thermodynamics - What do the horizontal lines in a P-V phase diagram mean?

I have been studying phase diagrams of pure substances, and for a substance such as carbon dioxide for example, it's diagram looks something like this:

The horizontal lines in the liquid phase puzzle me. It seems if we shrink the specific volume by a certain amount, the pressure change is much much less. This doesnt seem to be what is observed in reality (liquids have a very high bulk moduli and are generally considered incompressible), which would require a large pressure change for a less change in specific volume. The solid phase has vertical lines, which seems to be true, but the liquid portion baffles me.

Can someone please help me understand what I'm missing here?

Is the volitional form of i-adjectives often used?

According to this question the volitional form of i-adjectives is used quite often -- on a daily basis. But I almost never hear it. I almost see it exclusively in books (or written documents). And if it would be used in a dialogue it would almost always be used by a man.

On the other hand, I hear quite often adj-i+でしょう.

So my question is the ～かろう form that much used?

Answer

This form is classified as modern 口語 (as opposed to 文語), but it sounds old-fashioned nevertheless. It's not something we hear every day. We mostly see this form in fictional old person's speech (like in the original question) or in a few fixed expressions like 安かろう悪かろう. よかろう is often used by a pompous, old and/or noble person in fiction. If someone around you used よかろう in reality, it's likely to be a joke.

By the way, is that form really called the "volitional" form while the meaning is ～だろう? It appears similar to 行こう/見よう/食べよう, but the meaning is totally different.

halacha - Does closing a browser with His name count as a sin?

Possible Duplicate:

Hashems name on device
Is it permissible to erase the name of G-d from an E-reader?
What are the practical limits of shaimos in the common era?

Forgive me if I get some of the conventions wrong in this question; I'm a non-Jew. After listening to the "This American Life" podcast, specifically episode #332. I was struck by the story of young Shalom and how his rabbi would not permit him to write his name on papers. My understanding of the situation is that it is a sin to destroy the name of God unless it is done in an approved way.

Given that the internet contains many places where the name of God is referenced, is the act of closing the browser a sin since it is technically removing that word from the screen? I'm assuming that since the information still exists somewhere (on the remote side server) that the information hasn't technically been destroyed. However, at some point the pages will be revised, the wording will change, and perhaps the name of God will be removed in those future pages.

Is this a huge grey area in the realm of shemos or am I not looking at this from the right angle?

parshanut torah comment - does one have to take a Midrash/Aggadah literally?

Does one have to take a Midrash/Aggadah literally?

nomenclature - How to name binary (inorganic) compounds given their chemical formula, and vice-versa?

I wish to understand how to name binary (inorganic) compounds when given their formula. When I am a given compound like $\ce{B2F2}$ or $\ce{N2O4}$, I have little to no clue on how to write their chemical names. Similarly, I also trip up when trying to convert a given chemical name - say diboron difluoride - to its chemical formula.

Moreover, I have seen that a few times we do not need the numeric prefixes - as in lithium oxide or magnesium chloride - but sometimes we do - as in dinitrogentetroxide or iodine monochloride. So, I also need help understanding when to include numerical prefixes and when to not.

Please limit the answer to simple, binary, ionic and covalent compounds, and exclude hydrocarbons.

Answer

Prerequisites

These are the necessary prerequisites for this topic. If you're uncomfortable with any, please first head over to the corresponding links before continuing.

1. Chemical symbols are a shorthand method of representing an element. Instead of using the full name of an element, we simply refer to it with one or two letters. $\ce{N}$ for nitrogen and $\ce{Na}$ for sodium. More details on the Wikipedia page.



2. Polyatomic anions/Radicals: anions with more than one element, like nitrate ($\ce{NO3-}$) or sulfate ($\ce{SO4^2-}$). More details on the Wikipedia page.


3. Oxidation state: is an integer or decimal number assigned to an element in a chemical species. It is a tool that helps us do nomenclature easily. Read a detailed introduction here.


4. Ionic and covalent compounds: You must understand what ionic and covalent compounds are. You must also know the few elementary examples of each. For example, you should know that $\ce{N2O4}$ would be a covalent compound, while $\ce{NaCl}$ would be ionic. Here's an introduction by LibreTexts if you need a refresher.

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Introduction

There are two separate cases here for ionic and covalent compounds.^[1]. Some of the logic overlaps, but some does not, and care must be taken to avoid using one's rules for another.

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Naming an ionic compound from its formula

1. Name the cation and then the anion. ("sodium sulfate", but not "sulfate sodium"). (How to identify the cations and anions in an ionic compound? The cation is usually a metal and the more electropositive element, while the anion is a non-metal and more electronegative element)


2. Keep everything lowercase (details) ("sodium sulfate", but not "Sodium Sulfate" or "sodium Sulfate" or "Sodium sulfate")


3. Do not apply numeric prefixes to either the cation or the anion. ("sodium sulfate", but not "disodium sulfate" or "sodium monosulfate")


4. Remember the suffixes for anions. The single atom anions of group 15, 16, and 17 have the suffix ending "-ide". Examples: fluoride, oxide and phosphide. However, polyatomic anions generally do not end in an -ide. See the Appendix for details.


5. Transition metal cations (and some p-block metals) also need their oxidation-state to be specified in parentheses, as they exhibit variable oxidation states. Hence, "mercury(II) chloride", but not "mercury chloride". Notice that the oxidation state is denoted in capital Roman numerals.^[2]

Let's take an example: $\ce{MgCl2}$. We can identify it's composed of magnesium and chlorine. Thus, the name would be magnesium chloride – in all lowercase and with the cation (metal) preceding the anion (non-metal). There is no need to denote the oxidation state as magnesium isn't a transition metal.

Examples:

$\ce{CsF}$, $\ce{NaNO3}$, $\ce{Al2(SO4)3}$, $\ce{FeCl2}$, $\ce{Pt3(PO4)4}$

Answers: (hover to peek!)

caesium fluoride, sodium nitrate, aluminium sulfate, iron(II) chloride or ferrous chloride, platinum(IV) phosphate

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Writing the formula for an ionic compound from its name

1. First write the cation and then the anion ($\ce{KBr}$ but not $\ce{BrK}$)


2. Use parentheses to denote multiple polyatomic anions ($\ce{Mg3(PO4)2}$ but not $\ce{Mg3PO42}$). Avoid them for a single polyatomic anion ($\ce{Na2SO4}$ but not $\ce{Na2(SO4)}$)


3. Use the trick of cross-transferring oxidation states between the ions to determine the count of each cation and anion involved. This trick works because the formula should denote an electrically neutral species. (you can verify this mathematically) So, to write the formula for aluminium sulfate:
   
   
   Note that:
   
   
   
   • In case both oxidation states have a common factor, you should cancel them. Example: magnesium oxide:
     .
   
   
   • drop the number 1. Hence, potassium sulfide is written as $\ce{K2S}$ but not $\ce{K2S1}$.
   
   
   
   

Examples:

potassium phosphate, calcium chloride, magnesium cyanide

Answers: (hover to peek!)

$\ce{K3PO4, CaCl2, Mg(CN)2}$

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Naming a covalent compound from its formula

1. Name the less electronegative element and then the more electronegative element ("carbon monoxide" but not "oxygen monocarbide")


2. Apply suffixes to anions in exactly the same way as we did for ionic compounds. ("sulfur hexafluoride" but not "sulfur fluoride") Also, keep the name all lowercase as before.


3. Use numerical prefixes.^[3] Hence "dinitrogen tetroxide" for $\ce{N2O4}$ but not "nitrogen oxide". Here's the first ten suffixes: $$\begin{array}{|c|c|} \hline \mathrm{prefix} & \mathrm{number}\\ \hline \mathrm{mon(o)} & 1 \\ \mathrm{di} & 2 \\ \mathrm{tri} & 3 \\ \mathrm{tetr(a)} & 4 \\ \mathrm{pent(a)} & 5 \\ \mathrm{hex(a)} & 6 \\ \mathrm{hept(a)} & 7 \\ \mathrm{oct(a)} & 8 \\ \mathrm{non(a)} & 9 \\ \mathrm{dec(a)} & 10 \\ \hline \end{array}$$ Note that:
   
   
   
   
   • the letter in parentheses is dropped when the anion begins with a vowel ("tetroxide", but not "tetraoxide")
   
   
   • we do not specify the mono- prefix for the first element ("carbon tetrachloride" but not "monocarbon tetrachloride")
   
   
   • we can construct similar numerical prefixes for larger counts by using the Greek system. Example: "undeca" for 11. Look at a larger list on Wikipedia.
   
   
   
   

Let's take an example: $\ce{P4O6}$. In one molecule of $\ce{P4O6}$, we can see that it has four atoms of phosphorus and six atoms of oxygen. So, its name should be of the form "Xphosphorus Yoxide". The table of numerical prefixes tells us that we should use the prefix "tetra" for nitrogen and "hexa" for oxygen. Since the name "oxygen" begins with a vowel, we shall write "hexoxide" (and not "hexaoxide"). Thus, the correct name for this chemical formula is "tetraphosphorus hexoxide".

Examples:

$\ce{CO2}$, $\ce{P4O10}$, $\ce{N2O}$, $\ce{N2S5}$

Answers: (hover to peek!)

carbon dioxide, tetraphosphorus decoxide, dinitrogen monoxide, dinitrogen pentasulfide

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Writing the formula for a covalent compound from its name

This is much simpler from the previous case, rather it follows an exactly reverse process.

We'll just take a look at two examples:

• boron triiodide: we see that its formula would be: $\ce{B_$x$I_$y$}$. Now, $x=1$ since boron lacks any numerical prefix, and $y=3$ due to the "tri" prefix. Hence, the formula is $\ce{BI3}$.



• dinitrogen pentoxide: we see that its formula would be: $\ce{N_$x$O_$y$}$. Now, $x=2$ and $y=5$ due to the "di" and "pent(a)" prefixes. Hence, the formula is $\ce{N2O5}$.

Examples:

hydrogen bromide, iodine heptafluoride, diboron hexahydride

Answers: (hover to peek!)

$\ce{HBr}$, $\ce{IF7}$, $\ce{B2H6}$

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Naming of hydrogen compounds

Several hydrogen compounds have non-systematic names that have persisted through the years in standard nomenclature and are now well recognized. Note that for alkali metals and alkali earth metal hydrides, the name is simply "metal + hydride", like sodium hydride, on the basis of rules described earlier.

However, covalent hydrides have varying names. There are not much rules around them, but rather "patterns" that the following list would show you:

1. Group 13: $\ce{BH3}$: borane, $\ce{AlH3}$: alumane, $\ce{GaH3}$: gallane, etc. Pattern: half of the element name suffixed by "-ane".


2. Group 14: $\ce{CH4}$: methane, $\ce{SiH4}$: silane, $\ce{GeH4}$: germane. Pattern: half of the element name suffixed by "-ane". Methane is a remnant of organic chemistry, and is a part of nomenclature of hydrocarbons.


3. Group 15: $\ce{NH3}$: ammonia, $\ce{PH3}$: phosphine, $\ce{AsH3}$: arsine, $\ce{SbH3}$: stibine, $\ce{BiH3}$: bismuthine. Pattern: half of the element name suffixed by "-ine". "Ammonia"'s origins, though, are a bit more interesting (read the Wikipedia page).


4. Group 16: $\ce{H2O}$: water, $\ce{H2S}$: hydrogen sulfide, $\ce{H2Se}$: hydrogen selenide, $\ce{H2Te}$: hydrogen telluride. Note that while "oxidane", "sulfane", "selane", etc. are acceptable, in the case of oxidane, that name is only used when denoting water derivatives. Read Do chemists refer to water as "dihydrogen monoxide"? and Does water have a chemical name?.


5. Group 17: they are simply named as "hydrogen halide". Example: "hydrogen bromide" $\ce{(HBr)}$. It is not named "hydrogen monobromide", as you may believe from earlier examples, and that it because hydrogen can only form a single halide with the halogens (see Note 3 below).

The curious students would also notice that – when writing chemical formulae – for groups 13, 14, 15, the hydrogen atom is written after the group atom $\ce{(NH3)}$, while in groups 16 and 17, it is written before the group atom $\ce{(H2O)}$. See this answer to understand why it is so.

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Notes:

1. It is true that no compound is 100% ionic or 100% covalent. The above rules for "ionic compounds", thus, apply to compounds with dominant ionic character. Similarly, rules for "covalent compounds" apply to compounds with dominant covalent character.


2. Another way to write such a name is to use an "-ic" suffix for a higher oxidation state and "-ous" suffix for a lower oxidation state. As in "mercuric chloride" for "mercury (II) chloride". But, according to the IUPAC Recommendations 2005, it is no longer acceptable.


3. Why are numerical prefixes necessary? Note that in covalent compounds, a given anion can be present in more than one count. For example, the $\ce{F}$ in $\ce{BrF_x}$ can be present as $\ce{BrF}$, $\ce{BrF3}$, or even $\ce{BrF5}$. Hence, it is necessary to indicate if it is a monofluoride, a trifluoride, or a pentafluoride.


4. Several covalent compounds and ionic compounds have their own unique, common/trivial names. These names do not follow any systematic rules and are based on the source (location/discoverer) or properties of that compound. Learning these common names and their formulae comes by experience over time. Examples include: diborane $\ce{(B2H6)}$, Epsom salt $\ce{(MgSO4)}$, oil of vitriol (sulfuric acid), etc. Read more on the Wikipedia page.

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Appendix: polyatomic anion names

Apart from the regular -ide suffix for monoatomic anions, there are some more suffixes for the polyatomic anions.

• most pseudohalides retain the "-ide" suffix. (except cyanate derivatives)


• the other two suffixes are "-ate" and "-ite". "-ate" is used when the central atom is in a higher oxidation state, whereas "-ite" is used for the lower oxidation state.


• the "per" prefix is used when the central halogen atom is in its highest oxidation state, while "hypo" is used when it is in its lowest oxidation state.

A few examples would make these rules clearer:

1. Sulfate $(\ce{SO4^2-})$ and sulfite $(\ce{SO3^2-})$: both are sulfur and oxygen anions, but in sulfate, sulfur has higher oxidation state as compared to that in sulfite. Similar case applies to nitrate, nitrite and phosphate, phosphite.


2. Hypochlorite $\ce{(ClO^-)}$, chlorite $\ce{(ClO2^-)}$, chlorate $\ce{(ClO3^-)}$, perchlorate $\ce{(ClO4^-)}$: have chlorine in increasing oxidation numbers. Similar series exist for other halogens (except fluorine).

Of course, there are many more polyatomic anions in chemistry, but these ions are relevant to our discussion at an elementary level.

talmud gemara - How do we understand the idea of something missing from the mishnah חסורי מיחסרא והכי קתני?

The gemoro often reconciles the argument of a mishnah with other evidence by saying חסורי מיחסרא והכי קתני - there is something missing from the mishnah and this is how you must learn it. See for example Shabbos 37a at the top.

How do we understand this idea of something missing from the mishnah?

Could it mean

(a) “the mishnah is taught in a short form to make it easy to remember and if you examine it, it is obvious that something is lacking” or

(b) the mishnah is actually lacking a bit

or (c) some other explanation?

halacha - Tefilin with obstruction on hand

How should one tie his shel yad on his hand if his finger(s) have something on them, such as a splint for a broken bone in the left middle finger?

Answer

The Rama rules (OC 27:4 based on Teshuvat HaRashba 1:827) that there is only a problem of a chatzitza (separation between the tefillin and the skin) under the boxes not the straps. The Mishna Berura there (sk 16) notes that most later authorities only accept this for the parts of the straps that do not directly relate to the tying (ie. the parts between the box and the knots). In your case, where the potential chatzitza is very far away from the box, it shouldn't be much to worry about.

Furthermore, Rav Ovadia Yosef rules (Yabia' Omer 2 OC 2) that one need not remove his watch when putting on his tefillin because it is far enough away from the box. Seemingly he would agree that in your case (especially since there is a medical need) you may be lenient and not worry about a chatzitza.

organic chemistry - Why alkanes containing even number of carbons can be packed more efficiently than alkanes with odd number of carbon atoms?

Variation of boiling and melting points of alkanes with increase in the number of carbons

The odd-numbered alkanes have a lower trend in melting points than even numbered alkanes. This is because even numbered alkanes pack well in the solid phase, forming a well-organized structure, which requires more energy to break apart. The odd-numbered alkanes pack less well and so the "looser" organized solid packing structure requires less energy to break apart.

Source: https://en.wikipedia.org/wiki/Alkane#Melting_points

Why is that the alkanes containing an even number of carbons can be packed more easily compared to the alkanes containing an odd number of carbons?

Both types of alkanes can be laid next to each other; hence, why should the number of carbons even matter?

---

I started drawing and noticed something.

The diagram makes it pretty obvious that the alkanes with odd numbers cannot be packed efficiently.

I am not sure if this is the correct answer.

halacha - Shaliach Tzibbur missed out one or more blessings in the repetition of the amidah. What to do later?

What should one do if the Shaliach Tzibbur missed out one or more blessings in the repetition of the amidah and it was only pointed out to him after he had finished?

Does he have to repeat the amidah correctly, or do we say that, since nowadays he doesn't acquit anyone of their obligation to pray, he does not have to repeat?

Answer

Shulchan Aruch (OC 126:3) rules that for any mistake that would require an individual to repeat Shemonei Esrieh, if the Chazzan made such a mistake in his repetition he would have to say it over again. (There are some exceptions, but they are not relevant to our question.) The Sefer Shegiyos Mi Yavin (a book dealing with the laws of mistakes that occur during davening and brochos, 15:14) brings as an example of this if he skipped out one of the brochos. (In such a case, he writes that they would say kedusha again, and the congregation would say modim derabanan, and he brings several opinions regarding birkas kohanim).

image compression - What is the least JPG-compressible pattern? (camera shooting piece of cloth, scale/angle/lighting may vary)

I am trying to design a cloth that, from the point of view of a camera, is very difficult to compress with JPG, resulting in big-size files (or leading to low image quality if file size is fixed).

It must work even if the cloth is far away from the camera, or rotated (let's say the scale can vary from 1x to 10x).

Noise is quite good (hard to compress), but it becomes grey when looking from far, becoming easy to compress. A good pattern would be kind of fractal, looking similar at all scales.
Foliage is better (leaves, tiny branches, small branches, big branches), but it uses too few colors.

Here is a first try:

I am sure there are more optimum patterns.
Maybe hexagon or triangle tessellations would perform better.

JPG uses the Y′ Cb Cr color space, I think Cb Cr can be generated in a similar way, but I guess it's better to not use uniformly the full scope of Y' (brightness) since camera will saturate the bright or dark areas (lighting is never perfect).

QUESTION: What is the optimum cloth pattern for this problem?

hashkafah philosophy - Books on the significance of the months in the Jewish calendar

I am looking for books/sefarim (Hebrew or English) that discuss the different months of the Jewish year, and their overall significance in relation to:

• Zodiac Signs



• Tribes


• Chagim


• Animals


• Tanach/Chazal


• Jewish Philosophy/Machshava


• Anything else

Any recommendations would be appreciated.

Answer

"The Wisdom of the Hebrew Months", by R' Zvi Ryzman sounds like what you're looking for. I haven't read it myself, but I've heard good things.

physical chemistry - How should I think about potential energy surfaces for reactions of complex systems?

I've recently started doing some computational chemistry, studying the reaction dynamics of some moderately complex organic and inorganic reactions. I'm doing things like finding maxima, minima, TS's, saddle points, geom. optimizations, and finding conformational isomers of all of the above. I'm really enjoying myself.

One thing I would like to better understand, though, is how to think of the potential energy surface (PES) of these sorts of systems. The way I see it, a PES is just a potential energy profile (PEP) with one or more dimensions beyond energy and reaction coordinate. I understand that you cannot really compute a complete PES for a complex system. Most of the PES's I've seen are for simple systems like this solvent study of an SN2 reaction:

(R. Otto et al. 2011, Nature Chemistry 4, 534-538)

This is simple enough to understand. They have added the dihedral angle as another dimension of their picture of the reaction dynamics. But what about a large system, especially a non-rigid one? Since there are so many more possible ways the system can move, does that mean its 'true' PES is polydimensional? I like to think of these mechanistic studies of big reactions as us 'exploring the PES', even though we cannot see the whole thing. How should I think about this surface? Am I understanding this concept properly?

Answer

In order to understand what the PES really is, it is useful to see where this concept comes from.

A system of $M$ nuclei and $N$ electrons should be described by a multidimensional wavefunction $\Psi(\vec{r}_1,\dots,\vec{r}_N,\vec{R}_1,\dots,\vec{R}_M)$, where $\vec{r}$ denotes electronic coordinates and $\vec{R}$ denotes nuclear coordinates (we neglect spin for simplicity). Within the Born-Oppenheimer approximation, the total wavefunction is split in an electronic part $\phi$ and a nuclear part $\chi$: $$ \Psi(\vec{r}_1,\dots,\vec{r}_N,\vec{R}_1,\dots,\vec{R}_M) = \phi(\vec{r}_1,\dots,\vec{r}_N;\vec{R}_1,\dots,\vec{R}_M)\chi(\vec{R}_1,\dots,\vec{R}_M) $$ where the electronic wavefunction depends parametrically on nuclear positions (as it will be clear in a moment).

If you inject the Born-Oppenheimer ansatz in Schrödinger equation for a system of interacting nuclei and electrons and you integrate out electronic degrees of freedom you get an equation for the nuclear wavefunction only $$ \left[ -\sum_I \frac{1}{2M_I} \nabla^2 + \sum_{I

Since a multi-dimensional function is impossible to visualize, usually we study the PES by considering few interesting degrees of freedom (as the O-C distance and O-C-I angle in your example). Therefore, as you say, you can think as if you are exploring the PES locally and in a reduced space.

---

ADDITIONAL INFORMATIONS

Since the nuclear wavefunction is sharply picked, (heavy) nucley can usually be considered as classical particles. Thus instead of the nuclear quantum Hamiltonian $$ H_n = -\sum_I \frac{1}{2M_I} \nabla^2 + \sum_{I

I never looked to this into details but I think computational programs climb the PES uphill from the initial and final state of your system (i.e. they follows -$\vec{F}_I$) in order to find the TS.

halacha - May a non-Jew have an abortion?

Are non-Jews permitted to have abortions? (Consider the gemara in Sanhedrin 57b where "a baraita brings in the name of Rabbi Yishmael that a Ben Noach gets capital punishment if he intentionally causes an abortion, which he derives from a pasuk. Rashi takes the simple understanding of the gemara that this prohibition applies only to a non-Jew, whereas for a Jew the prohibition of murder only applies to a baby once he/she is born.")

Edited in response to msh210's comment: I'd be interested in knowing both whether non-Jews may have abortions and, perhaps more interestingly, whether they may perform them (see the source above). Would there be any special considerations for a non-Jew performing an abortion on a Jew?

Answer

Are non-Jews permitted to have abortions? According to Sefer Sheva Mitzvot Hashem only if a noahide woman is in risk of dying in childbirth (due to her fetus). The base for this is Rambam in Rotseach u'Shmirat Nefesh, Perek alef Halacha 9 which reads:

לפיכך הורו חכמים שהעוברה שהיא מקשה לילד--מותר לחתוך העובר במעיה, בין בסם בין ביד: מפני שהוא כרודף אחריה להורגה. ואם משהוציא ראשו, אין נוגעין בו, שאין דוחין נפש מפני נפש, וזה הוא טבעו של עולם.

Regarding if they are permited to perform abortions, again, only if the main intention is to save the mother (because it is as if the fetus is persuing her to kill her).

word choice - Respectful way to say "policeman"

Let's say I want to call a policeman, or I am in a n-person conversation involving a policeman and I want a word to refer to the policeman. And let's say I want a respectful word.

I believe おまわりさん could sound a bit insulting (low rank).
Should I say 警察さん?

Is there a more respectful way to call a policeman, who actually might be an officer?

organic chemistry - Ether cleavage with conc HBr

I've been asked to draw the mechanism by which benzene with $\ce{Me}$ on position 1 and $\ce{OMe}$ on position 2 goes to benzene with $\ce{Me}$ on 1 and $\ce{OH}$ on 2 by reaction with concentrated $\ce{HBr}$.

I'm really unsure as to what is going on, I think its probably most likely that $\ce{Br}$ acts as a nucleophile and attacks the $\ce{C-O}$ $\sigma^*$ and then $\ce{OH}$ attacks the $\ce{C-Br}$ $\sigma^*$ but it doesn't seem like a likely pathway as $\ce{OMe}$ has a higher pKaH than $\ce{Br}$ and substitutions don't occur at $\mathrm{sp^2}$ centres.

Answer

Cleavage of ethers using strong acids (classically $\ce{HI}$ but $\ce{HBr}$ should work as well) can proceed by either an $S_N1$ or $S_N2$ mechanism. In this case the cation formed would be primary or phenyl, neither of which are stable, and so the reaction proceeds via an $S_N2$ mechanism.

The oxygen is protonated in an equilibrium reaction. The bromide ion then attacks at the least hindered carbon and the $\ce{C-O}$ bond breaks in a concerted $S_N2$ mechanism.

(source)

coordination compounds - Why is hexafluoridocobaltate(III) the only common high-spin cobalt(III) complex?

Almost all $\ce{Co^3+} (\mathrm{d^6})$ complexes are low spin, including $\ce{[Co(H2O)6]^3+, [Co(ox)3]^3–, [Co(NH3)6]^3+}$ and $\ce{[Co(CN)6]^3–}$. The only common high-spin cobalt(III) complex is $\ce{[CoF6]3–}$. Why is the hexafluorido complex in a high-spin state?

words - What are the ways to express someone's condolences?

All is in the title, what are the ways to express someone's condolences when somebody died.
I know お気の毒に but is there something else?
What can/should you say to friends? To collegues? To bosses? etc.

Answer

There are some fixed expressions such as:

• ご愁傷さまです


• お悔やみ申し上げます

Both are formal, and can be used regardless of the relationship; you can say this to friends/colleagues/bosses. "ご愁傷さま" is sometimes used when nobody dies (e.g. ironically when somebody is disappointed) while "お悔やみ申し上げます" is almost always limited to the context of condolences, but both are perfectly fine. Additionally:

• ({at least originally} In Buddhism) ご冥福をお祈り[します/申し上げます]

---

お悔やみ（おくやみ） or 弔辞 is the translation for condolence, so if you need something more than fixed expressions, you can search with these words --- many people don't know what to say to somebody experiencing a great loss, and seek for guidance. Additionally, it is common to send a telegram of condolence ("弔電") for funerals (when one can't attend), and expressions for these might also be worth reading.

frequency domain - What's the meaning of a complex zero/pole?

I have been studying signal processing and control for a while now, and I use Laplace and Fourier transforms almost everyday. Also another tools such as Nyquist or Bode plots.

However, I had never thought of this until today: what is the physical meaning of a complex number when dealing with frequencies?

This may sound silly, but I was asked this question and I didn't know what to answer. Why do we talk about $j\omega$ and not just $\omega$ in, for example, Fourier transforms and Bode or Nyquist plots? What is the physical sense of the real and imaginary part of a zero or a pole in the Laplace domain?

Answer

We usually talk of $j\omega$ when we're also interested in the Laplace transform of a signal / system, but want to just talk about the frequency response.

The physical meaning of the imaginary part is that it refers to purely sinusoidal signals and are constant "amplitude". The real part refers to signals for which the "amplitude" decays or grows exponentially.

parshanut torah comment - What is the difference in meaning between לתור and לחפר with regards to spying the land?

I am combining concepts from this week's Torah and Haftarah:

In the Torah portion, it says with the spies that they went לתור את הארץ (Bamidbar 13:16). With Yehoshu'a it says לחפר את הארץ (Yehoshu'a 2:2). Both of them spied the land. But, I assume that there is a difference in meaning of these two words, that hints at why Moshe was unsuccessful, and Yehoshu'a was successful. (I'm aware that the obvious reason is that Yehoshu'a learned from Moshe and didn't make the same mistakes, and that we were dealing with a different group of people and mindset. I am seeking a reason for the success that may be hinted to in the meaning / choice of these two words.)

avot patriarch fathers - Why does Rashi not comment on the repetition of the word “shono” in the age of Yishmoel?

Rashi comments on the repetition of the word “shono” in the ages of both Soroh Braishis 23 (1) and Avrohom Braishis 25 (7). Why is there no comment for the age of Yishmoel which also repeats “shono” Braishis 25 (17).

Answer

We find 4 ways in which the amount of years they lived are presented:

1. 
   

   (Breshit 5:6 onwards) From Sheth to Noach (Including Noach): "And all their days were..."

   
   


2. 
   

   (Breshit 25:17) Yishmael: "And the years of his life were..."

   
   

None of these have anything special that invites a question. You may ask why the change between days and years but we saw Rashi in Breshit 24:25 that days may mean a year.

1. 
   

   (Breshit 23:1) Sarah: But when we see the pasuk about Sarah it says after giving the amount ".. the days of her life." This addition asks for an explanaition ("Omer darsheni"), which is why Rashi explained what he did.

   
   


2. 
   

   (Breshit 25:7) Avraham: Here too we see an addition: "The days ot the years of Avraham's life which he lived.." which Rashi felt had to be explained.

   
   

Now the repetition of the word "years" following the units is a common way of saying it, maybe to teach us that the years of someone's life are not just a number.

Japanese grammar structure order

Everything I have known about Japanese grammar structure till now is S-O-V. Japanese is S-O-V language. But what's about adj? Adverb?... Something like that. Of couse that I did some research about this. But all I found is this:

Sentence Topic, Time, Location, Subject, Indirect Object, Direct Object, Verb. [Source]

But I understand nothing at all. I mean it isn't answer my question: the order of adj, adverb... Is it standing before noun or after, what happen if I got 2 adj... Do you guys know it? Please teach me about it. It terribly confuses me.

And thank you for reading my... query?

mitzvah - What is the difference between the following words referring to commandments?

What is the difference between the following words?

• Commandments


• Law


• Testimonies


• Precepts


• Judgements


• Statutes


• Ordinances

Deut 26:16 - 19 reads

16: This day, the Lord, your God, is commanding you to fulfill these statutes and ordinances, and you will observe and fulfill them with all your heart and with all your soul.
17: You have selected the Lord this day, to be your God, and to walk in His ways, and to observe His statutes, His commandments and His ordinances, and to obey Him.
18: And the Lord has selected you this day to be His treasured people, as He spoke to you, and so that you shall observe all His commandments,
19: and to make you supreme, above all the nations that He made, [so that you will have] praise, a [distinguished] name and glory; and so that you will be a holy people to the Lord, your God, as He spoke.

Deut 6:1 reads:

This is the commandment, the statutes, and the ordinances that the Lord, your God, commanded to teach you, to perform in the land into which you are about to pass, to possess it.

There are many other places in the Hebrew Bible where these words appear, but I couldn't quite grasp distinctly what they mean.

FIR filter with linear phase, 4 types

I know there are 4 types of FIR filters with linear phase, i.e. constant group delay: (M = length of impulse response)

1. 
   

   Impulse response symmetrical, M = odd

   
   


2. 
   

   Imp. resp. symmetrical, M = even

   
   
   


3. 
   

   Imp. resp. anti-symmetrical, M = odd

   
   


4. 
   

   Imp. resp. anti-symmetrical, M = even

   
   

each with its traits. Which of these types is most commonly used in FIR filter with linear phase design and why? :)

Answer

When choosing one of these 4 types of linear phase filters there are mainly 3 things to consider:

1. 
   

   constraints on the zeros of $H(z)$ at $z=1$ and $z=-1$

   
   


2. 
   

   integer/non-integer group delay

   
   


3. 
   

   phase shift (apart from the linear phase)

   
   
   

For type I filters (odd number of taps, even symmetry) there are no constraints on the zeros at $z=1$ and $z=-1$, the phase shift is zero (apart from the linear phase), and the group delay is an integer value.

Type II filters (even number of taps, even symmetry) always have a zero at $z=-1$ (i.e., half the sampling frequency), they have a zero phase shift, and they have a non-integer group delay.

Type III filters (odd number of taps, odd symmetry) always have zeros at $z=1$ and $z=-1$ (i.e. at $f=0$ and $f=f_s/2$), they have a 90 degrees phase shift, and an integer group delay.

Type IV filters (even number of taps, odd symmetry) always have a zero at $z=1$, a phase shift of 90 degrees, and a non-integer group delay.

This implies (among other things) the following:

• 
  

  Type I filters are pretty universal, but they cannot be used whenever a 90 degrees phase shift is necessary, e.g. for differentiators or Hilbert transformers.

  
  
  


• 
  

  Type II filters would normally not be used for high pass or band stop filters, due to the zero at $z=-1$, i.e. at $f=f_s/2$. Neither can they be used for applications where a 90 degrees phase shift is necessary.

  
  


• 
  

  Type III filters cannot be used for standard frequency selective filters because in these cases the 90 degrees phase shift is usually undesirable. For Hilbert transformers, type III filters have a relatively bad magnitude approximation at very low and very high frequencies due to the zeros at $z=1$ and $z=-1$. On the other hand, a type III Hilbert transformer can be implemented more efficiently than a type IV Hilbert transformer because in this case every other tap is zero.

  
  


• 
  

  Type IV filters cannot be used for standard frequency selective filters, for the same reasons as type III filters. They are well suited for differentiators and Hilbert transformers, and their magnitude approximation is usually better because, unlike type III filters, they have no zero at $z=-1$.

  
  



• 
  

  In some applications an integer group delay is desirable. In these cases type I or type III filters are preferred.

  
  

organic chemistry - Photosynthesis, science fair

So I was thinking about something to do for a science fair and photosynthesis sounded like a good idea. I was wondering what the exact process of photosynthesis was on a chemical level. I know the formula, but how exactly is water and carbon dioxide converted into glucose and oxygen? And where does sunlight come in, not in the equation but the chemical process. Finally, any ideas for artificial photosynthesis?

tefilla - Tehilim for an illness

What are the Chapters of Tehilim (Psalms) said for an ill person and what is the source in seforim and the reason for these particular chapters being chosen?

safety - Is the Hollywood portrayal of the effects of ingesting HCN correct?

In the 2012 movie Skyfall, the antagonist Raoul Silva rues that the "hydrogen cyanide" he took ("Do you know what it does to you, hydrogen cyanide?") didn't kill him, leaving him horribly disfigured instead.

Firstly; Could it have actually been HCN that he took?

From what I know about this, HCN is a gas at room temperature, and gases aren't typically the poison of choice for suicide pills. To begin with, suicide pills are preferrably kept as small as possible to make it easy to conceal. Keeping the size constraint in mind, simply filling it with HCN gas wouldn't allow the pill to store enough to (seriously) harm you, much less kill you.

From what I gather, suicide pills (WW2 era) often contain a concentrated solution of potassium cyanide, and not HCN.

Well, I'm bringing this up since this is a James Bond movie, so... what're the chances the MI6 could've compressed a significant amount of HCN in the suicide pill (possibly pressurizing it until it's a liquid), without having the easy-to-crush-between-the-teeth pill exploding on account of pressure? I'm not sure how easy it is to liquify HCN, but if it is possible to do so at room temperatures without an exorbitant amount of pressure, could that have been the 'suicide pill' he had taken?

Are there any known instances ( some half-arsed experiments and such) where a gas at room temperature was liquified and stored within such a small volume.

Secondly: Could hydrogen cyanide, or any other simple cyanide compound for that matter, cause such a disfiguration?

More than having tried to kill himself with some sort of HCN pill, I was taken aback to see what it did to Silva.

Just look at what happened to the guy:

Seriously, just look at him:

This is what I found on Wikipedia, on cyanide poisoning:

If cyanide is inhaled it can cause a coma with seizures, apnea, and cardiac arrest, with death following in a matter of seconds. At lower doses, loss of consciousness may be preceded by general weakness, giddiness, headaches, vertigo, confusion, and perceived difficulty in breathing. At the first stages of unconsciousness, breathing is often sufficient or even rapid, although the state of the person progresses towards a deep coma, sometimes accompanied by pulmonary edema, and finally cardiac arrest. A cherry red skin color that changes to dark may be present as the result of increased venous hemoglobin oxygen saturation. Cyanide does not directly cause cyanosis. A fatal dose for humans can be as low as 1.5 mg/kg body weight.

I don't seem to find anything on 'severe-tissue-damage-and-jawbone-dissolution', so I'm still skeptical.

I mean, sure, HCN is a weak acid, but that is not what a weak acid does to you.

So did Raoul Silva bite down on a cyanide pill (of sorts...) or did he gargle a bottle of drain-cleaner and just forget about it?

Is there anything realistic about that scene, or is it just another movie gaffe?

minhag - Schlissel Challah

What is the source for the "Key Challah" Segulah (charm) that is said to bring Parnassah (prosperity)? And which is it: do you put the key in the Challah or do you make the Challah in the shape of a key? I've heard of it both ways.

molecules - Why do different substances have different boiling points?

For example, why does for example oxygen turn into gas at a much lower temperature than water?

Does it have anything to do with the molecular structure? A water molecule does have a more complex structure than oxygen, though the R-410A (a mixture of two gases commonly used in heating pumps) is much more complex than water, and it boils at -48.5 degrees Celsius.

Answer

The boiling point of a liquid depends on the intermolecular forces present between the atoms or molecules in the liquid since you must disrupt those forces to change from a liquid to a gas. The stronger the intermolecular forces, the higher the boiling point.

Two oxygen molecules are attracted to each other through London dispersion forces (induced temporary dipoles between the molecules) while water molecules are attracted to each other by hydrogen bonding (attraction of the + dipole on H in one molecule to the – dipole on an oxygen in an adjacent molecule) that is relatively strong. (Hydrogen bonding is an important intermolecular force for molecules where H is directly covalently bonded to F, O or N, which are quite electronegative and thus form bond with H with a relatively strong dipole.) London dispersion forces become more important for atoms and molecules with more electrons. Dipole–dipole attractions are also important in some molecules.

word choice - Usage of たくさん vs. 多い

When do we use たくさん and when do we use 多い? I found both modifiers are used within similar sentences, for example:

人が多かったです
人がたくさんいました

I had this impression that 多い is used with countable nouns (i.e. similar to "many") while たくさん can be used with both countable and uncountable, but seems like it is used with "お金":

ふだんの生活で使うお金が多いからか――ということです

At first, I thought maybe in Japanese language "お金" is considered as countable, unlike the word "money" in English, but again I realized I was wrong when I found:

きょうは水が多いですね

Now I'm thinking that maybe the concepts of countable vs uncountable in Japanese are not as significant as in English. It seems to me that both たくさん and 多い may be used interchangeably.

Am I right? Or are there actually places where only one of them can be used but not the other?

EDIT:

Additional question: how are they related to potentially antonyms 少し and 少ない? Is 少し antonym of たくさん while 少ない is antonym of 多い, or vice versa, or it does not matter either way?

Answer

I don't think the existing answers are hitting this question from quite the right angle, so here is my take:

First, in sentences where you only wish to mention the presence of "a large number" or "a large quantity", 多い and たくさん can often be interchanged, provided you do some grammatical fiddling to get the rest of the sentence to work:

人が多いですね。 There are a lot of people here, huh?

人がたくさんいますね。 There are a lot of people here, huh?

多くの人が参加しました。 Many people participated.

たくさんの人が参加しました。 Many people participated.

But there's an alternate interpretation for the third sentence: 多くの could simply mean "a lot", but it could also mean "a large proportion". It's this idea of largeness in proportion or ratio that たくさん does not have. This shows up in sentences comparing one quantity to another:

今日は水が多いですね。 There's more water [than before] today.

これからは機会が多くなりそうです。 It looks like we'll have more opportunities [than before] from now on.

今年の春は去年の同じ時期より雨が多く降りました。 This spring, more rain fell than during the same time last year.

Note that 雨が多く降った is a legal sentence, but only within the proper context of comparing proportions, as demonstrated by the third sentence above.

By extension, 多い comes with a meaning similar to "more than necessary". This is another meaning たくさん does not have:

10人ならいいけど、20人はちょっと多いですね。 10 people would be good, but 20 is a bit much.

あのさ、これ、多くない？ Hey, isn't this too much?

You cannot replace 多い with たくさん in the above examples, because たくさん lacks the ability to compare a quantity to a certain level.

In response to your additional question about 少し and 少ない: Yes, you can think of these two as corresponding with たくさん and 多い, respectively. 少し only refers to quantity, but 少ない has the additional meanings of "small in proportion" and "less than necessary".

organic chemistry - Soap versus Shampoo

Soap and shampoo are both cleaning agents in our daily life.

Why is soap in solid form and shampoo is in a liquid form, though? Is it because of the chemical components inside them or another factor? Which cleaning agent has a higher efficiency in cleaning grease from the body?

Answer

Well, whether these products are liquids or solids typically has more to do with the additional ingredients than the actual cleansing agent.

Soap, chemically speaking, is a surfactant composed of the salt of a fatty acid, typically lauric, palmitic or stearic acids. It's typically produced by adding a strong hydroxide base to liquefied plant or animal fat, which liberates the fatty acids from the triglyceride via hydrolyzation, where they then bind with the free cations from the base forming an amalgam of salts.

Shampoo, or more specifically the detergents present in it, are similar, but produced by a different process, to create a surfactant that is less likely to bond to the mineral compounds in hard water, and so is more effective than soap when using it with tap water from most regions. Sodium lauryl sulfate and sodium laureth sulfate are the two frontrunners here; the former is very powerful, and doesn't foam as much, so it's typically used for laundry detergent. The latter is gentler on human skin (less irritating) and so is typically used for various hand and body cleansers including shampoos. The two split about 50-50 in dish soaps, with a third surfactant, lauramine oxide, also making an appearance as a heavy-hitting degreaser.

Both of these substances act in a similar way; they have a hydrophilic (water-attracting) side, and a hydrophobic (water-repelling) side. When dissolved in water (which happens slowly unless the surfactants are already dissolved), the hydrophobic side is attracted to anything that isn't water, and so it will loosely bind via various van der Waals forces to mineral compounds and organics such as those found in dirt, grease, grass stains, oil, lipstick etc. These molecules end up surrounding small particles of these substances on all sides in a bid to "shelter" their hydrophobic end, forming a "micelle". The hydrophilic side exposed to the water, then, allows the micelle to float away in the water and resists the substance in the core of the micelle reattaching to the surface it had been on (dishes, clothes, skin, hair etc), so it can be easily rinsed away.

Now, the form in which a detergent is most useful typically determines whether its sold or packaged as a liquid or solid. Overall, its state is most directly determined by the amount of water in the product. If you've ever had a housemate that never wipes off or closes the nozzle on a bottle of dish detergent, you will have learned that these "liquid" soaps don't have much trouble being solid, either. The liquid products sometimes have an alcohol that helps keep the water from evaporating (and some, like cetyl alcohol, are what make certain products opaque as well as thickening them to give the appearance of a cream), but if marketing wants the product to be a solid, all the chem-engineers have to do is run the mix through a warm (160-250*F) oven to evaporate excess water, leaving behind a pliable solid that can be pressed into bars or minced into soap flakes such as for laundry powders. As far as efficacy in any given form, as I said, liquids tend to disperse in wash water more easily than solids (which is good in the case of a bar soap, not do good with a dishwasher or laundry detergent), though the powder forms are designed to dissolve well, usually through use of some sort of "filler" that spaces out the active ingredients and dissolves easily (and also allows for "everyday" units of measure, so it feels like you're adding enough soap to the water to get your clothes or dishes clean, when in reality a tablespoon of the concentrated active ingredients is more than enough as evidenced by the little gel packs).

words - Counter intuitive meaning of お開き

Apparently 開き means "opening" but お開き means "closure", which seems very counter intuitive. What is going on here? Are there any other similar cases in Japanese language?

Answer

Euphemism vs. Taboo Words

[婉曲語法]{えんきょくごほう} vs. [忌]{い}み[言葉]{ことば}

「[閉]{と}じる」 ("to close") is considered a taboo word for auspicious events such as a wedding party (even though the word itself is something we use without thinking on a daily basis). Thus, we choose to say 「お[開]{ひら}きにする」 to mean "bring (a happy event) to an end".

「閉じる」 is not the only 忌み言葉 that one needs to avoid using if one is giving a speech at a wedding party. Words with negative meanings in the particular context of "marriage" are to be avoided - [終]{お}わる (to end)、[出]{で}る (to leave)、[別]{わか}れる (to part), etc.

Other examples:

「[葦]{あし}」⇒「[葭]{よし}」: "Reed". 「あし」 sounds like 「[悪]{あ}し」("bad"), so let's call it 「よし」 so that it will sound like 「[良]{よ}し」("good")!

「[梨]{なし}」⇒「ありの[実]{み}」: "Pear". 「なし」 sounds like 「[無]{な}し」("nothingness", "non-existent"), so let's change it to 「ありの実」(literally, "fruit of the 'being/existing' kind")!

「スルメ」⇒「アタリメ」: "Dried squid". 「する/掏る」 means "to steal" and it can also mean "to lose" in gambling. That does not sound too positive so let's make it sound like "to win (money or object)" = 「[当]{あ}たる」!

(I chose the examples that I thought would be more interesting instead of the obvious ones used in weddings and funerals.)

matlab - Help in understanding if the maximum likelhood estimation is working properly

I am learning estimation theory and need help in understanding for educational purpose how the concept of ML works with the help of a step by step implementation. I am trying to find out the ML estimates of the coefficients of a moving average model. I am unable to understand what I need to do in order to get the log-likelihood curve, so that I can select the coefficients based on the curve. There are implementations in the internet but I wanted to make my own in order to get a clear picture. The way I have done is for the model

 y(i) =  0.6*x(i-1) ;
 z(i) = y(i) + w(i)

where the true coefficient is h = [ 0.6], the input is x and w is zero mean additive white gaussian noise with variance 1. I have used 4 different values of the estimates out of which one value is the true. If the implementation is correct, then I should get estimated coefficient as 0.6 because I am using the true known coefficient in the estimation procedure. However, this is not so. Where am I going wrong?

Answer

The maximum likelihood estimator will give you precisely the true value for the parameter for a vanishingly small number of instances --- unless the noise is zero.

Your noise instance w is not zero-mean, which will probably give more of a bias away from the true value.

If I take your numbers are just change the last entry in w from -0.65 to 0.1 then I get the "right" answer. Note that this changes the mean of w form -0.16 to -0.042 (i.e. closer to zero).

Your values:

The new values:

purim - Happiness in the Second Half of Adar

The Gemara tells us that in the same way one must decrease joy in Av, one must increase joy in Adar:

אמר רב יהודה בריה דרב שמואל בר שילת משמיה דרב כשם שמשנכנס אב ממעטין בשמחה כך משנכנס אדר מרבין בשמחה

What about the second half of the month? I think most people assume that the amount of joy is in preparation for the upcoming holiday within that month.

In Av, for example, seemingly after the 15th of Av there is no longer a need to decrease joy. Does one need to continue increasing joy after Purim? Please be sure to provide sources.

Related: Time Parameters of Mishenichnas Adar Marbin B'Simcha

halacha - Receiving financial benefit to give maaser money

Is there any problem with receiving money in exchange for giving maaser or tzedeka to a particular person.

For example Reuvan has $1000 maaser and Shimon comes to him and says "give the money to levy and I'll give you a $100"

Or if levy himself comes and says "give me the $1000 and I'll give you $100".

Is it permitted to accept the money?

Even further may a person advertise himself that he has a $1000 of maaser to give away and he'll "sell it" to anyone for $100.

mistakes - If your rabbi accidentally tells you that something is allowed, and you follow him, are you punished?

Imagine that you're 119 years old.

You ask your rabbi whether or not something is allowed. He answers. But, unbenownst to you, his answer is 100% mistaken. The Talmud and all others agree unanimously that the thing is forbidden. But your rabbi misremembers what it says in the Talmud, and he says it is allowed.

For the next two years, you do the thing, thinking it's allowed.

On your 121st birthday, while doing the thing, you suddenly die instantly. Not due to doing the thing: just due to old age. You die without having said the deathbed confessional prayer (see the "Death and Bereavement" section of the ArtScroll Siddur).

Will G-d punish you for having done the thing?

_{(This question was inspired by a discussion between Akiva Miller and R' Yosef Gavriel Bechhofer.)}

Gibbs free energy=potential free energy? (Transition state theory)

Online I found the plot Gibbs free energy vs. reaction coordinate:

https://en.wikipedia.org/wiki/Transition_state_theory

and on many books I found the plot potential energy vs. reaction coordinate (e.g. page 237 Atkins, Physical Chemistry for the Life Sciences, 2nd Ed).

In the first case activation energy is defined as $\Delta G$, whereas in the second case is defined as difference of potential energy.

Thus is the Gibbs free energy a potential energy?

Thank you very much.

halacha - Shoe-tying order when tying another's shoes

Shulchan Aruch, Orach Chayim 2:4–5:

ינעול מנעל ימין תחילה ולא יקשרנו ואחר כך ינעול של שמאל ויקשרנו ויחזור ויקשור של ימין

One should don his right shoe first but not tie it, then don his left and tie it, then tie his right.

Mishna B'rura explains that we tie the left shoe first

דלענין קשירה מצינו שהתורה נתנה חשיבות אל השמאל שקושר עליה תפילה של יד

because regarding tying we find that the Torah lends importance to the left, for we tie the hand-t'filin there.

He adds that

ואיטר יד שמניח תפילין בימין של כל אדם יקדים ימין גם להקשירה

a left-handed person who wears t'filin on his right should also accord the right precedence for tying.

Thus, a left-handed person ties his right shoe before his left; a right-handed person ties his left shoe before his right.

Suppose a left-handed person is putting and tying shoes on a right-handed person's feet, or vice versa (a right-handed person is doing so on a left-handed person's feet). What order should he do so in?

I'd appreciate any source that discusses this (though B'er Moshe (the Debreciner), volume 2 number 3 section 1, and Yad Eliezer (English, Rabbi Krohn, fifth ed., 1996), section A-14, do not), or arguments in support of either position.

frequency spectrum - Nyquist Plot for transfer functions with poles at the origin

I'm learning Nyquist plots and something has been seriously bugging me when treating poles or zeros in the origin. Nyquist plots obtains information based on the argument principle which states

"If f(z) is a meromorphic function inside and on some closed contour C, and f has no zeros or poles on C, then

$${\displaystyle \oint _{C}{f'(z) \over f(z)}\,dz=2\pi i(N-P)} \oint_{C} {f'(z) \over f(z)}\, dz=2\pi i (N-P)$$ where N and P denote respectively the number of zeros and poles of f(z) inside the contour C, with each zero and pole counted as many times as its multiplicity and order, respectively, indicate."

So we just ignore the fact the transfer function contains a pole over the contour $C$? How can we treat them normally when it clearly violates the argument principle?

Answer

We don't ignore poles on the contour. As mentioned in a comment, poles are avoided by modifying the contour as shown in the figure below, where a contour appropriate for a pole at $s=0$ is shown.

Fig. 1: Nyquist contour for a pole at $s=0$ (from "Modern Control Engineering" by K. Ogata).

The contour moves around the pole along a semi-circle centered at the location of the pole. The radius of that semi-circle approaches zero, such that the whole right half-plane is enclosed by the resulting contour. Note that by choosing the contour in this way, a pole on the imaginary axis is outside the contour, and will not add to the encirclements of the origin in the Nyquist plot.

Of course we could also move along a semi-circle in the left half-plane to avoid a pole on the imaginary axis. In that case, the pole would be inside the contour.

As an example, consider the function

$$F(s)=\frac{(s+2)^2}{s(s+1)}$$

It has a double zero in the left half-plane, one pole in the left half-plane, and one pole on the imaginary axis at $s=0$. If we use the contour shown in Fig.1, we get the Nyquist plot shown in the right-hand side figure below (the corresponding contour is shown on the left).

There is no encirclement of the origin, in agreement with the fact that there are no poles and zeros inside the contour. Note that due to our choice of the contour, the pole at $s=0$ is outside the contour.

If we choose a different contour with a small semi-circle in the left half-plane to avoid the pole at $s=0$ (left-hand side figure below), the pole at $s=0$ is inside the contour, and, consequently, the Nyquist plot shows one counter-clockwise encirclement of the origin (right-hand side figure below), corresponding to one pole and no zeros inside the contour.

In sum, poles on the imaginary axis are avoided by moving along semi-circles of infinitesimal radius, and, depending on whether the semi-circle is in the right or the left half-plane, the poles on the imaginary axis are either outside or inside the contour, which is reflected in the Nyquist plot by the number of encirclements of the origin.

physical chemistry - Pauli-forbidden term symbols for atomic carbon

Carbon has a $\mathrm{p^2}$ configuration, and within the Russell-Saunders coupling scheme, we have

$$\begin{align} s_1 = s_2 &= \frac{1}{2} & S &= 1,0 \\ l_1 = l_2 &= 1 & L &= 2,1,0 \\ \end{align}$$

which gives rise to $^3D$, $^1D$, $^3P$, $^1P$, $^3S$, and $^1S$ terms. Out of these six, only $^1D$, $^3P$, and $^1S$ are allowed by the Pauli principle.

It's not hard to show that the $^3D$ term is forbidden, since this term has to contain one state with $m_{l1} = m_{l2} = 1$, which would correspond to a spatial wavefunction that is symmetric with respect to interchange of the two electrons. Pairing this with a triplet spin wavefunction, which is also symmetric, would lead to an overall symmetric wavefunction, which is not allowed.

But that's all the textbooks say - they don't describe why the $^1P$ term is forbidden, for example. I know how to construct a table of microstates, and I know I can use the direct product table of the full rotation group to find that $P \times P = S + [P] + D$, and I know that both of these methods show that the allowed term symbols are only $^1D$, $^3P$, and $^1S$.

Essentially, I am looking for a more intuitive explanation of why the $^1P$ and $^3S$ states are forbidden that preferably links back to the requirement that the wavefunction be antisymmetric - if that is possible.

Alternatively, an explanation of why $P \times P = S + [P] + D$ would also work. I know that from the Clebsch-Gordan series we get $S$, $P$, and $D$ terms, but not why the $P$ state should be antisymmetric. I do know the general idea of how to obtain the vector coupling coefficients (by repeated application of raising/lowering operators), and these do show that the $P$ state is antisymmetric, but I'd like a more interpretative answer than just "that's how the maths works out".

Answer

Okay, actually I managed to find somewhat of an explanation myself.

We could construct a state with $M_L = 1$ and $M_S = 0$, for example: $$\begin{align} \psi = \frac{1}{2}\left[\mathrm{2p_1}(1)\mathrm{2p_0}(2) + \mathrm{2p_0}(1)\mathrm{2p_1}(2)\right]\left[\alpha(1)\beta(2) - \beta(1)\alpha(2)\right] \end{align}$$

where $\mathrm{2p}_m$ represents the 2p orbital with $m_l = m$.

However, such a combination of $(M_L,M_S)$ can only occur once, since the two electrons are indistinguishable. In other words, the following two other wavefunctions are not permissible because permuting the two electrons changes the wavefunction: $$\begin{align} \psi &= \frac{1}{\sqrt{2}}\left[\mathrm{2p_1}(1)\mathrm{2p_0}(2)\right]\left[\alpha(1)\beta(2) - \beta(1)\alpha(2)\right] \\ \psi &= \frac{1}{\sqrt{2}}\left[\mathrm{2p_0}(1)\mathrm{2p_1}(2)\right]\left[\alpha(1)\beta(2) - \beta(1)\alpha(2)\right] \end{align}$$

and the $^1D$ state, which has $S = 0 \Rightarrow M_S = 0$ and $L = 2 \Rightarrow M_L = 2,1,0,-1,-2$, already has to encompass one state with such a combination of $(M_L,M_S)$. Therefore, a state with $(M_L,M_S) = (1,0)$ cannot contribute to a $^1P$ term.

It is logically not the strongest argument (sufficiency vs necessity), but it is kind of what I was looking for. If anybody can provide another viewpoint though I will be glad to accept the answer.

organic chemistry - Can solid acids and bases have pH values? If not, how are they classified as acids or bases?

This answer states

$\mathrm{pH}$ is the aqueous concentration of $\ce{H3O+}$ or $\ce{H+}$ ions in soution. I would not say that ice lacks $\ce{H3O+}$ and $\ce{OH-}$ ions as ice's structure would allow for such, however, since the ions are not in aqueous solution, the material cannot rightfully have a "$\mathrm{pH}$" as we know it.

How does that generalize to solid acids and solid bases? Can solid acids and bases have pH values? If they don't have a pH, how would the solid form of a new compound then be classified as an acid or a base?

Answer

"Technically", the answer is yes. The $\mathrm{pH}$ value is $+\infty$. $\mathrm{pH}$ is simply a logarithmic scale to reference the concentration of (cationic) ionized hydrogen in a sample, and is defined by(*)

$$\mathrm{pH} := -\log_{10}\left([\mathrm{H}^{+}]\right)$$

where the measurement unit is the usual SI derived $\mathrm{\frac{mol}{dm^3}}$ (equiv. $\mathrm{\frac{kmol}{m^3}}$). That's it. The reason this is typically seen in association with acids and bases is that most common (i.e. excluding "Lewis acids") acids are substances which can give up $\mathrm{H}^{+}$ and, moreover, which do so when they are dissolved, meaning that measuring the concentration of such ions in a solution gives a clue as to how much acid may be present. A solid crystal of acid material has its $\mathrm{H}^{+}$ still bound in the acid molecules and is not ionized, thus the concentration of $\mathrm{H}^{+}$ is zero, hence by the above definition, the $\mathrm{pH}$ is $+\infty$ (it is customary to use the extended reals instead of the usual reals when dealing with logarithmic measures as they provide exactly this capability so one can represent zero).

The usual rule that "$\mathrm{pH}$ of 7 is neutral" comes from solutions in water: Water has the property that it can be converted into, and self-converts between ("auto-ioniziation") separate $\mathrm{H}^{+}$ and $\mathrm{OH}^{-}$ ions and its usual molecular form, $\mathrm{H}_2\mathrm{O}$. When one is dealing with pure water with no adulterants present, there is always, due to this process, around $10^{-7}\ \mathrm{\frac{mol}{dm^3}}$ of $\mathrm{H}^{+}$ present (though actually, this depends on temperature, but around room temp, it is around this much). Decimal logarithm of $10^{-7}$ is -7, hence the $\mathrm{pH}$ is 7. When you throw some acid in and it releases its protonic payload, the concentration of $\mathrm{H}^{+}$ rises by that amount, thus the $\mathrm{pH}$ drops.

The key here is that $\mathrm{pH}$ itself is not inherently a measure of acidity or basicity. Rather, it is a measure that is typically associated with such, and thus, serves as a useful proxy therefor, at least under some common circumstances. When you are not dealing with a solution in water - i.e. either as you are talking about here a pure solid chunk of acid material, or you are dealing with acid dissolved in something other than water - the usual signifiers of $\mathrm{pH}$ beyond it being a logarithmic measure of the $\mathrm{H}^{+}$ ion concentration go out the window. Likewise, outside of water, $\mathrm{pH}$ cannot be used to measure bases, either, even simple (Arrhenius) bases since the presence of $\mathrm{OH}^{-}$ does not imply a corresponding deficit in (now non-existent) $\mathrm{H}^{+}$. Non-aqueous basic solutions, even of Arrhenius bases, will have $\mathrm{pH}$ of $+\infty$ as well, hence useless. Indeed, anything that has no free $\mathrm{H}^{+}$ ions knocking around has, by definition, a $\mathrm{pH}$ of $+\infty$.

Insofar as classification goes, that is not done using $\mathrm{pH}$, but rather the chemical behavior of the compound: an acid is signified by its ability to give up $\mathrm{H}^{+}$ under suitable circumstances, e.g. dissolution (Arrhenius' definition) or when brought into contact with a base (Bronsted-Lowry definition, as proton donor). Bases are the complement to this.

(*) ADD (2019-04-28, IE+1935.17 Ms): Upon review, I found and so should point out that this is not technically the "strictest" definition of pH. Technically, it is not log of concentration per se, but rather of the "activity" of $\mathrm{H}^{+}$, which is defined as a "modulated" concentration

$$a_{\mathrm{H}^{+}} := f_{\mathrm{int}}(S) \cdot [\mathrm{H}^{+}]$$

by a factor $f_{\mathrm{int}}(S) \in [0, 1]$ which accounts for interactivity between dissolved $\mathrm{H}^{+}$ due to the fact of their extended charge (Coulomb / electrostatic) interactions and that modifies the acid behavior. This factor depends on the thermodynamic state $S$ of the system which includes both temperature and the concentration itself and thus makes the "proper" $\mathrm{pH}$ nonlogarithmic in the concentration. Nonetheless, as concentration approaches zero, $f_{\mathrm{int}}(S)$ goes to $1$ and $a_{\mathrm{H}^{+}}$ still vanishes, hence the $\mathrm{pH}$ is still $+\infty$ and moreover, at low nonzero concentrations the two definitions are very close. The "concentration $\mathrm{pH}$" as given above is more "properly" written "$\mathrm{p[H]}$".

pronunciation - Does Japanese have a silent ん?

Often, I can't hear ん in words. Most recently I've seen this in 攻殻機動隊.

Examples:

• 
  

  もう少し詳しい検査をしてみないと何とも言えませんが、おそらく外的な要因は見つかりそうもありません... 要因 sounds like ようい

  
  


• 
  

  しくじれば、Spring-8の4倍の税金をかけた橋を… Sounds like ぜいき

  
  
  


• 
  

  何か途中から犯人のメッセージが一人称から三人称にすり替わってしまったような感じで I hear はんにん just fine, but then I hear いちにいしょう and さんにいしょう

  
  


• 
  

  総監暗殺予告の件で任意同行してもらうぜ！ 任意 sounds like にいい to me

  
  

The latter example I also heard in the drama お天気お姉さん(in episode 9).

• ①任意です｡②任意というには無理がありすぎる！ This is probably the single best example of it. I don't hear anything like someone intentionally trying to produce a sound(edit:That is, a sound between に and い in にんい).

So is this a silent letter? Is it a quirk that Japanese people are conscious of? Is it an accent? What allophone is this? Anything else I should know about it?

Thanks for the help!

Answer

ん has different pronunciations(allophones) depending on surrounding context.

• [m] before /p/, /b/ and /m/


• [n] before /d/, /t/, and /n/


• [ŋ] (What some might know as "ng") before [k] and [ɡ].



• [ɴ] at the end of prosodic units. This is close to [ŋ] but pronounced further down in the throat.


• Before vowels, /j/,/w/,/r/,/s/,/z/ and /h/, it is pronounced as a nasalized version of the preceding vowel.

This varies slightly based on speaker and register, but works as a general guideline. According to this, your example 税金を /ze:kiɴo/ would be pronounced

[~iĩo]

However, the nasality of the nasal vowels often tends to spread to the surrounding vowels by a phenomenon called "nasal assimilation". This causes the pronunciation to become

[~ĩ:õ]

Likewise, はんい would become

[hã:ĩ]

You mention in a comment that you don't hear anything nasal in it, but that might be because you're not used to listening for nasal vowels.

Finally, just to illustrate that nasal assimilation isn't a concept as alien as you might expect, it's quite common in English too. For example, the word "can't" is commonly pronounced [kã:t].

halacha - How much does one have to eat to become Fleishigs?

Is there a minimum amount of meat or chicken required to be eaten in order to change one's status to being "fleishig" (i.e. so that he would have to wait before eating dairy)?

[same question can be said of dairy for "milchig" status...]

Would it matter if the meat or chicken is spit from the mouth before swallowing?

torah reading - Sitting During Laining accd to R Abadi

I have seen that Rabbi Yitzchak Abadi is careful that all present at his Shul must sit during Torah reading.

Why is that?

history - Why do we bow down in the direction of the ark?

This is a question I've had for many years, to which I've never received a satisfactory answer:

In Hebrew school, we were taught that idolaters bowed to a idol of their god. They would claim that the idol itself wasn't thought to be physically their deity, but rather a representation of it so they could direct their worship at the statue. We were also taught that Jews don't bow to idols.

Fast-forward to modern-day synagogue judaism. The room where services are held includes an ark for the torah scrolls, and we pray facing it. The congregation even bows in the direction of the ark. I've asked several rabbis about this informally, and I usually get the answer that we're not bowing to the ark but the ark as a representation of God.

My question is: How is this any different from non-Jews bowing to an idol? If Judaism has God who is everywhere, why do we need to bow towards a physical object that's a stand-in for God? Or is this simply human nature, to need to physically see a thing in front of us?

(Please let me know if I can make this clearer, or if I'm stepping on anyone's toes here. Have tried to phrase this respectfully while maintaining clarity.) 

Answer

Well, here's what comes to mind.

1. Bowing is not reserved for G-d. There are many cases in the Bible when prominent Jews bowed to kings such as the prophet Natan bowing to David (Melachim 1:1:23) and Yosef’s brothers bowing to Yosef (Breishit 42:6). Even Avraham (Breishit 18:2) bowed to strangers whom he suspected of being idolaters (Rashi to verse 4).


2. 
   

   Bowing in the direction of the Ark (or Aron Kodesh, as I shall call it) is not bowing to the Aron Kodesh at all, but rather bowing in the direction of the Holy of Holies in Yerushalayim (Jerusalem). When there is no Aron Kodesh (like a minyan that is not in a synagogue), we bow in the direction of Yerushalayim. Wikipedia (quoting Rambam and Shulchan Aruch) says:

   
   

   
   

   "...the Aron Kodesh should be placed "in the direction in which people pray in that city," i.e. toward Yerushalayim. The Shulkhan Arukh records the same rule, but it also recommends that one turn toward the southeast instead of east to avoid the semblance of worshiping the sun".

   
   

   
   



3. 
   

   The law is (not sure if this is across the board) that if the Aron Kodesh is not on the eastern wall (for whatever reason), one faces Yerushalayim irregardless, and does not face the Aron Kodesh.
   The Shulchan Aruch Harav says:

   
   

   
   

   "...One should turn towards Eretz Yisrael if they are in the diaspora, and to Yerushalayim if one is in Eretz Yisrael, and towards the Temple if one is in Yerushalayim. We are located in the west so we face east, and therefore we put the Aron Kodesh on the eastern wall, however, even if the Aron Kodesh is on a different wall, one should still face east"

   
   

   
   

---

As regards why we should pray in a specific direction at all if G-d is everywhere, I seem to remember learning that the main thing is that your heart be pointed (focused on) towards the Holy of Holies because that is where G-d's presence was strongest on earth.

Edit: (Thanks to Tom Shmuel for the source) The Mishna (Berachot 4:5) says that if one is unable to face Yerushalayim:

"he should direct his heart toward Yerushalayim."

---

As regards what you were taught in hebrew school, my guess is it was probably over-simplified - depending on how old you were. When I was young, I was taught similarly, but the truth is one is forbidden to worship idols in any way. Some idols are worshiped, not by bowing, but by other means, i.e. throwing rocks at them (source here), sacrificing one's children (not Isaac style, they went all the way, (according to some¹)), sacrificing animals to them, burning incense, as well as other things we won't mention here. The point is, worshiping an idol in any way that we worship Hashem is forbidden, as well as worshiping them in any way in which they (specifically) are worshiped. But it must be an idol, or the intent must be that it is, for it to be forbidden. Bowing out of respect to someone is not worship.

^{1: Some do say that they just passed them through fire.}

inorganic chemistry - why "amu" is used as a unit in relative atomic mass?

Unified atomic mass unit (amu) is defined as $1/12$ of the mass of a Carbon-12. I want to know is this amu equal to $\pu{1.99e-23 g}$ and why do we use amu which is $1/12$ the mass of carbon? Why use "amu"?

tanach - How could Ruth do yibbum if she converted only after her husband died?

How could Boaz be required to do Yibbum with Ruth being that she was a non jew when she was married to?

Answer

Since all of Naomi's children had died, Ruth was free of the requirement of yibum and did not perform yibum with Boaz. Indeed, one of the reasons Naomi gave trying to convince Ruth and Orpah to leave her was that there would be no child available to perform yibum. Ruth 1:12 - 13

12. 
    

    Return, my daughters, go, for I have become too old to marry, that I should say that I have hope. Even if I had a husband tonight, and even if I had borne sons,

    
    


13. 
    

    Would you wait for them until they grew up? Would you shut yourselves off for them and not marry? No, my daughters, for it is much more bitter for me than for you, for the hand of the Lord has gone forth against me."

    
    

sources mekorot - Rav Moshe and Giving Your Time for Charity

I recall hearing that Rav Moshe Feinstein rules that one should donate a tenth of his time to learn with other Jews, in addition to the more commonly accepted 'tithe' of money. The only source I was able to find this referenced in was an Aish article that quotes an interview of Rav Moshe in the Jewish Observer where he made that claim.

Does anyone know if this is brought down anywhere else, specifically in Igros Moshe? Or alternatively, what it would be filed under in the Yad Moshe, as I couldn't find it?

Thanks!

halacha theory - What is the Sod HaIbbur and what is so secret about it?

What is the Sod HaIbbur (secret of impregnation)? I have seen it discussed in many places including the Pirkeu D'Rebbi Eliezer (8th chapter?) in reference to the intercalation for the lunar months of the year and applying a leap month (which creates an "impregnated" year) so that the lunar calendar doesn't continually fall behind the solar one.

If all this is, is the mathematics behind the lunar calendar, why is it a secret? Does this secret continue to exist now that we have a set calendar? Is there another interpretation of Sod HaIbbur?

words - What does かの日 mean?

In my Japanese Bible, I've seen several passages that use the phrase かの日. Here are a couple.

• ある人たちの習慣に倣【なら】って集会を怠【なまけ】ったりせず、むしろ励【はげ】まし合いましょう。かの日が近づいているのをあなたがたは知っているのですから、ますます励【はげ】まし合おうではありませんか。　－　ヘブライ人への手紙 / 10章 25節


• かの日には、大勢の者がわたしに、『主よ、主よ、わたしたちは御名【み・な】によって預言【よ・げん】し、御名【み・な】によって悪霊【あく・りょう】を追い出し、御名【み・な】によって奇跡をいろいろ行ったではありませんか』と言うであろう。 　－　マタイによる福音書【ふく・いん・しょ】 / 7章 22節


• かの日、主が来られるとき、主は御自分の聖なる者たちの間であがめられ、また、すべて信じる者たちの間でほめたたえられるのです。それは、あなたがたがわたしたちのもたらした証【あか】しを信じたからです。 　－　テサロニケの信徒への手紙二 / 1章 10節

I haven't been able to find the exact phrase in any dictionary. The best I can theorize is that it is 彼【か】の, which is basically the same as その or あの. So it would be something like "On that day..."

Is this correct? If so, is it some literary term? What advantage does it have over その or あの? If not (correct), what is it?

Answer

No, 彼【か】の isn't basically the same as 其【そ】の, but it is basically the same as 彼【あ】の, except that it's older and no longer used as much. In short, か became あ.

かの is preserved in some modern words and phrases:

• かの女【おんな】 became　かの女【じょ】 and stuck around (rather than becoming あの女【おんな】). Of course, you usually see this written 彼女, with the genitive の left unwritten.


• かの有名な still comes up, I think as a set phrase (rather than あの有名な)

But mostly it's just an old form of あの. So かの日 means あの日, but it sounds older.