbanot?

---

halacha - Can a Sheitel be made out of one's own hair?

Suppose a married woman is able to create a Sheitel that is entirely made up of her own hair (detached, of course). Does that satisfy the requirement for covering her hair?

Answer

This is a matter of disagreement among the poskim. Those who say this is an acceptable type of hair covering include Shiltei Giborim (Shabbos 29a in dapei haRif) and P'ri M'gadim (Eshel Avraham OC 75:5).

Those who say it is unacceptable, and differentiate between a regular wig and a wig made out of a woman's own hair, include Ateres Z'keinim (OC 75:3), Be'er Heiteiv (OC 75:8, quoting Ateres Z'keinim), and Magein Giborim (75:8).

CYLOR for a practical ruling.

analytical chemistry - How do I figure out how many hydrogens my compound actually has using a mass and NMR spectrum?

Question 3:

It said $m/z = 122,$ and $m/z = 124$ is in a $3:1$ ratio, so I figured that meant that chlorine is present. Then I thought $m/z$ was the actual compound's molecular mass.

So I used the rule of 13, and did:

Chlorine's molar mass = 35

122 - 35 = 87

Using the rule of 13

87/13 = 6C + 9H/13

So the molecular formula is $\ce{C6H9Cl}.$ But the integral values I rounded are: 2,2,2,2 and 3 adding up to 11. Did I use the wrong mass to charge ratio? What am I missing?

usage - Using くれる for doing something bad

Today I heard the phrase なんてことしてくれた, as in:

君！なんてことしてくれたんだ！

which I learned means "Look what you've done". I thought くれる was only used when someone does something nice for you. Is this just a set phrase, where くれる is being used sarcastically, or are there other times you can use くれる when someone does something you don't like?

Answer

Speaking from personal experience, I do hear the ~くれる form used this way all the time in video games and such, and it seems to me that it does carry a kind of sarcasm(the Japanese kind :D).

I mostly hear やってくれたな! when the opponent does something to the person, but I seldom hear it used this way on any word besides する and やる, so I'd assume yours is a good bet.

physical chemistry - While filling electrons, we follow Aufbau principle, but not while removing them. Why is this so?

I recently came across a question Why is the vanadium(3+) ion paramagnetic?, where the asker is wondering how $\ce{V^{3+}}$ is paramagnetic (he used Aufbau in reverse to remove the electrons), while the correct answerer to that question remarked that removing electrons must follow the order from outer shell to inner shell. For example, in the case of $\ce{V^{3+}}$ the electronic configuration of $\ce{V}$ is $\ce{[Ar] 3d^3 4s^2}$. The asker used reverse-Aufbau, which is $\ce{[Ar] 3d^0 4s^2}$; while the actuality was $\ce{[Ar] 3d^2 4s^0}$.

My question: Why does filling electrons follow a certain rule, while removing them follows a different rule?

Answer

Usually when adding electrons based on the Aufbau principle, you go from one element to the next highest one, e.g. from $\ce{Ti}: \ce{[Ar] 4s^2 3d^2}$ to $\ce{V: [Ar] 4s^2 3d^3}$. Thus you add not only an electron but also a proton to your atom.

When you remove electrons to get to a cation, you only remove electrons. Thus it is a different situation, with different interactions between nucleus and electrons, which affects the energy of the orbitals.

Also keep in mind, that the orbital picture is just a simplification. Strictly speaking (and from a purely theoretical point of view) orbitals do not exist, they are merely a mathematical crutch to solve the Schrödinger Equation. Although in practice this picture works surprisingly well, hence people use it a lot.

A proper quantum chemical calculation will give you the correct ground state, but you might have problems identifying it as something like $\ce{[Ar] 4s^2 3d^0}$. It will be a mixture (linear combination) of many electron configurations, although $\ce{[Ar] 4s^2 3d^0}$ might be the most important one for $\ce{V^{3+}}$.

inorganic chemistry - Why is carbon dioxide considered a Lewis acid?

$\ce{CO2}$ is considered a Lewis acid. How it is an acid? According to Lewis: “species that accept an electron pair are acids”. But $\ce{CO2}$ can't accept electron pairs because oxygen and carbon both are electron sufficient (have complete octets). If the reason is within a lone pair of electrons on oxygen then ammonia ($\ce{NH3}$), which also has a lone pair of electrons, should be acidic, too. But ammonia basic in nature.

So why can carbon dioxide be considered a Lewis acid?

acid base - Factors affecting mass of a gas-evolving reaction mixture over time

Excess magnesium was added to a beaker of aqueous hydrochloric acid on a balance. A graph of the mass of the beaker and contents was plotted against time (line 1).
What change in the experiment could give line 2?

1. The same mass of magnesium but in smaller pieces


2. The same volume of a more concentrated solution of hydrochloric acid


3. A lower temperature

Original question:

The answer is just II. However, I thought that both I and II would answer the question. Why is it just II?

Answer

The reaction that occurs here is $$\ce{Mg (s) + 2 HCl (aq) -> MgCl2 (aq) + H_2 (g)^}.$$

As the reaction progresses, $\ce{H_2(g)}$ is released and hence the mass decreases.

I believe you are right, both I and II could be correct.

II, because a greater quantity of $\ce{HCl}$ will lead to more $\ce{H2}$ leaving, hence a greater mass decrease.

I, because putting the magnesium in smaller pieces is likely to increase the speed of the reaction, and hence increase the mass of $\ce{H2}$ that has been created in a given time. However, since the end of both functions is "flat", one could assume that the reactions won't evolve any more, thus invalidating this answer (if one waits long enough for the reaction to not evolve any more, the speed of the reaction will in most cases not affect the end result).

molecular orbital theory - Band MO of Sodium Filling of electrons confusion

I wanted to ask a question about metallic bond - band electron theory.

Consider the diagram of Sodium below:

Circled are orbitals both containing $2$ electrons each which combine using LCAO to give a set of bonding and antibonding electrons.

However, the $4$ electrons involved in this bonding appear to only give $3$ electrons in the bonding and antibonding MO's produced.

This confuses me. Surely using $4$ electrons, I expect all $4$ of these electrons to also be present in the rectangle drawn.

Why are there only 3 electrons shown? Is one electron being used for the next addition of AOs?

Any answers would be greatful!

Answer

From left to right, it shows 1, 2, 3, and 4 atoms of sodium, with a total of 1, 2, 3, and 4 valence electrons. So this diagram is different from others which have the uncombined AO's on the left and right, and the combined MO's in the middle. Here, we are adding more and more atoms to go from discreet energy levels (left 4 columns, up to four atoms) to a band structure (rightmost column, many atoms in bulk metal).

The only column that shows the AO is the left-most because for that one, there is only one atom, which means that there can't be any MOs.

Maybe this diagram makes more sense to you (the full and empty circles on the right show how the AO's are combined to make the bonding, non-bonding and antibonding MO's):

Source: http://xbeams.chem.yale.edu/~batista/vaa/nabands.gif

word choice - What is the difference between [上手]｛じょうず｝ and [上 手い]｛うまい｝?

I've read that [上手]｛じょうず｝ is formal and [上手い]｛うまい｝　is casual... nothing else?

Answer

I think the biggest difference is that 上手 generally means "good at something", and うまい　can mean that, but it can also mean "tasty" (as in food). The related word うまみ means "savory" (the '6th' flavor, found in things like eggs).

Grammatically, 上手 is a na-adjective, whereas うまい is an i-adjective, so they conjugate differently.

うまく (the adverb form of うまい) can be used with いく for the common expression うまくいく ("to go well"), whereas you generally wouldn't say 上手にいく.

While I guess you could say 上手 is more formal than うまい, お上手 would be an even more formal way to describe someone else being good at something.

As a side note, generally when talking about yourself being good at something, I would recommend 得意 instead of either of these two words.

Counter for 熊 (bears): ひき or 頭?

While hiking I saw 3 bears, and I have heard a lot of people say ひき to count them. There was a mother and two small ones, if that matters.

But when talking about it I also have been told that 頭 should be used to count bears.

Are both usable? Does it depend on the age of the bear?

Answer

頭【とう】 is a counter for what are usually herd animals. Cows, elk, horses, elephants... The four legged thing might also be a factor. You don't necessarily have to see them on a ranch for foodstock purposes, but it's that kind of animal.

ひき is the counter for pretty much every other kind of animal that isn't covered by a more specific counter like 頭, or 羽【わ】 for birds.

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A point that arose in the comments below which is important enough to make sure it's seen with this answer:

A key factor seems to be the human relationship to the animal, and whether that animal can be reared, hunted, or exploited in some way. As was pointed out in the comments, 頭 can be used for bears if the context is hunters harvesting them. At least one example of this was found, though I suspect this usage is extremely limited in scope.

grammar - What does のに at the end of a sentence mean?

does it have a similar meaning to "が、ので etc." which basically make the sentence "softer" and imply something that isn't stated but that should be obvious to the listener?

something like "though" in English.

2 examples:

• 彼が出て行けばいいのに。


• あの建物さえなければ、きれいな景色が見えるのに。

Answer

のに at the end of a sentence can be rendered as something like "if only it weren't the case that ~"

From your examples:

彼が出て行けばいいのに。 (Aw man, it would have been so good had he gone)

あの建物さえなければ、きれいな景色が見えるのに。 (If only that building weren't there, we could see the beautiful scenery)

A~ いいのに is a fairly common usage, "would have been good if [only] ~A"

It usually reflects a state of regret or longing, or an improvement that can be made on the scene or experience. Hope that helps.

parshanut torah comment - Why did the Bnei Yisroel deviate from God's command to ask for gold and silver?

Hashem told The Bnei Yisroel to ask the Egyptians for "silver and gold" in Shemos, Chapter 11, Verse 2:

Please, speak into the ears of the people, and let them borrow, each man from his friend and each woman from her friend, silver vessels and golden vessels."
דַּבֶּר נָא בְּאָזְנֵי הָעָם וְיִשְׁאֲלוּ אִישׁ | מֵאֵת רֵעֵהוּ וְאִשָּׁה מֵאֵת רְעוּתָהּ כְּלֵי כֶסֶף וּכְלֵי זָהָב

In Shemos Chapter 12, Verse 35 it says that in addition to asking for "silver and gold" they asked for "garments":

And the children of Israel did according to Moses' order, and they asked the Egyptians silver objects, golden objects, and garments.
וּבְנֵי יִשְׂרָאֵל עָשׂוּ כִּדְבַר משֶׁה וַיִּשְׁאֲלוּ מִמִּצְרַיִם כְּלֵי כֶסֶף וּכְלֵי זָהָב וּשְׂמָלֹת

Why did the Bnei Yisrael deviate from what Hashem told them?

What can we learn from the discrepancy?

Furthermore, in Shemos Chapter 3, Verse 22 Hashem tells Moshe that in the future the Bnei Yisroel will ask for gold, silver and garments. He reports what will happen. Yet he did not include the "garments" in his command to Moshe for the Bnei Yisroel.

As it says:

Each woman shall borrow from her neighbor and from the dweller in her house silver and gold objects and garments, and you shall put [them] on your sons and on your daughters, and you shall empty out Egypt."

וְשָׁאֲלָה אִשָּׁה מִשְּׁכֶנְתָּהּ וּמִגָּרַת בֵּיתָהּ כְּלֵי כֶסֶף וּכְלֵי זָהָב וּשְׂמָלֹת וְשַׂמְתֶּם עַל בְּנֵיכֶם וְעַל בְּנֹתֵיכֶם וְנִצַּלְתֶּם אֶת מִצְרָיִם

parshanut torah comment - Why did Yosef's brothers speak freely in the presence of the interpreter?

In Parashat Miketz, Yosef's brothers encounter him disguised as the viceroy of Egypt, and he accuses them of espionage, jails them for three days, and makes a demand that they know their father would never allow. In his presence, they discuss their suspicion that they are being Divinely punished for their mistreatment of Yosef years earlier. They have no reservations discussing this in front of Yosef because (Gen. 42:23):

וְהֵם לֹא יָדְעוּ כִּי שֹׁמֵעַ יוֹסֵף כִּי הַמֵּלִיץ בֵּינֹתָם

They did not know that Joseph understood, for the interpreter was between them.

In other words (according to Rashi's intuitive explanation), during their entire encounter with their disguised brother, they'd been speaking Hebrew to an interpreter, who was translating into Egyptian for Yosef. So, they assumed that Yosef didn't know Hebrew and that they could therefore speak freely in this language.

I've always wondered why they weren't concerned that the translator himself would report their conversation to Yosef. Does the verse really mean that the interpreter had been between them, and now he was on a pistachio break? Or, was there some sacrosanct code of interpreters that they would never report on overheard conversations? If Yosef had Hebrew interpreters at his command, shouldn't they have suspected that he'd have Hebrew-understanding spies listening to their conversations also?

Answer

The sefer Binyan Ariel explains that since the gemara in Sotah implies that Pharaoh did not know Hebrew (Loshon Hakodesh), it was not the language of the land of Canaan, and so they were safe in assuming that the interpreter also only understood the Canaan language (the language which they had been using to speak to Yosef) but not Hebrew. Therefore they were not careful when they were speaking Hebrew amongst themselves in front of the interpreter.

However, they should have been careful not to speak amongst themselves in Hebrew in front of Yosef because he was ruler, and they should have therefore assumed that he knew all the languages since it was normal for rulers to know all languages. But because they saw that “the interpreter was between them” it was clear that Yosef did not know every language, because if he did he would not have needed an interpreter but would instead have spoken directly to his visitors in whatever language they spoke. From this they deduced that if he was not expert in all other languages, he certainly didn't know Hebrew, and therefore they were not careful when speaking amongst themselves in an language which not everyone spoke.

everyday chemistry - Mercury metal: Not toxic?

Now I (and most of us here, I guess) have grown up around "Mercury's toxic! Avoid handling it! Do NOT screw around with this thing, if you value your life" and other equally heartening pieces of advice regarding mercury. Apparently mercury poisoning makes you, really lose it.

Now a while back I chanced upon a video on Youtube (I checked today, and now there're multiple videos on the same thing) where someone was messing around with elemental mercury … with his/her (I don't remember) bare hands.

Naturally I was taken aback. A quick check provided sufficient evidence to ascertain that he/she hadn't died as a result.

Now I posed this to a teacher of mine, and after some deliberation, he concluded that it isn't the mercury metal that's toxic. He told me that it's the various compounds of mercury that are formed by elemental mercury once it gets in your system (i.e- once you drink it) which are responsible for the toxicity. So apparently touching metallic mercury with your bare hands isn't an issue, since the metal isn't subjected to all those metabolic reactions that go on inside the body; heck you can even gargle it and live (provided you spit it out afterwards) since mercury's fairly inert.

So what I'd like to know is

Is it true that metallic mercury by itself, isn't toxic?

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*Spin-off questions:

Is there any substance to my teacher's claim? How come those asses that performed this mundane task survived and now live (seemingly) normal lives without going insane? Were they already insane prior to touching the mercury? Should I just go and touch some mercury, partly to discover if it is indeed possible to touch metal mercury safely (and partly just to let out all the stress that built up while typing out this question)?

Answer

Mercury is toxic, but you need to carefully define what you mean by toxic or you draw incorrect conclusions

Toxic is a broad term. It means a lot of different things. The timescale matters. Some toxic things take years to exhibit their effects; others act instantly.

A binary distinction between toxic and not-toxic is pretty meaningless: you need to define the context and the timescale of the toxicity.

Mercury metal and mercury compounds are usually considered toxic. But their effects are varied in time and degree. Mercury metal is pernicious but only if you are exposed to it over a long time period. In fact you could probably drink it with few ill effects. The body just doesn't absorb it quickly. What is dangerous about mercury is not short term exposure to the metal but long term exposure to the vapour. This is why people don't suffer immediate ill effects when handling the metal even without skin protection.

Mercury vapour is readily absorbed in the body and will accumulate in tissue causing a variety of long term effects. This was discovered by mercury miners who often developed long term problems from their exposure. And it was documented for science by some chemists who started to suffer effects after working with the metal over long periods of time and managed to document their own decline (see Stock's work, for example). Mercury metal is often widely used in laboratories to provide a limited overpressure for gas distribution (you allow the gas to bubble through a mercury manometer).

Since the toxicity was recognised, chemists have been a lot more careful and always avoid vapour buildup by working in well ventilated spaces and making sure that manometers containing mercury are vented safely to the outside (via scrubbing filters) along with other potentially toxic vapours.

There is little immediate risk when working with metallic mercury as long as you don't spill it somewhere where it will collect and allow vapour to build up in the atmosphere.

Mercury compounds are a bigger risk. Some are readily absorbed into the body. The worst sort are mercury organometallic which are both volatile and penetrate the skin quickly. If you work with those you need to take extreme precautions. Even experienced chemists have been killed by accidents involving things like methyl mercury (see this tragic story).

halacha - Being a houseguest in a non-frum or non-Jewish home

I'm Jewish, so I have to keep many laws in mind. Kashrut, tefillin, yichud, kol isha, and more.

When staying as a houseguest in a non-frum or non-Jewish home, what are some of the issues I might face? What's your advice on dealing with these issues?

[Edit: Assume that the point of my trip is to attend a computer conference. Assume that my host is a quiet guy who's not attending the conference.]

Sources, links, and personal experiences are all welcome. Please tell us what web search terms you used, if any.

CYLOR.

Related, regarding kashrut:

Related, regarding tefillin:

Answer

If I were staying in a non-frum or non-Jewish home, the foremost thing on my mind (outside of all the more common halachos that you mention) would be the mitzvah of Kiddush Hashem, and the issur of Chilul Hashem.

Remember that you may be an uncommon sight for them, in some cases even the only orthodox Jew they've ever observed up close. As much as we'd like to think otherwise, most of us do draw stereotypes in our minds. (Imagine meeting only one Amish person, or only one Siberian; you'd be pretty likely to assume that most others from their place of origin are the same.) Keep in mind that your actions and behaviors will influence their thinking of all other orthodox Jews, and orthodox Judaism, and G-d.

No pressure. ;)

This is sobering, but empowering at the same time.

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(It's true that we always have to be careful about these mitzvos, but when you stay in someone's house, they see a side of you that they wouldn't see on the street. Therefore, it's more important than ever that you are meticulous in following halacha and derech eretz.)

tefilla - Interrupting Amida for a Mitzvah

Avraham leaves Hashem to deal with guests in Vayera - because welcoming guests is greater than Kabolas Pnei HaSh'china.

Does that mean we can interrupt our Shmoneh Esrei to do mitzvahs? At least to do hachnosas orchim?

minhag - Shliach Mitzva money

Many people give their friends money to give to Tzedakah when they are traveling. The reason they do this is that it says "Shluchei Mitzva Ainom Nizakim". If someone is travelling to Eretz Yisroel which is in itself a Mitzva - or to do a different Mitzva is there still a need for Shliach Mitzva money?

kibbud av veim honoring - Common denominator of the Mitzvot whose reward is "lengthened days?"

To my knowledge, there are 3 mitzvot in the Torah that explicitly state that the reward is lengthened days (long life):

1) Honoring one's parents (Exodus 20:12)

כַּבֵּ֥ד אֶת־אָבִ֖יךָ וְאֶת־אִמֶּ֑ךָ לְמַ֙עַן֙ יַאֲרִכ֣וּן יָמֶ֔יךָ עַ֚ל הָאֲדָמָ֔ה אֲשֶׁר־יְהוָ֥ה אֱלֹהֶ֖יךָ נֹתֵ֥ן לָֽךְ׃

Honor your father and your mother, so that your days be lengthened on the land that the LORD your God is assigning to you.

2) Sending away the mother bird (Deuteronomy 22:7)

שַׁלֵּ֤חַ תְּשַׁלַּח֙ אֶת־הָאֵ֔ם וְאֶת־הַבָּנִ֖ים תִּֽקַּֽח־לָ֑ךְ לְמַ֙עַן֙ יִ֣יטַב לָ֔ךְ וְהַאֲרַכְתָּ֖ יָמִֽים׃

Let the mother go, and take only the young, in order that you may fare well and your days be lengthened.

3) Honest weights (Deuteronomy 25:15)

אֶ֣בֶן שְׁלֵמָ֤ה וָצֶ֙דֶק֙ יִֽהְיֶה־לָּ֔ךְ אֵיפָ֧ה שְׁלֵמָ֛ה וָצֶ֖דֶק יִֽהְיֶה־לָּ֑ךְ לְמַ֙עַן֙ יַאֲרִ֣יכוּ יָמֶ֔יךָ עַ֚ל הָֽאֲדָמָ֔ה אֲשֶׁר־יְהוָ֥ה אֱלֹהֶ֖יךָ נֹתֵ֥ן לָֽךְ׃

You must have completely honest weights and completely honest measures, so that your days be lengthened on the soil that the LORD your God is giving you.

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Is there a common denominator as to why specifically these 3 mitzvot reward lengthened days?

equilibrium - Difference between freezing point and melting point

I do not understand why for mixtures freezing point is lower than melting point. Are not the two representing the same equilibrium between solid and liquid which we are approaching from two different sides, so why should the temperature at which this happens be different for the two cases?

inorganic chemistry - What's the point of solubility products?

What is the advantage of solubility products, e.g.

LiF(s) ⇄ Li⁺(aq) + F^-(aq) | K = [Li⁺(aq)] * [F^-(aq)] = 0.00184 M² at 25°C (source)

compared to just stating that

Solubility in water = 0.134 g/100 mL (25 °C) (source)

(There's a little difference between (0.00184 M²)^½ = 1.11 g/L and the solubility of 1.34 g/L above; I take it that's because of the difference between activity and concentration?)

It seems to me that solubility products are just a roundabout, complicated way of expressing the concentration of a saturated solution. I suspect that I'm missing something though: otherwise why would people publish long lists of solubility products?

What I read: Wikipedia; all my high school textbooks.

Answer

Solubility products figure prominently in equilibria involving precipitated species. Following is an example that may arise in a practical situation.

Problem: We have 0.01 M ferrous ion in water and we propose adding a base to drive out the iron as hydroxide. We do not want excess base dissolving into the water so we will try magnesium hydroxide. How well will it work?

The proposed reaction is then

$\ce{Fe^{2+} + Mg(OH)2(s) <=> Mg^{2+} + Fe(OH)2(s)}$

$K=\frac{[\ce{Mg^{2+}}]}{[\ce{Fe^{2+}}]}$

Compare this equilibrium constant with:

$K_{sp}(\ce{Mg(OH)2})=[\ce{Mg^{2+}}][\ce{OH^-}]^2=5.61×10^{-12}$ (source)

$K_{sp}(\ce{Fe(OH)2})=[\ce{Fe^{2+}}][\ce{OH^-}]^2=4.87×10^{-17}$ (Ibid.)

So then

$K=\frac{[\ce{Mg^{2+}}]}{[\ce{Fe^{2+}}]}=\frac{K_{sp}(\ce{Mg(OH)2})}{K_{sp}(\ce{Fe(OH)2})}=1.15×10^5$

Since the reaction stoichionmetry implies that the sum $[\ce{Mg^{2+}}]+[\ce{Fe^{2+}}]$ will be constant at the original iron concentration of 0.01 M, we find that the iron level remaining in the water may be reduced by five orders of magnitude, the equilibrium concentration is below $10^{-7}$ molar!

Magnesium hydroxide, despite being supposedly "weak" because of its limited solubility, is actually like a strong base here, displacing the weak iron hydroxide base almost quantitatively -- but, in effect, self-regulating because of that limited intrinsic solubility. The same property applies with respect to most heavy metals commonly found in water; their hydroxide solubilities, like that of iron, are much less than magnesium's. Thus magnesium hydroxide (or, in practice, magnesium oxide which becomes the hydroxide in situ) is a good agent for treating water to remove heavy metals. See here, under "Applications".

clothing - Is it permissible for a man to be seen without a shirt?

In many parts of the United States, it is socially acceptable for a man to be without a shirt while working at a physical activity. Examples might be cutting grass or digging a hole in the summertime. This takes place out of doors and so is generally in the view of the public.

What are Jewish perspectives on this behavior? The head might still be covered by a hat in this situation, but it is not as modest as you would often expect an observant Jew to be. Is it permissible? Would it matter if the shirtless activity was inside ones house instead (say washing dishes)? Were standards on this different at different times? For instance, I have read that in the middle ages, yeshiva students would swim naked in rivers (cannot lay my hand on where I read this right now).

Learning Hebrew

If I have a decent Hebrew knowledge, but not great, what books (i.e. dictionaries, lexicons, etc.) should I have at hand when I'm learning a sefer, such as the Mishneh Torah?

verbs - Is 来おった the 連用形{れんようけい} of くる plus おる → おった?

I came across the following dialogue, which occurs right as the hero arrives:

「やっと来おったか。」

I'm not sure how to parse 来おった. Is it 来{き} + 居{お}る? If so, what exactly does this form mean? Do other verbs have a similar form?

Searching online, I see examples like とうとう来おった and ついに来おった, so my best guess right now is that the nuance is related to とうとう・ついに・やっと.

I've tried looking this up in paper dictionaries and online, but I'm having trouble finding it anywhere, so I thought I'd ask here!

Answer

Yes, [来]{き}おる is a combination of [来]{く}る and [居]{お}る, although 居る in this usage is usually written in hiragana in the modern Japanese. Adding おる after the continuative form of a verb usually means that the speaker is looking down upon the subject of the verb. See sense 〔2〕-[2] in Daijirin and sense 3-① in Daijisen.

grammar - How is the passive form used with を?

I encountered this sentence in my textbook:

いつか、日本人政治家の中にも世界で尊敬され、名前を知られるような人物が現れるようになるには、まず日本国民一人一人の意識を変えるべきなのだろう。

In all cases of passive form that I learned so far, I only ever seen it used with が

Referring to the answer from this post:

Why is を used with passive form here?

I understand that を marks the direct object and が marks the indirect object of the verb.

However I have trouble understanding the difference in meaning between the two particles when I replace them in a sentence:

彼の秘密が知られる His secret will be known

彼は秘密を知られる His secret is known (?)

So can I rephrase 名前を知られるような人物 to 名前が知られるような人物 without a change in meaning? What is the difference?

Unrelated to my main question, does the ような mean "like" in this context? 名前を知られるような人物, "a person like whose name is known"

Answer

彼は秘密を知られる

It's the so-called 持ち主の受身(Possessor Passive?), a kind of 間接受身(Indirect Passive).

[持ち主]が + [所有する物、体の一部など]を + 受身形の動詞

I think it's usually translated as "[Possessor] has [property, body part etc.] done".

彼の秘密が知られる His secret is known
彼は/が秘密を知られる He has his secret known (and he's inconvenienced)

These basically have the same meaning, but the latter can imply that the passivized verb causes inconvenience (or convenience, depending on context) to the subject.

A few examples of 持ち主の受身:

太郎が誰かに足を踏まれた。
Lit. Taro had his foot stepped on by someone (so he was annoyed).
太郎が先生に作文を褒められた。
Lit. Taro had his essay praised by a teacher (so he was happy).
太郎が泥棒に財布を盗まれた。
Taro had his wallet stolen by a thief (so he was inconvenienced).

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can I rephrase 名前を知られるような人物 to 名前が知られるような人物 without a change in meaning? What is the difference?

They mean the same thing, and I don't see much difference in nuance between the two.

does the ような mean "like" in this context? 名前を知られるような人物, "a person like whose name is known"

「名前を知られる人物」「名前を知られるような人物」 basically mean the same thing. The former sounds more direct, and the latter, a tiny bit more indirect or roundabout to me. And.. it may be just me, but the latter, at least in your specific context, sounds to me like "Someone who will/can be famous (in future)" as opposed to "Someone who is (already) famous".

When modelling noise,how do they decide whether additive or multiplicative?

How does one take a decision of whether noise is additive or multiplicative?

acid base - Is there any notion of pH out of solution?

For example, could one define a $\mathrm{pH}$ for pure acetic acid? It's a weak acid in water, but if someone handed you $1~\mathrm L$ of pure acetic acid, what would its $\mathrm{pH}$ be?

Answer

The IUPAC definition of pH is:

The quantity pH is defined in terms of the activity of hydrogen(1+) ions (hydrogen ions) in solution:

$pH = − lg [a(H^+)] = − lg [m(H^+) γ_m (H^+) / m^⦵]$

where a$(\ce{H+})$ is the activity of hydrogen ion (hydrogen 1+) in aqueous solution, $(\ce{H+})$(aq), $γ_m(\ce{H+})$ is the activity coefficient of $\ce{H+}$(aq) (molality basis) at molality m$(\ce{H+})$, and m$^⦵ = 1$ mol kg $^{−1}$ is the standard molality.

So since the definition specifically refers to "aqueous solution", pH is undefined unless an aqueous solution is being considered.

There would be a p[H+] in pure acetic acid based upon the self dissociation of acetic acid, where [H+] is the concentration of hydrogen ions in acetic acid solution, but this is not pH according to the IUPAC definition.

According to Acid-Base Equilibria in Glacial Acetic Acid. III. Acidity Scale. Potentiometric Determination of Dissociation Constants of Acids, Bases and Salts J. Am. Chem. Soc., 1956, vol. 78, pages 2974–2979:

the autoprotolysis constant of acetic acid is calculated to be $3.5 \times 10^{-15}$ (pK = 14.45)

Therefore p[H+] = 7.2 for pure acetic acid.

This value is not a measure of acidity, but simply the concentration of solvated hydrogen ions in pure acetic acid.

women - May a woman shave her legs on Chol hamoed?

The Shulchan Aruch tell us that one may not shave on Chol Hamoed (Orach Chaim 531:2). Does this prohibition apply to women as well? Is a woman allowed to shave her legs on chol hamoed?

minhag - Baal haTanya's donning shel yad seated

I have heard that the baal haTanya put on his t'fila shel yad while seated (as S'faradim do).

• Does anyone have a source for this (or for the opposite: that he put on his shel yad standing)?


• If he did put it on sitting, does anyone know why he did so?

Answer

I don't know whether he personally did, but he does mention this custom in his siddur, and gives the Zohar as the source. (It states that the seated part of davening corresponds to the shel yad, and the standing part - primarily Shemoneh Esrei, I guess - to the shel rosh.)

Dayan Raskin, in his notes to the siddur there, has an extensive discussion of this issue, and cites a source that R. Shalom Dovber of Lubavitch indeed followed this practice. (Present-day Chabad custom, though, is to put both tefillin on while standing.)

filtering - Other techniques like overlap save/overlap add

I know overlap save and overlap add are used for long data sequence filtering. Are there any other similar or better techniques like these?

Answer

The main alternative that I can think of is the hybrid method proposed by Bill Gardner and patented by Lake DSP (now part of Dolby). There appears to be a copy of Gardner's paper here.

Products of Electrolysis of NaCl

I have gone online to see many times that the electrolysis of $\ce{NaCl}$ dissolved in water produces Lye: $$\ce{2NaCl + 2H2O -> 2NaOH + H2 + Cl2}$$ Other times $\ce{NaClO3}$ or some other compound. I just want to know with one solid answer (anyone), what does this reaction produce?

Thank you.

Answer

The one solid answer is that everything you've heard is right, given the appropriate conditions.

If the cathode and anode spaces are properly separated with a porous membrane or a salt bridge, then it is just like that: $$\ce{2NaCl + 2H2O -> \underbrace{2NaOH + H2}_{cathode} + \underbrace{Cl2}_{anode}}$$ If they are not, then the products inevitably mix with each other and react further: $$\ce{2NaOH + Cl2 -> NaCl + NaClO + H2O}$$ or, at elevated temperatures, $$\ce{6NaOH + 3Cl2 -> 5NaCl + NaClO3 + 3H2O}$$ See, chemistry is diverse. Oh wait, and there are more options. Think of the mercury cell.

word choice - What's bugging the Japanese language?

In my JLPT workbook, it has a section which gives a list of idioms that use [虫]{むし}.

仕事{しごと}の虫 (worker bee)

点取{てんとり}虫 (derogatory term for a student who tries too hard)

虫がいい (selfish)

泣{な}き虫 (cry baby)

弱{よわ}虫 (weakling)

腹{はら}の虫がおさまらない (extremely angry)

虫が知{し}らせる (forebode)

虫が好{す}かない (antipathy to)

虫の居所{いどころ}が悪{わる}い (in a bad mood)

娘{むすめ}に悪{わる}い虫がつく (daughter has a lousy boyfriend)

I'm curious about the origins of the "bug" being used in these phrases.

In one sense, some of them are evocative of a sort of character, a "bug" that is present when things are bad, when there's a sense of foreboding, when one feels down. Almost like the bug is an entity that causes trouble wherever it goes.

In another sense, sometimes the person being described is the "bug", as if they have become the "bug" by being weak, by being a drone, by being a whiner, or whatever the case is.

So, do some or all of these uses of 虫 come from the same origin?

What exactly is "the bug" when it's the first sense of a character that is present, such as when it's "in the stomach"?

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Bonus questions:

Is there any connection in terms of origins between the phrases 「腹{はら}の虫がおさまらない」 and 「腹が立つ」?

Is 「仕事{しごと}の虫」 equivalent to "workaholic"? Or does it not have negative connotations of over-work?

Is 「点取{てんとり}虫」 equivalent to "teacher's pet"? Or does sucking up to the teacher having no relation?

Answer

According to the Wikipedia article for 虫:

1. 
   

   体内の架空、仮想の生物の意味で用いるもの。
   Used for the meanings of "imaginary inside the body, imaginary creatures":

   
   

   
   
   

   
   
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     三尸{さんし}の虫: A 庚申{こうしん} belief originating from Taoism from China that inside the bodies of humans there are three bugs.

     
     
   
   
   • 
     

     虫の知らせ: A premonition. As if given a prediction by the inner-body "bugs", a feeling about things that aren't generally known and events that will occur in a distant place.

     
     
   
   
   • 
     

     虫が（の）いい: Only think about oneself (selfish.)

     
     
   
   
   
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     虫の居所が悪い: In a bad mood. This is because it was believed that unless the inner-body "bugs" settled down, the person's mood would worsen.

     
     
   
   
   • 
     

     虫が（の）好かない: Something (you) don't like.

     
     
   
   
   • 
     

     獅子身中の虫: Though a friend, has an element that does harm (treacherous friend.)

     
     
   
   
   • 
     
     

     腹の虫が治まらない: Cannot contain one's anger.

     
     
   
   
   • 
     

     腹の虫が鳴く: The sound which comes out of your stomach when you're hungry.

     
     
   
   

   
   

   
   


2. 
   

   実際の虫のイメージで用いるもの。
   
   Used the way the image of bugs is in reality:

   
   

   
   

   
   
   • 
     

     虫の息: At death's door. Originates from the the fact that breath is small like a small bug or creature, but isn't necessarily used to refer to breath in reality.

     
     
   
   
   • 
     

     悪い虫が付く: To get involved with an unsavory/bad person.

     
     
   
   
   • 
     
     

     虫酸が走る: To be disgusted.

     
     
   
   
   • 
     

     虫も殺さぬ: Obedient and quiet ("wouldn't hurt a fly.")

     
     
   
   
   • 
     

     飛んで火に[入]{い}る夏の虫: Jump into failure, things that are dangerous to oneself. ("like a moth flying into the flame.")

     
     
   
   
   • 
     

     蓼食う虫も好きずき: "To each their own (taste)." From that the leaves of 蓼{タデ} have a characteristic harsh taste and there virtually aren't any bugs which eat them, but there are some which are fond of their taste.

     
     
     
   
   
   • 
     

     一寸の虫にも五分の魂: Even if small, has power and presence ("tread on a worm and it will turn.")

     
     
   
   

   
   

   
   


3. 
   

   他に、嫌な人の意味で使う事もある。
   Otherwise used to refer to a detestable person:

   
   
   

   
   

   
   
   • 
     

     弱虫: A weak-hearted person.

     
     
   
   
   • 
     

     泣き虫: Someone easily moved to tears.

     
     
   
   
   • 
     

     点取り虫: A derogatory term for someone who gets high scores in school exams (I'm guessing it doesn't mean "teacher's pet". Space ALC defines it as "grade grabber" and "obsessed with grades".)

     
     
     
   
   

   
   

   
   

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The Gogen-allguide article for 虫の知らせ seems to back up the Wikipedia article. It says that the 虫 in those expressions refers to the 三尸{さんし}/三虫{さんちゅう} bugs that influence subconscious awareness and feelings/emotions and corroborates that 虫の知らせ, 虫がいい and 腹の虫が治まらない have that etymology.

According to the etymology page for 虫唾が走る, 虫唾 comes from the acidic liquid that comes from your stomach out of your mouth while feeling nauseous in your chest, and the 走る refers to it coming out of your mouth. In other words, something that's as unpleasant as the acidic liquid coming out of your mouth. There are theories of the etymology coming due to saliva that comes up out of your stomach output by parasites as well as acidic liquid due to parasites. For that reason, it can be written as 虫唾 (bug saliva) and 虫酸 (bug acid) and historically has been written as both むしづ and むしず.

The page for the etymology of 腹 says that in ancient times it was thought that one's mind was inside the abdomen/stomach, so it says a lot of words use 腹 to mean emotions/feelings and I think it's likely that might be the root of 腹が立つ rather than 虫.

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EDIT: Removed the Kanjigen section as I wasn't sure of it's accuracy and added a section on 虫唾が走る.

passover seder hagada - Why is Chad Gadya a mix of Hebrew and Aramaic?

Chad Gadya (recited at the end of the Passover seder) is written in a mix of Hebrew and Aramaic. Specifically, most of the verbs are in Hebrew, except for זבין (bought) and אתא (came), and most of the nouns are in Aramaic, except for HaKadosh Baruch Hu, Malach HaMaves (angel of death), and HaShochet (slaughterer). Why?

Answer

The first attestation of Chad Gadya in print is in the Prague Haggadah of 1590 (online source). It is thought by some to have been modelled on a German folk song, and thus composed at such a time as Aramaic was no longer being spoken. This may account for what some have seen as grammatical errors within the text (online source).

An example of a "grammatical error" (taken from that website, which is in Hebrew) is שונרא... דאכלה ("the cat... which ate"). Aside from possible problems with vocalisation, which may be found in other passages in Chad Gadya also, שונרא (cat) is a masculine noun, but אכלה (ate) is a feminine verb. Really, the text should say either שונרתא (which is the feminine word for "cat") or דאכל (which is the masculine verb, "ate").

In any case, an admixture of Hebrew and Aramaic in mediaeval Jewish literature (a time when people are neither speaking Aramaic nor Hebrew outside of liturgical settings) is par for the course, and is the result of both languages being read with roughly equal frequency. Hebrew, the language of scripture and prayer; Aramaic, the language of scholarship.

purim torah in jest - What to do if your husband is muktzeh

My husband is muktzeh (he was born in the eighth month and is now nineteen). Our marriage is going well. However, sometimes on the three-day Yom Tov it becomes difficult that neither I nor anyone else can p̶a̶s̶s̶ ̶h̶i̶m̶ ̶t̶h̶i̶n̶g̶s̶ pass him to things at the table. Is there any solution for this?

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What is the math behind median filter's noise reduction property?

I am interested in understanding the mathematical reason for why does applying a median filter on an image (or signal) result in reduction of noise.

Answer

Intuition: The intuition is this: Your noise is some event or events that are rare, and that when compared to other events, look like outliers that shouldn't really be there.

For example, if you are measuring the speeds of every car on the highway as they pass by you and plot them, you will see that they are usually in the range of say, $50$ mph to $70$ mph. However as you are inspecting your data for your boss, you see that you recorded a speed of $1,000,000$ mph. Not only does this value not make physical sense for the speed of an actual car on a highway, but it also sticks out wildly from the rest of your data. Chalking this event up to some strange measurement error, you remove it, and give the rest of your data to your boss.

However as you continue your measurements day in and day out, you notice that every now and then, you get those wild measurements of speed. For example, over the span of 1 hour, you measure 1000 cars, and their speeds are nicely between $50$ and $70$ mph, however 3 of those have speeds of $23,424$ mph, $12,000,121$ mph, and $192,212,121,329,982,321,912$ mph, breaking not only local state laws, but also those of theoretical physics.

You get tired of continuously having to go in, and remove those errant data points caused by your cheapo-radar by hand. Afterall, your boss is really only interested in the statistics of the speeds, not so much every actual value. He likes to make nice histograms for his bosses.

Those errant and large numbers are a kind of 'noise' you reckon - 'noise' caused by your cheapo-radar that you bought from a shady pawn shop. Is the noise additive white gaussian noise? (AWGN). Yes and no - It's spectrum is wideband and white, but it is temporally rare, sparse, and very localized. It is better referred to as 'salt and pepper' noise, (especially in the image processing domain).

Thus, what you can do, is run your data through a median filter. Your median filter will take a block of say, $5$ speed points, (points 1 to 5), find the median, and spit that value as the 'average' speed. Then it will take the next 5 points, (points 2 to 6), take that median, and spit out this as the average, etc etc.

What happens when you come across one of your faster-than-light speeds?. Let us say that your 5 speeds were [45, 65, 50, 999999, 75]. If you took the normal average, your 'average' speed here will be something quite large. However if you take the median, your 'average' will be 65. Which best approximates the average that you are really trying to measure? The median metric.

Thus, if you filter your data with a median filter, you will be sure to remove those outliers - and you have thus faithfully 'de-noised' your signal. In contrast, if you tried to remove your noise via traditional filtering, (nothing but a moving weighted sum), you will instead 'smear' the error across your data, and not get rid of it.

Math: The math is this: The median measurement is what is referred to as an order statistic. That is, it returns the value of your data, along some point, after it has been ordered. The max and min are also both order statistics - they return the extreme points of your data after it has been ordered. Taking the median also returns the value of your ordered data, but right from the middle.

But why are they different from mean filters? Well, mean-filters compute an average using all the data. If you notice from max, min, and median, you are getting an answer without using all the data. In fact, all the median does is order your data, and pick the value in the middle. It never 'touches' the outliers, like those large speeds that you measured.

This is why median - an order statistic - is able to 'remove' outlier noise for you. Outlier noise segregates itself in front of the median, and the median never comes near it or considers it, while still giving you a nice estimate of central tendency.

halacha - Halachot of Lashon Naki (clean speech)

What is the halachik source, if any, for lashon naki (clean speech)? Is there a portion of Talmud that deals with the specifics? On the surface, it seems to be employed inconsistently, by which I mean there are times where the torah or chazal will go out of their way to use euphemism instead of the proper noun or description (the below example from Pesachim is great). However, other times we find very graphic descriptions for instance, of female genitalia in shir hashirim, (albeit assumedly metaphorical) or tzoah rosachas (gitin 57a) with no compunction for 'lashon naki'.

Answer

The Talmud discusses this issue in Pesachim 3a.

There it brings a number of instances where a verse uses extra letters to avoid saying a negative word. Here's one example that it brings:

The verse by Noach (Genesis 7:8) says to bring into the ark animals that are טהורה (pure) and animals that are אשר איננה טהורה (lit. that are not pure). This is instead of the shorter and more conventional טמאה (impure). I know this doesn't work out in translation so well, but in Hebrew it uses 8 extra letters to avoid saying 'impure'.

See there for more proofs and examples.

tefilla - How do I say vidui in Selichos in a meaningful way?

We say vidui three times in selichos. Many words are uttered in a relatively short time. How can we do this in a meaningful way that is not "vidui peh"?

I have heard tell of one of the gedolei Torah that in the vidui of everyday Tachanun, he said only one word of the “oshamnu, bogadnu” prayer. Is that a derekh for non-gedolim?

Answer

1. Learn the meaning behind the vidui before saying it.


2. Buy a sefer that translates them or an interlinear siddur, and daven from that.


3. Write your own commentary to them whilst learning the meanings.

physical chemistry - Is there any formula that can be used to find loss of mass due to binding forces in atomic and sub atomic particles?

Atomic weight of Br-79 is 79.641 if you add the masses of protons and neutrons. However, in periodic table, it is less than the value given here. How is the difference arrived at for all the elements listed in the periodic table?

molecular orbital theory - Methane T2 SALCs

So I have a question on the form of the $T_2$ SALCs of methane. Below I show the $T_d$ character table and the accompanying reducible representation for the sigma framework (using, in the case of methane, the $4$ $1s$ H orbitals).

It is easy to show, and many people have, that the irreducible representations contained therein are $A_1$ and $T_2$.

If we then perform the projection operation for all of the elements of $T_2$, I get the following:

(The X's are intended to be "Chi's" here, signifying the $4$ $1s$ H orbitals that go into the procedure).

Meaning that, if we take the first line for instance, and perform the sum in the projection operator, we get: $$ 3\chi_1-\chi_2-\chi_3-\chi_4 $$

As our first un-normalized $\phi_t$ SALC. I can easily see by intuition how we can obtain the (again, not normalized) known SALCs for a $\sigma$ framework tetrahedron from this: $$ 3\chi_1-\chi_2-\chi_3-\chi_4 = $$ $$ \chi_1-\chi_2+\chi_3-\chi_4 $$ $$ \chi_1+\chi_2-\chi_3-\chi_4 $$ $$ \chi_1-\chi_2-\chi_3+\chi_4 $$

What I do not understand, is how we can derive this result without intuition. If I perform any number of Schmidt orthoganalizations using the other 3 rows of the projection operator table, I always end up with an exceedingly strange SALC, regardless of normalization and inclusion of overlap integrals $\chi_i{\times}\chi_j = S_{ij}$.

Is there any mathematical tool that can be used to generate these known SALCs from the one above?

Again, let me stress, I can clearly see the intuitive path, but I always rest easier when I know there is a reproducible, rigorous theory that leads there.

Answer

UPDATE: added more detail for those without access to the referenced text.

As noted in the comments, the details of this process can be found in "Group Theory and Chemistry" by David M. Bishop (Courier Corporation, 1993) p. 238-9. Here's a summary:

Following the same process that you started, you can get two other projections as (using your notation):

$-\chi_1+3\chi_2−\chi_3−\chi_4$

and

$-\chi_1−\chi_2+3\chi_3−\chi_4$

All three of these normalize with a factor of $\frac{1}{\sqrt{12}}$.

The challenge with degenerate orbitals is that there is an infinite number of linearly independent combinations that will combine to give the desired $T_2$ symmetry properties. Schmidt orthogonalization can be used to generate an orthogonal set, but there is an infinite number of those as well.

To prove that the canonical set is valid, one need only show that all three are linear combinations of the above projections and that they are orthogonal to each other. But to derive the canonical set without prior knowledge, we use the procedure below.

We want a set that is orthonormal and matches up with the central atomic orbitals. That is, each has symmetry that matches a member of the $p$ orbital set of the central atom. First, we set the $t_2$ central atom orbitals as $p_x$, $p_y$ and $p_z$. Then we consider that we must be able to make the hybrid orbital that coincides with each ligand bond from a linear combination of the $s$ and $p$ atomic orbitals. This is essentially a statement of the principle underlying the concept of hybridization. Furthermore, since the $s$ orbital only adds magnitude, not direction, an unnormalized hyrbid orbital can be made from a linear combination of $p$ orbitals only. Finally, any member of the $t_2$ ligand group orbitals must similarly be able to be constructed from a linear combination of the central atom $p$ orbitals.

Thus, $(3\chi_1-\chi_2−\chi_3−\chi_4)/\sqrt{12} = (a_1^2+b_1^2+c_1^2)^{-1/2}(a_1p_x+b_1p_y+c_1p_z)$ for some $a_1, b_1, c_1$ and likewise for the other two projections (adding a minus sign where necessary for directionality with respect to the positive lobes of the $p$ orbitals).

We can then take advantage of the linearity of the symmetry operators to set up equations and solve for $p_x$, $p_y$, and $p_z$ in terms of $\chi_1$, $\chi_2$, $\chi_3$ and $\chi_4$, and the coefficients of those solutions are the coefficients for the H1s orbitals in each of the three $t_2$ ligand group orbitals.

For example, let $\chi_1$ be the hybrid orbital oriented in the positive $x,y$ and $z$ octant of Cartesian space, and let the $C_{3a}$ axis run through it. Thus,

$O_{C3a}(\chi_1)=\chi_1$

$O_{C3a}(\chi_2)=\chi_3$

$O_{C3a}(\chi_3)=\chi_4$

$O_{C3a}(\chi_4)=\chi_2$

Because the operator is linear, we now have that

$O_{C3a}[(3\chi_1-\chi_2−\chi_3−\chi_4)/\sqrt{12}]=(3\chi_1-\chi_2−\chi_3−\chi_4)/\sqrt{12}$, i.e. this projection is unchanged by that transformation because $\chi_2$, $\chi_3$, and $\chi_4$ are equivalent in the expression.

Therefore, we can further state that

$O_{C3a}[(a_1^2+b_1^2+c_1^2)^{-1/2}(a_1p_x+b_1p_y+c_1p_z)]=(a_1^2+b_1^2+c_1^2)^{-1/2}(a_1p_x+b_1p_y+c_1p_z)$

We can also determine by inspection that $O_{C3a}(p_x)=p_z$,$O_{C3a}(p_y)=p_x$, and $O_{C3a}(p_z)=p_y$. Therefore, we also have that

$O_{C3a}[(a_1^2+b_1^2+c_1^2)^{-1/2}(a_1p_x+b_1p_y+c_1p_z)]=(a_1^2+b_1^2+c_1^2)^{-1/2}(a_1p_z+b_1p_x+c_1p_x)$

and we can conclude that $a_1=b_1=c_1$. Thus,

$(3\chi_1-\chi_2−\chi_3−\chi_4)/\sqrt{12}=(p_x+p_y+p_z)/\sqrt{3}$.

Repeating this for the other symmetry transformations (for example $C_{3b}$ and $C_{3c}$) gives a system of equations that can be solved to yield:

$p_x=\frac12 (\chi_1−\chi_2+\chi_3−\chi_4)$

$p_y=\frac12 (\chi_1−\chi_2-\chi_3+\chi_4)$

$p_z=\frac12 (\chi_1+\chi_2-\chi_3−\chi_4)$

The coefficients of $\chi_1$, $\chi_2$, $\chi_3$ and $\chi_4$ in these three expressions are the coefficients of the H1s orbitals to each canonical $t_2$ ligand group orbital.