equilibrium - Calculating approximate pH of polyprotic acids

When I took up ionic equilibria and titrations after a long break, I found it hard to solve the questions regarding pH calculations of polyprotic acds. Consider these two questions as examples:-

1. Find the approximate pH of a solution with $0.4M\text{ }\ce{HCO3-}$ and $0.2M\text{ }\ce{CO3^2-}$$K_{a1}=4\times 10^{-7}$, $K_{a2}=4\times 10^{-11}$


2. Find the approximate pH of the resulting solution formed after mixing $20ml$ of $0.1M\text{ }\ce{H3PO4}$ and $20ml$ of $0.1M\text{ }\ce{Na3PO4}$. Express in terms of $pK_{a1},pK_{a2},pK_{a3}$.

I have mentioned 2 questions here because I want to know the method to solve such type of questions and not these two questions here in particular. The problem arises when there is a polyprotic acid with hydrolysable salts. For the second case, the ongoing equilibria are the dissociation of the three acids and the hydrolysis of their respective salts. For the first one, there are just two dissociation equilibria(and the dissociation of water). Even by writing down the equilibrium expressions of these reactions, I am unable to reach the final expression with pH or pOH. And, all the solutions have to be approximate (using approximations like the negligible contribution of hydrogen from the dissociation of water, low value of the successive ionization constants) and not at all accurate.

I would appreciate if someone explained how to do such numericals, taking one of the above as an example (I already have the answers for the aforementioned questions. I just want to use them to illustrate the general principle behind these questions).

Let me know if my question looks too homework-like and off-topic.

halacha - Why is fish and milk permitted but not poultry and milk?

E.g. Chicken and milk is forbidden, but fish and milk is permitted. (Some Hassidim and Sefardim do not mix fish and milk as I understand it).

If going off the common answer of not to confuse chicken with meat, why is fish any different?

Answer

About quails they eat in the desert what says the verse? Bamidbar (11, 33).

הַבָּשָׂר עוֹדֶנּוּ בֵּין שִׁנֵּיהֶם טֶרֶם יִכָּרֵת וְאַף יְהֹוָה חָרָה בָעָם וַיַּךְ יְהֹוָה בָּעָם מַכָּה רַבָּה מְאֹד:

Let's learn a little passage of Gemoro.
you start with a Mishno Chulin (8, 1)

ח,א כל הבשר אסור לבשל בחלב, חוץ מבשר דגים וחגבים; ואסור להעלותו עם הגבינה על השולחן, חוץ מדגים וחגבים. הנודר מן הבשר, מותר בבשר דגים וחגבים

The mishna added that in common language, fish is not called meat (in the contextual language of the Tana).
A little further the Mishnah tells us:

המעלה את העוף ואת הגבינה על השולחן, אינו עובר בלא תעשה.

to take poultry with cheese on the table is not prohibited from the Torah

further the Mishnah teaches us

רבי עקיבה אומר, חיה ועוף אינן מן התורה, שנאמר "לא תבשל גדי, בחלב אימו" "לא תבשל גדי, בחלב אימו" (שמות כג,יט; שמות לד,כו; דברים יד,כא): שלושה פעמים--פרט לחיה, ולעוף, ולבהמה טמאה. רבי יוסי הגלילי אומר, נאמר "לא תאכלו כל נבילה" (דברים יד,כא), ונאמר "לא תבשל גדי, בחלב אימו" (שם)--את שהוא אסור משום נבילה, אסור לבשל בחלב; עוף, שהוא אסור משום נבילה, אינו דין שיהא אסור לבשל בחלב: תלמוד לומר "בחלב אימו"--יצא העוף, שאין לו חלב אם

After Rabbi Yossi Haglili, we would think that poultry is the equivalent of lamb with regard to the legislation of Bassar Behalav. This is because poultry can have the status of carcass (a special kind of impurity and more things. This is not the case for fish). But the verse refers to the milk of the mother and mothers of birds don't product milk.
The Gemoro Daf 116A says that Rabbi Yehudo ben Betera permits poultry with milk, and may be Rabbi Yossi Haglili also.

So Fish may not be carcass (Neveylo) and is not linked with the verse that prohibit Bossor Becholov. (We may read an important translation of the mishna in tosfoth that undertand that Rabi Akiva comes to counter an opinion that poultry is prohibed min Hatorah as lamb.in Mechilta at the end of Mishpotim, this is the opinion of Rabbi Yoshia. It is not the place for an extended explanation.)

Fish with milk in the Minhogim:
Chulin 111B

איתמר דגים שעלו בקערה רב אמר אסור לאכלן בכותח ושמואל אמר מותר לאכלן בכותח Blockquote

Fishes that has absorbed (we will not discuss here the nature of the absorption) meat, if this absorbtion is significant, we do not eat them with a kind milky condiment.
This says that fish alon can be eaten with milk! The Beyth Yossef YD 88,3 says that following the Rashbo in torath Habayt it is prohibited due to a danger (a medical threat as for fish with meat, a danger to become leprous.). For danger there arre Poskim that prohibit indirect absorption to. (for a further topic)

In SA OC 173, the Magen Avrohom SK 1, emits doubts about the sustainability of such medical considerations in actual world. (His subject is fish with meat but the Beyth Yossef in YD 88 compar the two, that is fish and meat and fish and milk) That is, the actual medicine don't identify any threat in this. But don't counter the din.

organic chemistry - Which is the correct way to name pentan-3-one?

I have seen this organic compound named in two different ways.

According to some sources it is written pentan-3-one.. Other sources call it 3-pentanone.

Which one is correct?

Answer

Whether you write pentan-3-one or 3-pentanone both are correct.

But according to IUPAC rule pentan-3-one this is correct format of writing the name of organic compound. So I prefer you to write pentan-3-one rather than 3-pentanone.

You should also read this.

phrases - would 「なんとか」 be an acceptable replacement for "something"?

like as an example: if i forgot the name of a song but i remembered part of it, so i said "zenryoku something" (i say something because i don't know what comes after zenryoku), would 「全力」なんとか be an appropriate translation?

sorry if i tagged this wrong, this is my first time asking on this forum.

Answer

Yes, 「なんとか」 is often used as a replacement word when the actual word has slipped one's mind.

「全力{ぜんりょく}なんとか」 is what you would say when you cannot remember the word that follows the 「全力」. You can use it the exact same way you would use "something" in English.

Informally and/or colloquially, some people use 「なんちゃら」 for the same purpose.

You will also hear 「なにがし」 at times almost exclusively replacing parts of proper nouns. 「なにがし」 is not informal.

Finally, I would like to introduce the whole other usage of the replacement 「なんとか」 that I feel would be important for Japanese-learners to be familiar with. That is 「なんとか」 used for a "replacement" for the word that you so clearly remember. It is used for replacing a word in a well-known saying for euphemism.

Original vs. なんとか-version.

・「バカのひとつ覚{おぼ}え」⇒「なんとかのひとつ覚え」 ("One who knows little often repeats it".)

・「ブタに真珠{しんじゅ}」⇒「なんとかに真珠」 ("Cast not pearls before swine.")

divorce - What problems are faced by children born out of wedlock?

I was previously under the impression that, since a man may acquire a woman with sexual intercourse (cf: Mishna, Qiddushin 1:1), if a couple have a son but no ketubah, the child still inherits his father's property. See, for example, the mishna in Ketubot 4:9, which stipulates that sons inherit whether that detail is included in the ketubah or not. Recently, however, I learnt a mishna that appears to imply the opposite: that sons born out of wedlock face some manner of "damage", even though the identity of their father is known.

My question concerns whether or not I am learning this material properly: does the term that I have translated as "damage" (פגם) refer to their inability to collect on their father's inheritance? If not, might it be referring to the notion that it is somehow socially damaging to suggest that somebody was born outside wedlock? Why would it be an insult if their parents were living together at the time of their conception?

The mishna in question, together with the relevant peirushim, is as follows:

בית שמאי אומרים: פוטר אדם את אשתו בגט ישן ובית הלל אוסרין. איזהו גט ישן? כל שנתיחד עמה אחר שכתבו לה

The school of Shammai says that a man may divorce his wife with an old document, but the school of Hillel forbids it. What is an old document? Any [situation] in which he was secluded with her after writing it.

• Gittin 8:4

As R' Menachem Meiri points out, the mishna is speaking of a document (a get, as it is colloquially known) that was both written and signed on the day in question, but which was not given to her until a period of time had elapsed. The reasoning for prohibiting such a document is explained by Rav Ovadiah of Bertinoro (based on the gemara in Gittin 79b) as follows:

גזירה שמא יאמרו גטה קודם לבנה שמא ישהה את הגט שנה או שנתים בין כתיבה לנתינה ויהיו לה בנים ממנו בתוך זמן ואח"כ יגרשנה בו וכשיראו זמן הגט קודם ללידת הבן יהיו סבורים שנתן לה גט משעת כתיבה והוי פגם שיאמרו מן הפנויה נולד

[This is an] enactment, lest people suspect that the document precedes [the birth of] her son. Should there be a period of one or two years between the writing [and signing - Meiri] of the document and its being given, and should she have children to him within that time, and should he divorce her with that document afterwards, then when people see that the document predates the birth of her son they will think that he gave her the document at the time of its composition, and there will be damage - for they will say that he [her son] was born of an unmarried woman.

• Bartinura, ibid.

(The full quote from Rav Ovadia includes the words "ב"ש סברי לא אמרינן" at the beginning, noting that the school of Shammai permit an old document because they don't hold by this enactment.)

halacha - Halachic permissibility of a vasectomy

What are the halachic concerns surrounding vasectomies? Are vasectomies permitted by halacha under any circumstances?

The issues that I could see as possibly being connected would be chavala (prohibition against inflicting harm to self or others), lo titgodedu and possibly even shmiras habris. On the other side, a vasectomy could be psychologically beneficial to a wife who has trouble with birth control, and could potentially help ensure shalom bayis.

From this question on plastic surgery, which I believe is somewhat related: "This is one of the major concerns voiced by Rabbi Eliezer Yehuda Waldenberg, author of Tzitz Eliezer, a multivolume set of responsa, much of which deals with medical issues. First, Rabbi Waldenberg29 objects to performing surgery on someone who is neither sick nor in pain. 30 He argues that such activities are outside the boundaries of the physician's mandate to heal (since he questions whether cosmetic surgery is truly included in the category of healing). He further asserts that the patient has no right to ask the physician to wound him or her for the purposes of merely enhancing beauty. Rabbi Waldenberg then makes the theological argument that as the ultimate artisan, God creates each person in His image, exactly as he or she should be, with nothing extra nor anything lacking. He therefore posits that cosmetic surgery that is not for pain or true illness is an affront to God and is forbidden."

Answer

To quote the Aish Rabbi:

According to Jewish law, a vasectomy is absolutely forbidden.

And for sources for more info:

Maimonides (Laws of Forbidden Relations, Chapter 16), and in the Code of Jewish Law (Even Ha'ezer, Chapters 5 and 16)

And there may even be problems with getting married and/or remaining married with one.

((I noticed that you used the phrase "under any circumstances." Perhaps if the man's life were in danger if he did not have one -- it would be permissible -- but I have absolutely no source. CYLOR))

halacha - Going into a Reform synagogue to take a test

In the following question "Orthodox Visits to Other Denomination Sanctuaries" it discusses whether one may go into a Reform or Conservative synagogue for prayer and/or a wedding. Is one allowed to go into a Reform or Conservative synagogue to take a SAT test? Most likely the test is not taking place in the sanctuary.

FIR Filter Magnitude Response

This is the shape of the bipolar amplitude function for a FIR filter with odd m:

I have 2 questions :

1. 
   

   If i want to use this FIR as a low pass filter between 0 and $\frac{F_{c}}{2}$ , how can i set the value of $G(f)$ to 0 between $\frac{F_{c}}{2}$ and $F_{c}$ ?

   
   


2. 
   

   My prof said that i can use the this FIR as a lowpass between 0 and $\frac{F_{c}}{2}$, but if i want to use the filter between $\frac{F_{c}}{2}$ and $F_{c}$ does it still behave as a lowpass ? (what does it mean that in that range $G(f)$ takes negative values ? )

   
   

time - Moshe Rabbeinu's knowledge of future events

If Moshe Rabbeinu was taught the entire Torah on Mt. Sinai (Rashi on Vayikra 25:1, Rambam), how do we explain events such as the incident involving the Bnos Tzelafchad (Bamidbar 27:1-11), or the tamei people who wanted to bring the Korban Pesach (Bamidbar 9:1-14), where Moshe evidently did not know the end of the story as recorded in the Torah?

Answer

The gemara in Sanhedrin 8a deals with bnos Tzelophchad. The first opinion holds that Moshe forgot the halacha as a punishment for when he appointed judges and said 'any law too hard for you, bring to me.' as if he were the final word and not Hashem. This is learned from the words Vayakreiv/Vatikr'vun.

The second opinion asks on this: Moshe didn't say (by the judges) I'll teach you, he says I'll listen to it (the difficult case, maybe he won't know it either and have to ask Hashem). This question in itself indicates that, at least according to this opinion, Moshe was not taught every nuance of halacha.

His answer also implies this: Moshe was worthy of writing the parasha (unlike opinion #1), but Bnos Tzelophchad merited to have it written through them (megalg'lin z'chus al y'dei zakay), so vayakrev es mishpatan.

It could be the 1st opinion also holds Moshe wasn't taught every nuance, but he darshans vayakrev/vatikr'vun. (efshar)

words - The use of ただ and だけ together redundant?

ただ一つだけ守りたいものを最後まで守り通せばいい。

This quote comes from episode 9 of the anime Mahou Shoujo Madoka Magica and the English subtitles translate it as "Protect the thing you want to protect until the very end."

However, ただ means "only" and だけ means... "only." Why did the character say "only one thing only"? Wouldn't either ただ or だけ have been sufficient alone?

Answer

It's not redundant to use ただ (or たった etc.) and だけ (or ばかり, のみ etc.) together. It's perfectly natural to say, for example:

「ただ広いだけの庭」

「ただ一人だけ生き残る」
「ただ笑うばかりだ」
「たった一度会っただけだ」
(Examples taken from 明鏡国語辞典)

---

ただ一つだけ守りたいものを最後まで守り通せばいい。
Wouldn't either ただ or だけ have been sufficient alone?

Yes, you could rephrase your sentence like this, without changing the meaning:

ただ一つ、守りたいものを最後まで守り通せばいい。
一つだけ守りたいものを最後まで守り通せばいい。

But ただ～～だけ would sound more emphatic (and could sound a bit more emotional, too).

grammar - What does なる mean in these cases?

I'm not sure if these two have the same meaning, but I don't think they bear the meaning that I know which is the basic なる (to become).

1. 
   

   内なる声と言いますか・・

   
   


2. 
   

   彼女よりさらに深遠の、未知なる人物こそが黒幕なのではないかと疑わせるのだ…。

   
   

Answer

This なる is a form of the old copula なり (equivalent to modern だ), and specifically an earlier form of the usage that became the modern な particle used with adjectives. There are a few adjectives that can still take なる instead of な in modern Japanese; this form generally has a literary or poetic-sounding effect.

In the case of the specific two adjectives used here, 内 and 未知, the なる form is actually the only form they can take as な-adjectives in modern Japanese - 内なXX and 未知なXX aren't really used. However, they can be used regularly as noun forms, so 未知なるXX could be rephrased as the equivalent but less poetic-sounding 未知のXX, and 内なるXX similarly as 内のXX (though in the latter case it's perhaps not the most natural expression).

halacha - What replies can be said while waiting for person behind you to finish davening?

One should not take his 3 steps backward after davening shmoneh esrei if there is a person directly behind him still davening ^{[citation needed]}. I believe this is true no matter how far the person behind him is, but I'm certain that it's true if he's less than 4 amot away. Since he is not able to take his steps back to complete shmoneh esrei, I would imagine that he is not able to reply to all (or perhaps any) parts of davening that would normally be responded to such as barukh hu uvarukh shemo and amein to the berakhot of chazarat hasha"tz, kedusha, amein yehei shemei rabba, etc. What kinds of responses are permitted in this state?

Assume that the person has said yihyu leratzon... but has not yet taken three steps back and said oseh shalom.

particle に - 今までに vs. 今まで - what is the difference in meaning?

I recently used a following sentence in my homework:

今日までに　私は　二百まいしゃしんを　とりました。

Now, in my homework I actually used 今日まで, without に, and I got it corrected. What's the difference between 今日まで and 今日までに?

Answer

This is one of those odd examples where we could drop the に (and perhaps replace it with a comma) and still have an understandable sentence:

[今日]{きょう}まで、[私]{わたし}は[写真]{しゃしん}を[200枚]{にひゃくまい}[撮]{と}りました。

But this sentence, while perfectly understandable, is ambiguous on a minor technicality, since まで by itself could be used to show when a state or an action ceases. (Humans are smart and can figure out which one you mean, but let's pretend we're robots. Grammatically correct robots.)

[募金活動]{ぼきんかつどう}は[来週]{らいしゅう}まで[行]{おこな}われる。
The fundraising efforts will go on until next week.

The 来週まで in the above sentence shows that the action will not continue after next week.

Since the point of 今日まで in your example sentence isn't to show that the action of taking the pictures ceases after today, but to show when you took the pictures, the particle に is tacked on to まで just like you would add it to any other time expression that can take に. 今日まで, though it refers to a range of time, is here treated like a single point in time that answers the question of when you took the pictures.

In short, the に can be dropped here. (In writing, when に is dropped, such as in the ために and ～ずに patterns, it's often replaced with a comma.) But to erase any ambiguity, it's best to leave it in, and I think that's what your teacher is getting at.

passover - Connection of the 10 plagues to the 10 sayings used to create the world

I have read in the name of the Vilna Gaon that the 10 plagues were corresponding to the 10 sayings God used to create the world (dont know the exact source). Thus the slaying of the first born corresponded to "In the beginning..", and the plague of darkness corresponded to the creation of light. Does anyone know the connection to the other plagues?

Answer

As seen here, the parallel is first made by the Maharal (Gevurot Hashem: 57)

word choice - Why did オレンジ replace 橙【だいだい】?

This question about colours got me thinking:

Why, and how, did オレンジ come to replace 橙【だいだい】 to refer to the colour orange?

It seems weird to me that a word taken from a foreign language became adopted as the norm when there seem to already have been a perfectly good local word for the same thing.

I've seen 橙 used very occasionally, but it seems to be reserved for deliberately attaching a Japanese style, or 和風【わふう】, context beyond just describing the colour.

Answer

Ah, I found something on this particular example...

支那の色名である「橙色（とうしょく）」が日本語になったと考えられている。[...]橙色は、英語のオレンジに対応する日本語の色名として用いられたが、橙色も元々は借入語であり、英語より橙色の方が借り入れたのが早かったに過ぎない。なお、「橙」の漢字が教育用漢字に採用されなかったために、赤と黄との中間色相は日本でもオレンジ色と呼ばれることが多くなった。

source: http://www.7key.jp/data/design/color/orange/daidaiiro.html
Not sure from what source this information is in turn, though.

Looks like Japan didn't have a name for the color orange (see here for what color they had). So the Japanese borrowed 橙色 from China, and オレンジ from English. The kanji 橙 was not one of the kanji that is taught in compulsory education, thus オレンジ became more common.

pentateuch chumash - Translation to Greek

I just read in parashat ki tavo that the torah was translated into 70 languages and written on giant stones, yet the talmud says the translation of the torah to Greek many years later was considered a tragedy.

Why was it considered a tragedy if it was already translated into 70 languages?

halacha - Should Jews be self-employed?

Under what method of employment should a Jew sustain himself? Is there a preference for self-employment over working for an employer?

I've heard that an employee is like a slave to the employer and maybe this is the source of this idea:

The Cohen Gadol's prayer:

ולא יהיו עמך ישראל צריכים פרנסה זה מזה ולא מעם אחר 

Footnote 14 to Baba Metzia 10a also states:

The fact that the labourer may terminate the employment any time he likes does not imply that he does not belong to the employer.

From the above Gemoro it appears it is not good for Jews to be slaves, as stated:

For unto me the children of Israel are servants ; they are My servants (Vayikra 25:55)  — but not servants to servants.

Additionally, the Shulchan Aruch states Even HaEzer 70:3:

וְיֵשׁ אוֹמְרִים עוֹד, דְּחַיָּב לְהַשְׂכִּיר עַצְמוֹ כְּפוֹעֵל וְלָזוּן אִשְׁתּוֹ

It seems the Shulchan Aruch is saying it is very negative to be an employee (i.e. the last resort if one can't provide food for his wife).

These sources appear to suggest that a Jew should be self-employed.

1. Is it indeed preferable for Jews to be self-employed?


2. If so, what are other sources contain these ideas?



3. Does the type of employment matter?

---

From http://www.hebrewbooks.org/pdfpager.aspx?req=35202&st=&pgnum=153 it seems it depends, and that if the employee can choose what hours he works he is not like a slave

Answer

It is obviously better to be self-employed acording to the sources below

Where he says it is less of an embarrassment to collect money then to rent yourself as a worker

In mitzvot habais page 236

"להשכיר את עצמו יותר גרוע מלחזור על הפתחים"

That to rent yourself is worse then to "return on the doors" (collect money from door to door)

That the Torah obligates a Jew to use money that he has for positive comments, and to collect money for negative comments, but to be a slave (rent yourself) you are only obligated if you steel to repay

His source is the oizer mkoidesh on even ezer 70.3 it is printed on the bottom of the page in the Shulchan aruch

halacha - Correct way to deal with a damaged mini-torah?

My son is 4 years old.
When he entered Hebrew School at the local (Reform) synagogue, they gave him a mini-torah as part of a Consecration ceremony. Specifically this one: http://www.israelbookshop.com/judaica-books/Mini-Torah-Gold.html

It's printed on regular paper but the actual text is there.

He was curious to see what was inside and he tried opening the scroll on his own, but in the process he accidentally tore the whole thing in two.

Is this as "serious" as damaging a real sefer torah?
Obviously I am not going to be able to get a 4-year-old to do any fasting, although we did sit him down and explain how he should be more careful and how holy the Torah is. And, to his credit, it was an accident caused by real curiosity.

Is it OK to repair something like this simply by scotch-taping it? Or is there another way we should get it repaired? Or should we dispose of it (and if so, what's the proper way?) and get him a new one?

Answer

Since they are together as a single scroll this poses a complex problem the Rashba brings a Teshuva regarding books of the chumash that were written separately and without being done leshem kedusha(which would in any even possul the sefer Torah from being used) part 1 chapter 144 writes

אם הם כגולל וכתקנן, הרי הם בספר תורה לכל דבריהם, אלא שאין קורין בהם בצבור, מפני כבוד הצבור בלבד.

If they are rolled and attached, behold they are a Sefer Torah in all respects, only we do not read from them in front of the congregation, and that is only on account of the honor of the congregation.

The Taz(Y"D 271:8) and the Beur Halakha aka the Chafetz Chaim(83:5) also seem to regard printed seforim, on an equal level of holiness with scribed seforim, and thus the above worries of the Rashba would apply.

From an article on Torah.org regarding printed seforim:

With the advent of the printing press in the fifteenth century, the Torah authorities of the time debated whether printed sefarim had the same level of kedushah as handwritten works. The consensus of the poskim was that a printed sefer is to be treated no differently from a handwritten one.

Further you have an interesting, even if widely rejected Teshuva by Rav Abadi that deems use of a printing press to actually be preferable to the use of scribe in writing a Sefer Torah. Which if correct would leave only the issue of it being printed on paper as a possible disqualification of being a genuine Sefer Torah.

Finally Rav Ovadia Yosef wrote a lengthy Teshuva on the issue of these gift scrolls in his journal Or Torah from Av 5762, in which he goes through the various opinions regarding how the scrolls should be treated, and whether damaging them is on the same level as damaging an actual sefer Torah. It's really worth a read if you can get hold of it. In short he goes back and forth and ends with, those who are stringent will merit a blessing, but doesn't actually settle on a final decision in that regard. Regarding what to do with however, he says clearly that it is necessary to entomb it.

In that respect, regarding whether it can be fixed, it would depend on where the rip took place. If it happned in the margin, then, like a normal Torah Scroll it could be fixed. If it tore through the words, while technically one could replace the torn panel, it would seem by and large it cannot be fixed and would have to be entombed just as an irreparable Sefer Torah.

Whether one needs to fast and such as is normal when damaging an actual Sefer Torah, again from this it would seem that such is the case, however one should ask a reliable posek.

hashkafah philosophy - Why Adam wasn’t explicitly commanded to pass his knowledge on to others?

I'm still trying to grasp the way of transmission of the Torah knowledge from day 1. This question can equally deal with two phenomena: the commandment of eating the forbidden fruit or the commandment of the 7 Laws.

IIRC (please correct me if I'm mistaken):

1. G-d creates Adam


2. G-d commands Adam not to eat the fruit and (independently) keep the 7 Laws


3. It is clear that G-d expects all humans to observe the commandments given to Adam.


4. 
   

   G-d doesn't command Adam to pass it on to other humans, his wife or sons or descendants.

   
   


5. 
   

   G-d harshly judges Eve and Adam's descendants for not keeping the commandments.

   
   

The necessity of passing the commandments is absolutely crucial for the justification of G-d's judgment both for Eve eating the fruit or Kain killing Abel.

This is true for all following generations that could claim that though Adam was commanded, he didn't bother teaching the future generations, just as he didn't bother to teach his own wife.

Why didn't G-d care to command Adam (and following generations) on passing the original Law on?

Open Database of Phase Diagrams?

Is there some kind of database that has information about phase diagrams of different substances? I'm mostly looking for phase diagrams of elements (silicon, iron, hydrogen, etc.) because I'm trying to write a planetary generator, but I cannot find any information about the mathematics of a phase diagram.

Better yet, is there some way to simply approximate the phase diagrams of different compounds? I'm looking for simulation complexity and variation more than I want realism.

color - why are simple organic molecules usually white?

I have heard that it is because they absorb electronically in the ultraviolet range, if this is true, why is it true. What is it about the nature of organic molecules that make them absorb in the ultraviolet range.

halacha - Equal volume when doing birkat kohanim with a microphone

I attended a musical davening this week, and to accommodate the large crowd, the chazzan wore a microphone. The kohanim however did not. The result of this was that the chazzan's voice ended up much louder than the kohanim's.

I know that there is a halacha that neither the chazzan nor the kohanim should raise their voice louder than the other.

How does this halacha play out when one is artificially much louder than the other? Should the chazzan whisper into the mic to try and equalize the volume? Or perhaps it's fine if they both speak normally, and it doesn't matter what happens to the sound once it leaves their mouths?

matlab - FIR-Decimation and Low-pass filter (taps vs number of input points vs number of decimation stages)

I am new to digital filters and trying to understand parameters behind them.

Scenario

I am trying to get DC value from signals sampled at 100kHz sampling rate. such high frequency is used due to system hardware limitations. A very sharp low-pass filter is to be used with cut-off frequency at 1Hz. The plan is to capture 10000 ponints first and then FIR-Decimate the income signal with several stages:

1. stage 1: decimation factor 10, FIR cutoff frequency 1/20 (128 taps), 100kHz->10kHz
   
   
   
   • income 10000 points, result 1000 points
   
   
   
   


2. stage 2: decimation factor 10, FIR cutoff frequency 1/20 (128 taps), 10kHz->1kHz
   
   
   
   
   • income 1000 points, result 100 points
   
   
   
   


3. stage 3: decimation factor 10, FIR cutoff frequency 1/20 (128 taps), 1kHz->100Hz
   
   
   
   • income 100 points, result 10 points
   
   
   
   


4. stage 4: decimation factor 10, FIR cutoff frequency 1/20 (128 taps), 100Hz->10Hz
   
   
   
   
   • income 10 points, result 1 point
   
   
   
   


5. Then a FIR with cut off frequency will be implemented with cutoff frequency 1/10.

Questions

1. In the FIR decimation, the FIR cut-off frequency is always stricter than the decimation factor to avoid aliasing, is this design necessary?


2. What are the tradeoffs of choosing number of decimation stages and decimation factors?



3. At stage 4, there are only 10 income points. However, FIR has 64 taps... Would the one point result still be valid?

kanji - Why are there 3 ways of writing in Japanese?

Why are there kanji, hiragana and katakana? Is there a logical reason behind this or just tradition?

Answer

That's a good question, I used to wonder about that myself! This is what I've found out through my own experiences:

When the Chinese brought their written language to Japan, there were only Kanji (Literally, Chinese Characters). Unfortunately, although this kind of ideographic writing system works perfectly for the Chinese language, the Japanese language is structured differently. For example, in Chinese, if you want to say something in the past tense, all you do is add the word for "past" to the verb (it would be the equivalent if every verb in English could be put in the past tense solely by adding '-ed' to the end of it {fall-ed, go-ed}), and in Japanese (as in English) the actual word changes.

What the Japanese needed was a way to notate their verb changes. They developed Hiragana and Katakana from already existing Kanji and assigned them solely phonetic meanings. At some point Katakana came to be used for (among other things*) foreign loan-words, but you can still see examples of Japanese words written in Katakana (for example, on old gravestones) and loan-words written in Hiragana (for example, you can see たばこ for tobacco).

*See link in comments below

halacha - Is there any reason a Jewish woman should not shake hands with a non-Jewish man?

My question refers to the custom of certain groups to prohibit all physical contact between men and women who are not spouses or related.

Although it is clear enough that Jewish men should not touch women for reasons of niddah, is there a sound, halachic reason that a Jewish woman could not touch a non-Jewish man?

I am referring to non-affectionate touch, such as sitting next to someone or passing. (May be better to avoid the example of "handshake" because that brings in a lot of other considerations.) It would be interesting, though, to hear clear halachic reasons that "affectionate" touch (such as a hug) is also prohibited, which I assume it is.

Answer

Saifer chasidim 1090

A Jewish man can not slap hands with a non Jewish woman

And a Jewish woman can not slap hands with a non Jewish man

Even when the hand is coverd with clothing

(The commentaries explain that if they are both Jewish it is OK when the hand is covered with clothing (but only if it is not done for the man to be able to see the woman for a longer time))

tefilla - How precisely oriented towards Jerusalem should we face for praying?

I know we're supposed to face towards Jerusalem when praying/davening. For most of us in the Europe or the Western Hemisphere, we're used to facing "Mizrach", east.

How precise should we be? If I'm in Hotzenplotz and a straight line to Jerusalem is 5 degrees south of east, do I just face east, or 5 degrees south of east?

Similarly, if my house isn't strictly compass-oriented (e.g. it faces an avenue in Manhattan, 29 degrees east of north), do I daven towards a corner, or just pick the wall in the room that's most oriented towards Jerusalem?

product recommendation - English version of SHULCHAN ARUCH

Hi I'm looking for good set of SHULCHAN ARUCH in English, Not K'tzur I need SHULCHAN ARUCH.

Can someone please advise me on set that I can buy ?

Answer

There is no set of the straight Shulchan Arukh in English. You can find English versions of its commentaries, or sets of Kitzur. But as for just the Shulchan Arukh, you are out of luck.

halacha - Tzitzis Thrown Over Shoulder = Still Wearing Them?

Many times I've seen people throw the front half of their tallis katan over their shoulder so that it doesn't get in their way. Mostly teenagers playing sports or people doing something that might get it dirty. This way, the hole of the tallis katan is still around their neck, but now both halves of the beged are hanging in the back.

Is this considered "wearing" tzitzis? According to whom?

(This is an issue, since nowadays one is obligated to wear tzitzis all the time (Igros Moshe OC 4:4). Other possible nafkei minah: Making a brocha again if one didn't intend to "fix" it, but does. If the beged is put on l'chatchila this way, does one make a brocha. Walking 4 amos without tzitzis.)

Answer

From Sefer Haminhagim Chabad (page 2), based on the Alter Rebbe's Siddur:

The [minimal required] width of the tallis katan is one amah (cubit) of the Torah measure, which equals 24 generous-sized thumbwidths [i.e., 48 cm.]. This is also the [minimal required] length

a) from the neck hole to the garment's lower edge at the back, and

b) from the neck hole [or from the fillet that laces it closed] to the garment's lower edge at the front.

These measurements can be reckoned only when the garment is fully spread, and no part of it has been folded or creased: folds and creases cannot be included in the required dimensions. One who is careful to fulfill the precept of tzitzis throughout the day should therefore be constantly vigilant.

tefilla - Why pray for Y'hoshua and not Kalev?

Rashi to Sh'lach 13:16 notes that Moshe prayed that God save Y'hoshua from the other spies' plot. This is a paraphrase of a g'mara (Sotah 34b) which implies strongly that Moshe did not similarly pray for Kalev.

We know Kalev and Y'hoshua were the only two of the spies who did not participate in the other spies' bearing bad news about the land. (See Sh'lach chapter 13.) Presumably Moshe intuited that there was some planned wrongdoing, which explains his prayer for Y'hoshua; but why not pray for Kalev also? Is it that he thought Kalev was, like the rest of the spies, planning wrongdoing? or what?

grammar - When using もう and まだ does a negative verb always have to be in the (ている) present continuous form?

When using もう and まだ in a negative sense, does the negative verb always have to be in the present continuous form i.e. 来ていません、食べていません etc? If so why is that?

Example sentences:

いいえ、まだ買っていません。- Correct

いいえ、まだ買いません。- Incorrect

My translation: No, I haven’t bought (it) yet.

Answer

(This was written before @Choko posted her comment but the two seems to agree.)

The easiest answer to your question is no, it is not that simple. It depends on the nature of the verb and what you want to say.

You reference to "present continuous" suggests that your are not familiar with concepts such as "stative", "durative", "punctual", "subject change" and "continuous change" verb groups or the resultative state in Japanese.

This is quite a big subject to explain (there are probably several theories) but it is the key to the solution you are looking for: I found this paper, from snailboat, quite useful: http://web.archive.org/web/20161103070805/http://homepage3.nifty.com/park/aspect.htm (via Web Archive, since the original link is dead)

BRIEF EXPLANATION OF UNDERLYING GRAMMAR & USE OF ADVERBS

There are not really any short cuts to studying something like this but, in relation to your question, I would summarise this as follows:

Verbs like 来る can be classified as "subject change". In its plain form 来る describes an unexecuted and (probably) future action. In its ている form, 来ている, it usually describes an action that has been executed and the result is still being felt (eg the subject has come and is still here). This is also referred to as in the resultative state. These verbs are different from verbs such a 騒ぐ which in its ている form describes the continuous action (or state) state of making noise rather than a "resultative state".

As you know, adverbs such as まだ and もう are used to describe or refine the action. This can be can be quite important. For example, in the case of

まだ来ていない

来ていない, as the negative form of 来ている, describes the (opposite) state that has not happend. The subject has not come (and is therefore not here). The adverb まだ reinforces this meaning and might be used to imply that somebody was waiting for it to happen or it was over due.

However, getting back to your question, the adverbs もう and まだ can also be used with such plain form verbs in the negative form but their appropriateness also depends what you want to say. For example:

彼はもう行かない。= He is not going again. (ie in the future)

Further, although the ている form of subject change verbs are usually used to describe a resultant state this is not always the case. One way to describe a continuous state using a subject change verb is by choosing an appropriate adverb. A good example is the verb 死ぬ, to die. The following sentences should illustrate this:

僕の猫は死ぬ = My cat is going to die.
僕の猫は死んだ = My cat died.(see note 1)
僕の猫は死んでいる = My cat is dead.
僕の猫はだんだん死んでいる = My cat is slowly dying.

By adding the adverb だんだん the predicate 死んでいる has changed from resultant state to continuous state.

So perhaps the answer to your question is:

No. It depends on the nature of the verb and what you want to say. If the combination of an adverb and a verb does not feel right the best course of action is to consider what you want to say and whether the sentence you have made really means what you want it to mean. This is illustrated by the other example you give:

いいえ、まだ買っていません。 (A)
いいえ、まだ買いません。 (B)

(A) is correct if you want to say: No I have not bought it yet. (B) might be correct if for some reason you wanted to say "No, I am still not going to buy it." (note 2)

---

Note:
1. I am not sure if this really flies as an explanation of the difference between 死んだ and 死んでいる so I have made it a note:

If we accept the saying a cat has nine lives then perhaps we can say it has to die nine times before we can say it is "permanently dead", as in it leaves this world for next. If we can say this then perhaps before it loses its ninth life we can also say:

僕の猫は死んだことが8度ある：My has cat died eight times.

...and it would not be correct to use 死んでいる because the cat is still enjoying its final life.

2.This is consistent with @Choko's comment who suggested that you might not be buying because you were expecting a discount to be announced.

everyday chemistry - Why are smoke odors persistent in fabrics?

Obviously smoke is very complex, but apparently phenol compounds are the main components of wood smoke that produce the characteristic odor. (One of more significant of these compounds seems to be syringol.) The human nose seems to be pretty sensitive to these compounds.

Smoke seems to be very easily absorbed by various fabric-like materials, which then release the compounds back into the air over long periods of time, making the odor quite persistent. I'd like to know what is going on with these compounds and the fabric-like materials to cause this behavior.

minhag - What happens when the neshama has an aliya?

there is a common practice to learn torah for someone who is deceased 'l'iluy nishmato/a' - to raise her/his soul. There is also a common (american/ashkenazik?) custom for a relative of a deceased person to provide food and drink to others on the yartzeit of the deceased. Before making a blessing on the food and drink (or sometimes after) people will say "the neshama should have an aliya".

I would like to understand the mechanics of what is happening here. presumably the miztvot that are being done accrue some sort of merit for the deceased person. Is this correct?

I also assume that these merits cause the neshama to become closer to God which is what is implied by 'having an aliya'. How is this understood; especially in light of the Rambam's statement that a person's closeness to God is directly proportionate to the person's intellectual grasp of God

physical chemistry - what kind of suspension liquid should be used with ferrofluid (so it does not stain the glass)

Please take a look at the following video:

I am working on a new project, and I need to find whats the best liquid to hold ferrofluid inside the glass (or maybe even plastic) container, so that ferrofluid (that easily stains everything) does not stain or stick to glass?

Also, is there any special preparation for the glass needed?

Answer

I don't have a full answer, but a hint at how to choose your liquid. You want the ferrofluid not to mix with it, so your fluid has to be immiscible with the ferrofluid solvent (or carrier fluid; ferrofluids are colloidal suspensions). In the case of your “FerroFluid EFH-1”, the solvent is a light mineral oil, so you should go with a polar solvent.

Secondly, you want the ferrofluid solvent not to touch the glass, to avoid staining. In order to do so, you need your liquid to wet the bottle more than the mineral oil, i.e. to have a smaller contact angle. You can play on both the bottle material and nature of the fluid to achieve this. I suggest protic polar solvents, which should wet regular glass well: water, ethanol, isopropanol, acetic acid, …

What's the strongest known organic acid?

What's the strongest known organic acid? Is it maybe trifluoromethanesulfonic acid or tautomer of pentacyanocyclopentadiene?

EDIT: Since the question was reactivated I thought about formalising it. I can think of a few categories of compounds: neutral (actually created or only studied in silico) and cationic (also two options). Second Dave's answer and ANM's one do the trick for two groups, but two other options remain (still prefer answers without boro/silico/etc. stuff).

halacha - Is AquAdvantage salmon kosher?

After two decades of deliberation, the USA's Food and Drug Administration has approved the first ever genetically engineered food animal, a fast-growing Atlantic Salmon called AquAdvantage salmon.

According the agency, which announced the approval Thursday, the modified salmon are safe to eat, equally nutritious as other salmon, and should pose no threat to the environment.

First created in 1989 and submitted to the agency for approval in 1995, the Atlantic salmon are modified to carry a growth hormone gene from Chinook salmon. That gene is further engineered to be under the control of a tiny bit of DNA, called a promoter, from the eel-like ocean pout fish. In general, DNA promoters are non-coding sequences that help control the expression level of a gene—how much protein product is synthesized from the gene. With the engineered promoter boosting hormone production, the modified salmon grow to market-size in about half the time of conventional Atlantic salmon.

^{["FDA approves first GM food animal—Atlantic salmon," by Beth Mole, ars technica, Nov 19, 2015]}

Atlantic and Chinook salmon are kosher, but ocean pout is not kosher.^[Source]

Is AquAdvantage salmon kosher?

halacha - Can Jews be rulers of countries other than Israel?

With the current political mayhem in the US, an interesting question regarding whether a Jew is halachically permitted to accept rulership of a country other than that of Eretz Yisrael has arisen.

So for example, if Bernie Sanders does become the Democratic nominee, is he permitted halachically to accept the presidency if he wins?

On a side point, is it written or taught anywhere that a Jew will never be a king or ruler of a gentile country? I have heard this but can't confirm sources.

Answer

Brachos 58a says that upon seeing a "melech Yisrael", one recites the blessing:

Baruch ... SheChalak MiKvodo Lirei'av.

Bless You God, who apportioned from Your honor to those who fear you!

Piskei Teshuvos Orach Chaim 224 writes that the exact same applies to an observant Jew who rules a land other than Israel.

If I recall correctly, one of the angles from which the Ran in Nedarim approaches Dina DeMalchusa Dina (Judaism's recognition of the law of the land) is that the ruler can say "keep my rules, or I'll throw you out!" He then addresses the land of Israel (in which he can't really throw you off the land), but also a Jewish ruler in France, who could.

fft - STFT and DWT (Wavelets)

STFT can be successfully used on sound data (with a .wav soundfile for example) in order to do some frequency-domain modifications (example : noise removal).
With N=441000 (i.e. 10 seconds at sampling rate fs=44100), windowsize=4096, overlap=4, STFT produces approximatively a 430x4096 array (first coordinate : time frame, second coordinate : frequency bin). Modifications can be done on this array, and reconstruction can be done with overlap-add (*).

How is it possible to do a similar thing with wavelets ? (DWT), i.e. get a similar array of shape a x b, with a time frames, and b frequency bins, do some modification on this array, and at the end, recover a signal ? How ? What is the wavelet equivalent to overlap-add ? What would be the Python functions involved here (I haven't found an easy example of audio modification with pyWavelets...) ?

(*) : Here is the STFT framework that can be used :

signal = stft.Stft(x, 4096, 4)    # x is the input
modified_signal = np.zeros(signal.shape, dtype=np.complex)

for i in xrange(signal.shape[0]):    # Process each STFT frame

    modified_signal[i, :] =  signal[i, :] * .....  # here do something in order to
                                                   # modify the signal in frequency domain !
y = stft.OverlapAdd(modified_signal, 4)   # y is the output

The goal is to find a similar framework with wavelets.

dft - Amplitude estimation of sinusoid in known spiky spectral noise

What is the "best" way to estimate amplitude of a known-frequency sinusoid in the presence of known spiky spectral noise (i.e. noise comprising a few spectral peaks at known frequencies)?

• By "best", I mean highest accuracy and lowest variance for a given sampling period (assume the sampling rate is greater than the Nyquist frequency).


• The phases of the spectral noise peaks are unknown, but the phase of the sinusoid of interest can be provided if it's useful.

The approaches I am aware of are:

1. Perform a DFT at the frequency of interest, and design the window function such that its nulls/zero-crossings are located at the known noise frequencies.


2. Use a least squares estimator (which is basically a DFT with a rectangular window?, and which wrongly assumes that the noise samples are uncorrelated), e.g. as described in this survey paper.

I can't think of a better way than method (1), which does not benefit from phase information, but I'm wondering if a better approach could be used which may even take advantage of phase information of the signal of interest.

Just as a note, though I don't quite understand why, I noticed that the nulls of a rectangular window fall at integer multiples of the frequency that completes exactly one cycle in the sampling period.

fft - What's the best criterion for determining a frequency peak?

I'm writing an algorithm that analyzes results of discrete Fourier transform (DFT). The algorithm should detect amplitude peaks in predefined ranges of frequencies. This is an example of such a peak:

Vertical red lines are range boundaries (left and right) and range center (middle).

What are the best criteria for determining the absence of this peak in a specified range?

For now I'm using standard deviation and comparing it to some calibration value. But it can be easily confused with some high amplitude noise like this:

organic chemistry - Why there is a huge difference between the basicity of urea and guanidine?

The two molecules have very similar structures, but urea has a $\mathrm{p}K_\mathrm{b}$ of $13.9,$ while guanidine have a $\mathrm{p}K_\mathrm{b}$ of $0.4.$ If guanidine cation can be stabilized by resonance, then why can't urea cation do so?

digital communications - How to derive the transmitted signal from a constellation diagram

Let us assume we have $16$ symbols to transmit. We can represent these $16$ symbols by $16$ unique signals and transmit. If at the receiver we can identify these $16$ signals correctly, we have identified the symbols transmitted correctly. I have used qammod([0:15],16,0) in MATLAB and got the output that is attached here.

>> a = qammod([0:15],16,0); a'

ans =

  -3.0000 - 3.0000i
  -3.0000 - 1.0000i
  -3.0000 + 1.0000i
  -3.0000 + 3.0000i

  -1.0000 - 3.0000i
  -1.0000 - 1.0000i
  -1.0000 + 1.0000i
  -1.0000 + 3.0000i
   1.0000 - 3.0000i
   1.0000 - 1.0000i
   1.0000 + 1.0000i
   1.0000 + 3.0000i
   3.0000 - 3.0000i
   3.0000 - 1.0000i

   3.0000 + 1.0000i
   3.0000 + 3.0000i

$0,1,\ldots,15$ represent the $16$ symbols. $16$ represents the number of symbols or the number of unique signals - sinusoids with different amplitudes and phases - to be transmitted. $0$ represents the offset phase.

Now I want to interpret the output. I actually got $16$ complex numbers.

• What do they represent?


• What are the magnitude, phase, real part and imaginary part of these complex numbers that they represent? I guess they represent the parameters of sinusoidal signals.


• In both the real and imaginary parts we see $-1, -3 , 1$ and $3$. We do not see $-2, 0$ and $2$. Why?

Answer

This is a basic question about how passband pulse-amplitude-modulation (PAM) works. It has nothing to do specifically with QAM, but it applies to any type of passband PAM (such as PSK, or any other choice of a constellation).

The question is how to obtain a transmit signal from a given point in a constellation diagram. Let's say that at time $t=kT$ we want to transmit a signal corresponding to the point $a_k$ in the constellation diagram, where $a_k$ is a complex number:

$$a_k=\text{Re}(a_k)+j\text{Im}(a_k)=|a_k|e^{j\phi_k}$$

The complex number is multiplied by a (real-valued) transmit pulse $g(t)$ and by a complex carrier, and the transmitted signal is the real part of that complex-valued signal:

$$\begin{align}s_k(t)&=\text{Re}\left(a_kg(t-kT)e^{j\omega_0t}\right)\\&=\text{Re}(a_k)g(t-kT)\cos(\omega_0t)-\text{Im}(a_k)g(t-kT)\sin(\omega_0t)\\&=|a_k|g(t-kT)\cos(\omega_0t+\phi_k)\end{align}\tag{1}$$

In practice you transmit a sequence of symbols, and the corresponding transmitted signal is given by

$$\begin{align}s(t)&=\sum_ks_k(t)\\&=\cos(\omega_0t)\sum_k\text{Re}(a_k)g(t-kT)-\sin(\omega_0t)\sum_k\text{Im}(a_k)g(t-kT)\\&=\sum_k|a_k|g(t-kT)\cos(\omega_ot+\phi_k)\end{align}\tag{2}$$

As you can see from $(1)$ and $(2)$, the transmitted signal can be represented either as two amplitude-modulated orthogonal carriers (sine and cosine), or as an amplitude and phase modulated carrier. In the first case the real and imaginary parts of $a_k$ determine the amplitudes of the two carriers, and in the second case the magnitude $|a_k|$ determines the amplitude of the carrier, and $\phi_k=\arg\{a_k\}$ is the phase of the carrier.

Calculate IFFT using only FFT?

Say you start out with $A=\left\{3,−1,0,0\right\}$, run fft() and end up with $B=\left\{2,3+j,4,3-j\right\}$.

What specific steps would need to be done to obtain $A=\left\{3,−1,0,0\right\}$ again using some pre-calculation on $B$, then fft(), then maybe post-calculation steps before obtaining $A$? I have heard that this is possible but have not been able to work out how.

Answer

We want to do inverse DFT: $$ x(k) = \frac{1}{\sqrt{N}}\sum_n y(n) e^{j 2\pi kn/N}, $$ but can only do forward DFT. So let's try to make it "look" like a forward DFT. Note that we want a minus sign in the complex exponential. We can introduce it via complex conjugation: $$ \overline{x(k)} = \frac{1}{\sqrt{N}}\sum_n \overline{y(n)} e^{-j 2\pi kn/N}, $$ That is starting to look like a forward DFT now! So the recipe is:

1. Complex conjugate the given sequence that we want to inverse DFT


2. Calculate its forward DFT


3. Calculate complex conjugate of the result.

That gives you the inverse DFT of the original sequence.

(Note that I cheated a little bit on the scaling factor to make it easier!)

product recommendation - What should I use for Mishna study?

I'm new to Mishna study, and I want to participate in a communal effort to study Mishna. I picked out a section to study, and now I need to find a convenient resource to learn from. I don't necessarily have time to make a comprehensive study of all of the relevant commentaries and Talmud, but I do want to understand what's going on in the Mishna. I prefer resources that include English translation, and I'm open to both in-print and electronic resources.

What resource would you recommend, and why?

organic chemistry - Steroisomerism in cyclic compounds

What about stereochemistry of 1,2,3,4-tetrahdroxy cyclobutane How will we decide the stereocentre it's eating me can anybody help.

Answer is 4 stereoisomers

grammar - Why is やりたい放題 used as opposed to やり放題?

A common word in Japanese, meaning "all-you-can-drink", is "飲み放題". It is "放題" - as much as you would like - appended to the verb-stem of "飲む". It is the same rule for instance, for: 食べ放題, 読み放題, （電話）かけ放題 etc...

Why is it then "やりたい放題" as opposed to "やり放題"?

---

Answer

やりたい放題 is a bit different from other ○○放題. It's an idiomatic phrase which primarily refers to someone's tyrant-like, irresponsible, self-indulgent behavior. Because it usually has a negative connotation, it's less likely to serve as a marketing phrase (except something like this).

母親が亡くなって以降、あの王女はやりたい放題だ。

やり放題 is less common and may refer to the same thing as やりたい放題. But actually やり放題 is the word that sounds closer to "all-you-can-X" as in 飲み放題, 食べ放題, マンガ読み放題, etc. That's why you got many results from manicure salons (ネイルが○○円でやり放題) and sex-related articles. Unless properly modified (eg レトロゲームやり放題, インターネットやり放題), I personally feel やり放題 can be easily associated with sexual contexts. Please use it wisely.

meaning - Did standalone noun “好き” mean a person in classical Japanese?

In classical Japanese, did standalone noun “好き” mean a person who likes something? I do not think that it does in modern Japanese, although it sometimes means a person when used as a suffix (e.g. 野球好きが集まる公園).

If it did, it explains why 好き can be equated with ものの上手 (a very skilled person) in the proverb “好きこそものの上手なれ,” which I failed to explain in my answer to the question “Help on a specific usage of こそ” by yadokari.

Answer

I don't think it did. I haven't encountered it with that meaning, I can't find that meaning in a dictionary, and there was already the word "sukisha" or "sukimono" (spelt various ways) with that meaning.

All that is just negative evidence, but there is additional evidence re what "好き" means in this context if you look at the full version of the proverb. 日本国語大辞典's oldest attestation is from 其角十七回 (1723), and is inside a poem, as follows:

器用さとけいことすきと三つのうちすきこそものの上手なりけれ、と口ずさみせられけるが

There are other websites that attribute the poem, or a very similar one, to Sen no Rikyū (1522-1591), which would obviously predate Kikaku, but I haven't been able to find a reliable source for this. Here's an example of a slightly different version attributed to SR:

器用さと 稽古と好きの そのうちで 好きこそものの 上手なりけれ

In both of these you can see that 好き first appears in the same "slot" as 器用さ (skill) and 稽古 (practice), which are definitely abstract nouns. I guess the second appearance of 好き might be intended to mean "a person who has 好き", but interpreting the なりけれ part more flexibly (or adopting dainichi's "liking = excelling" suggestion) seems like a more natural strategy to me than forcing 好き to behave that way.

history - When did Matza become dry?

It's pretty commonly accepted that Matza used to be soft (sort of like a tortilla) and was used by Hillel to make a wrap (not a sandwich).

When did this change in various geographic locations which now use Matza that is dry and cracker-like? I'm looking for explicit statements by Rishonim, Achronim or other reputable historical sources regarding the consistency of their communities' Matza, not theoretical discussions about hard or soft Matza in general.

(I am not interested here in debating if one can use soft or hard Matzas today, various Hashgachas on soft Matzas, the practices of communities who today still use soft Maẓẓa traditionally, or any other Jewish Law type issue.)

resampling - What are the relative merits of various upsampling schemes?

I recently encountered a DSP system which did some internal upsampling via zero padding. Expecting zero-order-hold, I was surprised to find that a DC signal did not produce a DC output; many harmonics of the internal (lower) sampling frequency were also present in the output.

This leads to my question: What upsampling techniques are commonly used, and what are their relative merits? Why would I choose zero padding, zero order hold, or first order hold, and what other techniques are available?

Some clarifications:

• The system is real-time, so the upsampling scheme must be causal.



• The upsampler is followed by a an anti-aliasing filter that can also be specified.

Answer

For the purposes of this answer I will use Matlab's terminology and define "upsampling" as the process of inserting $m-1$ zeros in between the input samples, and "interpolation" as the combined process of upsampling and filtering to remove the $m-1$ aliases ($m$ being the interpolation factor) that upsampling introduces. For an explanation of how/why upsampling introduces aliases, please see this thread.

It is important to understand that any low-pass filter can be used to get rid of the aliases and thus complete the interpolation. Some filters have advantages when used in interpolation, though. I'll discuss the various flavors of interpolation filtering below.

FIR Filter

Interpolating FIR filters are efficient because they combine upsampling and alias filtering into one step. This is most easily seen in an example. Suppose we have a data sequence $x[n]$ and we want to interpolate it by a factor of two. The first step is to upsample by a factor of two. This changes the original data sequence from $x_0, x_1, ... x_N$ to $x_0, 0, x_1, 0, ... x_N$.

Now suppose we have a low-pass FIR filter, $h[n]$, that we will use to remove the alias. When we convolve the upsampled data sequence with the filter, half the filter taps are stimulated by the non-zero samples, and half the taps are inactive because they correspond to the zero samples. The half that is stimulated and the half that is inactive flips back and forth as the filter goes through the data. These two sets of taps are sometimes referred to as the filter phases.

This same effect can be achieved implicitly by eliminating the upsampling, and filtering the original data sequence with an interpolating FIR filter. The interpolating FIR filter produces $m$ outputs for every input sample. For all $m$ outputs the filter will operate on the same $ceil(K/m)$ input samples (where K is the number of filter taps and "ceil" is the ceiling function).

An example will hopefully illustrate how this works. Suppose that we have a six tap filter and we are interpolating by a factor of two. The filter taps are [1 -2 4 4 -2 1]. If we literally interpolated and then filtered the samples and filter taps would line up (once there was full overlap) as follows:

$$ 0 : 1\\ x_2 : -2 \\ 0 : 4 \\ x_1 : 4 \\ 0 : -2 \\ x_0 : 1 \\ $$ Next sample...

$$ x_3 : 1\\ 0 : -2 \\ x_2 : 4 \\ 0 : 4 \\ x_1 : -2 \\ 0 : 1 \\ $$ Next sample...

$$ 0 : 1\\ x_3 : -2 \\ 0 : 4 \\ x_2 : 4 \\ 0 : -2 \\ x_1 : 1 \\ $$ And so on. The point of the interpolating filter is that it skips actually inserting the zeros and just alternates which set of taps it uses at the moment instead. Thus, the preceding sequence would now look like the following:

$$ x_2 : -2 \\ x_1 : 4 \\ x_0 : 1 \\ $$

$$ x_3 : 1 \\ x_2 : 4 \\ x_1 : -2 \\ $$

$$ x_3 : -2 \\ x_2 : 4 \\ x_1 : 1 \\ $$

Zero Order Hold

A zero-order hold interpolator is one that simply repeats each sample $m-1$ times. So a factor of two zero-order hold interpolator converts $x_0, x_1, ... x_N$ into $x_0, x_0, x_1, x_1, ... x_N, x_N$. This method is attractive because it is exceedingly easy, both in terms of coding and computational load, to implement.

The problem with it is that its low-pass filtering is quite poor. We can see that when we recognize that the zero-hold interpolator is a special case of FIR interpolation. It corresponds to upsampling followed by an $m$-wide rectangle filter. The Fourier transform of a rectangle filter is a sinc function, which is a rather shabby low-pass filter. It's shabbiness can be fixed with a compensating FIR filter, but if you are going to do that you might as well just use a good low-pass filter to begin with.

First Order Hold

First order hold is a step up from the zero-hold interpolator in that it linearly interpolates the upsamples using the two nearest input samples. So, a factor of two first-order hold interpolator would convert $x_0, x_1, ... x_N$ into $x_0, \frac{x_0+x_1}{2}, x_1, \frac{x_1+x_2}{2}, ... x_N$.

Like the zero-order hold interpolator, the first-order hold interpolator is a special case of FIR interpolation. It corresponds to upsampling and filtering with a triangle filter. For factor-of-two interpolation the filter is $[\frac{1}{2} 1 \frac{1}{2}]$, for factor-of-three interpolation the filter is $[\frac{1}{3} \frac{2}{3} 1 \frac{2}{3} \frac{1}{2}]$, and so on.

The triangle filter is two rectangle filters convolved together, which corresponds to sinc squared in the frequency domain. This is a definite step up from the zero-order hold, but is still not great.

IIR Filter

I have never used an interpolating IIR filter so I won't say a lot about them. I assume that the same arguments apply as in regular filtering- IIR filters are more efficient, can be unstable, don't have linear phase, etc. I do not believe that they can combine the upsampling and filtering steps like a FIR filter can, but I could be wrong about that.

FFT Interpolation

I'll throw this one in even though it's not very common (of course, I don't think the zero-hold is common either). This thread discusses FFT resampling, where resampling is both interpolation and decimation.

Higher Order Holds

Second-order hold interpolators are usually referred to as "quadratic interpolators". They are non-linear and thus cannot be implemented as FIR filters, which are linear. I do not understand the math behind them well, so I won't discuss their performance. I will say, though, that I believe that they are somewhat common outside of signal processing.

Higher order (three or more) methods also exist. These are referred to as "polynomial regressions".

EDIT:

Cascade Integrator Comb (CIC) Filters

I forgot to mention CIC Filters. CIC filters are used for two reasons: they use only adders/subtracters (not as big a deal now that multiplies are fast and cheap), and they can do really large sample rate changes pretty efficiently. Their down side is that they are essentially an efficient implementation of a cascaded rectangle filter, so they have all of the disadvantages of rectangle filters as discussed above. CIC interpolators are pretty much always preceded by a compensating FIR filter that pre-distorts the signal to cancel out the distortion introduced by the CIC. If the sample rate change is large enough the cost of the pre-distortion filter is worth it.

organic chemistry - Why do cyclic ethers have higher boiling points than their acyclic isomers?

TL;DR version is the question title. Some context and data follow.

I was creating an assignment for my organic chemistry students in which they would need to draw as many isomers as they could from a simple formula, for example $\ce{C3H6O}$ (which fits 7 structures - 9 if you count minor enol tautomers and 11 if your count stereo). In this set (ignoring stereo and enols) there are:

Two alcohols

Two carbonyl compounds

• Propanal - boiling point $=46\ ^\circ\text{C}$


• Acetone - boiling point $=56\ ^\circ\text{C}$

Three ethers

The boiling point of methyl vinyl ether immediately stood out as anomalous. The fully saturated ethyl methyl ether has a boiling point of $7.4\ ^\circ\text{C}$.

Here are some more data comparing cyclic ethers to their acyclic isomers (and some analogs). The gap appears to be closing as the number of carbons increases.

Four carbons

Five carbons

Answer

The data I could find suggests that cyclic ethers have higher dipole moments than their acyclic counterparts.

$$\mathbf{Four~carbons}$$ \begin{array}{c @{} c} \hline \text{THF} & \mathrm{1.63~ D ^1, 1.75~ D ^2} \\ \text{1-butene oxide} & \mathrm{1.89~ D^2} \\ \text{ethyl vinyl ether} & \mathrm{1.26~ D ^2} \\ \text{diethyl ether} & \mathrm{1.15 ~D ^3, 1.15 D ^2} \\ \text{methyl propyl ether} & \mathrm{1.11 ~D ^2} \\\hline \end{array}

$$\mathbf{Five~carbons}$$ \begin{array}{c @{} c} \hline \text{Tetrahydropyran} & \mathrm{1.58~D ^2, 1.87~D ^4} \\ \text{2-Methyltetrahydrofuran} & \mathrm{1.38~ D ^5} \\ \text{dipropyl ether} & \mathrm{1.21~D^2, 1.00~D^6} \\\hline \end{array}

This seems consistent with intuitive expectations based on conformational models where, in the cyclic ethers where the molecular geometry is constrained by the ring, the lone pairs are pointing in the opposite direction from the carbon skeleton. Whereas the lone pairs and carbon chains in the conformationally more mobile acyclic isomers are less geometrically fixed and therefore less "directed" in space.

It seems likely that the higher dipole moments in the cyclic compounds would lead to greater alignment / ordering in the liquid phase, which in turn would lead to higher boiling points.

References:

_{1: http://en.wikipedia.org/wiki/Tetrahydrofuran
2: https://physicalchemistryrosamonte.wordpress.com/material-balances/material-balances-on-a-crystallizer/physical-properties-of-pure-methanol/dipole-moment/
3: http://en.wikipedia.org/wiki/Diethyl_ether
4: http://www.drugfuture.com/chemdata/tetrahydropyran.html
5: http://www.stenutz.eu/chem/solv28.php?s=1&p=20
6: https://books.google.com/books?id=G6jaBwAAQBAJ&pg=PA50&lpg=PA50&dq=propyl%20ethyl%20ether%20dipole%20moment&source=bl&ots=VA52gqJ0kn&sig=GM8tua_QpXccFW3VXpy9qiNf7rk&hl=en&sa=X&ei=rzRvVZ__Cc32yQT9gIPACQ&ved=0CDsQ6AEwBQ#v=onepage&q=propyl%20ethyl%20ether%20dipole%20moment&f=false}

halacha - What's a better choice: Treif meat or human flesh?

If one is stuck on a deserted island with no kosher food and he has a choice between eating human flesh of a dead person or the flesh of a non-kosher animal, which is preferable to eat?

halacha - If I sign a contract without reading it (such as a website's Terms and Conditions), is it halachically binding?

Many websites and computer applications require users to agree to "Terms and Conditions". However, few users actually read them. Are such conditions halachically binding? Does it depend on whether such conditions are reasonable in some way?

Answer

The signature of a person on a contract or on any other document involved in any form of transaction between two or more parties is considered be an absolutely valid Halachic Kinyan. A person who has signed such a document may not back out of the agreement that he has signed without the express permission of the other party involved.

The signature of a person on a document constitutes agreement to all terms mentioned in the document, even if witnesses testify that the signer did not read or understand all of the terms mentioned therein. Therefore, before signing any document a person should carefully examine everything mentioned in it, or ask someone whom he trusts to explain to him what exactly it is that he is signing to.

The Halachos discussed above are stated explicitly in the Shulchan Oruch (Choshen Mishpat 69:1), in the Shach there, in the Nesivos in Biurim, and in the Teshuvos HaRashba (Siman 77).

http://www.torah.org/advanced/business-halacha/5757/vol2no33.html

(This answer assumes the digital EULA\Terms and Conditions is a valid halachic contract, and the checkbox is a valid halachic signature. Whether this is true is asked here and here.)

inorganic chemistry - Dihedral angle of gaseous and crystalline HOOH

Why does hydrogen peroxide exhibit a dihedral angle of 111.5 degrees in the gaseous state? And a dihedral angle of 90.2 degrees in the crystalline phase?

I know that in general, there is likely to be more hydrogen bonding in the crystalline phase than in the vapor phase.

But what's up with 1) the bond angles themselves in the first place and 2) the bond angle expansion in the gas phase? How can one rationalize them?

I know that there exist lone pairs on the oxygens and lone-pair/lone-pair repulsion should probably be minimized, but what it is about these conformers that minimizes energy? I'm guessing that we'd also want to minimize eclipsed and gauche interactions ... Newman projection time?

It seems that there is only one Newman projection possible for HOOH; i.e. we'll have the inevitable lone-pair/lone-pair interaction, and the lone-pair/hydrogen interaction. I guess all we can do is minimize these interactions; i.e. the energy-minimized conformer is probably not the one with them all eclipsed. However, why does it seem that the energy-minimized conformer for vapor HOOH is one that puts the lone-pairs so close to each other in terms of dihedral angles?

Answer

You've already answered your own question - hydrogen bonding.

First, don't think of it as why is the gas state different than solid state. Rather, think about why is the solid state different than the gas state. In the gas state there is very little intermolecular interaction (very, very few species do not follow the ideal gas law to many significant digits). The gas state geometry is close to what is expected for sp3 tetrahedral geometry and may be considered normal. The link below is a paper discussing the gas phase microwave spectroscopy of H2O2 in far greater detail than I can hope to here. The description of the torsional rotation energies was not trivial.

Internal‐Rotation in Hydrogen Peroxide: The Far‐Infrared Spectrum and the Determination of the Hindering Potential by Hunt, Robert H. and Leacock, Robert A. and Peters, C. Wilbur and Hecht, Karl T., The Journal of Chemical Physics, 42, 1931-1946 (1965), DOI: http://dx.doi.org/10.1063/1.1696228, mirror

When condensed to the solid state, molecules get close enough to allow intermolecular forces (in this case hydrogen bonding in a much greater extant than Van der Waals). Additionally, the energies of the crystal lattice must be considered. In this case, th

word choice - Differences between 「が」、「ても」、「のに」

What is the usage difference between these three definitively? As an intermediate Japanese speaker, I somewhat understand where I would say them, but I can't point out under which contexts any of them "wouldn't be allowed" compared of any of the others. In speech, I have no problem selecting one for usage, but I just can't pick out if, when somebody else uses one, they are using it in an "incorrect" way (I can figure out if it's natural or not).

〜が is largely a "but", where you give a contradicting statement afterwards

〜ても is closest to an "even though" suffix to a word

〜のに is a more emotional "が", with a connotation that even though an action was taken, that something has / hasn't happened.

Where is each NOT allowed under the other contexts?

Answer

が

 ○ 私は電車で行きますが、あなたはどうしますか。
 × 私は電車で行っても、あなたはどうしますか。
 × 私は電車で行くのに、あなたはどうしますか。

The spirit of が is not contradiction, but that the next phrase comes from "other direction". Since English language doesn't have a word wholly translates it, it could become "and", "while", "when", or even "so". But as far as I know, Korean, Vietnamese and Polish have similar notions.

The colloquial equivalent is けど.

ても

 × 何度食べたが、ブロッコリーは嫌いだ。
 ○ 何度食べても、ブロッコリーは嫌いだ。

 × 何度食べたのに、ブロッコリーは嫌いだ。
(○ 何度も食べた[が/のに]、ブロッコリーは嫌いだ。)

As you said correctly, this word corresponds to "even if", "no matter", or "-ever" in whatever, whenever. Thus, only this one is grammatical with bare question words.

のに

 × 約束したが、どうして来なかったんですか？
 × 約束しても、どうして来なかったんですか？
 ○ 約束したのに、どうして来なかったんですか？
(○ どうして、約束[したのに/しても]来なかったんですか。)
(△ 約束しましたが、どうして来なかったんですか？)

This one is a loaded word, that conveys the latter statement contradicts with expectation or obligation the former one implies. In most cases, it's almost ungrammatical to use other words when the latter clause carries accusatory connotation.

meal seudah - Shmiras Einayim Problem

Someone who's family sometimes has a certain modest young couple over their house on Shabbos for a meal.His Yetzer Harah can get him excited if the wife is a pretty girl. Would anyone have any good advice for someone in this situation ?

halacha - Feet together or just heels for Shmoneh Esrei?

During Shmoneh Esrei, i've always learned that the feet should be kept together, for whatever reason. However, lately i've noticed people who only keep their heels together, but not the rest of their feet. (Then there are the people who don't have their feet together at all, but that's of course wrong.)

Is this an acceptable practice?

Answer

See this article from yeshiva.org.il which quotes השו"ע על פי הגמרא:

שיהיו רגליו צמודות זו לזו עד שנראה כאלו שתיהן הן רגל אחת. מקור הלכה זו נלמד מספר יחזקאל, מתוך תיאור המלאכים בזמן עמידתם לפני ה', שכתוב עליהם

"ורגליהם רגל ישרה",

כלומר נראים כרגל אחת

the Shulchan Oruch according to the Gemoro that the two feet have to appear as one foot. This would seem to mean that they should be together all the way along the length not just at the heel.

selling mechirat chametz - Trash as Chometz

Is the trash in my trash cans that must stay on my property during Passover still considered under my ownership?

Do Jews believe that God's name is "God"?

I have recently asked a question about taking God's name in vain. And I have been told that swearing is taking his name in vain. So in teachings I see it mentioned G-d or Gcd. Showing to me a resistance of even saying the word "God". Why is this necessary? For when I say "God" I most likely am not swearing an oath. Do Jews believe that God's name is "God"?

Answer

The name is supposed to capture the essence of a thing. Since we have no way whatsoever to comprehend God, the names of Him we find in the torah are just representative of His mode of conduct, how He relates towards us. So, to answer your question. Strictly speaking - No. because He does not have a name since we cannot represent as He truly is.

Here's a relevant quote from the chovos halevavos shaar yichud ch.10 (see there for much more)

Since it is impossible to form a representation of Him with the intellect or picture Him with the imagination, we find that Scripture ascribes most of its praises to the "name" of G-d, as written: "And they shall bless Your glorious Name" (Nehemiah 9:5), and "that you may fear this glorious and revered Name" (Devarim 28:58), and "Let them praise Your Name, great and revered" (Tehilim 99:3), and "and of My Name he was afraid" (Malachi 2:5), and "But unto you that fear My Name shall the sun of righteousness arise with healing in its wings" (Malachi 3:20), and "Sing unto G-d, sing praises to His Name, extol Him that rides upon the skies, whose Name is the L-ORD" (Tehilim 68:5).

All this is in order to honor and exalt His glorious essence because, besides clarifying that He exists, it is impossible for us to clarify in our minds anything about His Being except for His great Name.

But as for His glorious essence and His true nature - there is no picture or likeness that we can grasp in our minds. Therefore, His Name is frequently changed in the torah and likewise in the books of the prophets.

Because we cannot understand anything about Him except for His Name and that He exists. His glorious Name is also associated with heaven and earth and the Spirits, as Abraham said: "And I will make you swear by the L-ord, the G-d of heaven and the G-d of the earth" (Bereishis 24:3), and Yonah said: " I fear the L-ord, the G-d of heaven" (1:9), and Moshe said: "the G-d of the spirit of all flesh" (Bamidbar 27:16). And the verse proclaims: "Behold, I am the L-ord, the G-d of all flesh" (Yirmiya 32:27).

and the Tov Halevanon Commentary there:

(Tov Halevanon: His name is changed in the torah) such as the name "Yud-Hey-Vuv-Hey" which teaches that He was, is, and always will be. Or the name "Adon-ay" which teaches that He is master over the creations, or the name "Elo-him" - that He is powerful and all-capable, or the name "Sha-day" - that He is "meshaded" the marachos. The verse adds "of heaven and earth" to teach that we do not completely understand His true Name but rather we see Him according to what we understand through His existence and deeds)

halacha - Shomer Negiyah- negated by Mikvah?

If a woman in an unmarried relationship goes to Mikvah, does that allow for freedom of touching in any way, besides for actual intercourse or spilling of seed in vain, between said couple (both according to Halacha deoraita and derabanan, including modern takanot)?

Such a practice certainly removes the problem of touching a niddah- but, aside from "spirit of the law" considerations (which are certainly important) would one transgress any prohibition?

halacha - What blessing does a midget say on seeing himself?

Following "reciting-the-blessing-of-meshaneh-habriyos-who-makes-creatures-different":

1. 
   

   what does a man that falls into that category, e.g. a midget, says upon himself?

   
   


2. 
   

   Does he have to see himself (like in a mirror) or just look at his body?

   
   


3. 
   

   How often does he say the blessing (if any)?

   
   
   

discrete signals - IDFT of $Y[k]=2X[k]$ for even $k$

If the 16-point DFTs of $x[n]$ and $y[n]$ are given as $Y[k]=\begin{cases}2X[k], & k=0,2,4,...,14 \\ 0, & k=1,3,5,...,15\end{cases}$, where $x[n],y[n]=0, \forall n<0, n>15$, how can I write $y[n]$ in terms of $x[n]$?

If I take $H[k]=1+(-1)^k$ and multiply it with $X[k]$, I should get $Y[k]$. But when I take its IDFT, it turns out to be zero. How to solve this?

Answer

Below is a block-diagram of your signal processing chain (ignoring multiplication by 2).

$$ x[n] \longrightarrow \boxed{ \text{ DFT-N } } \longrightarrow X[k] \longrightarrow \boxed{ \downarrow 2 } \longrightarrow \boxed{ \uparrow 2 } \longrightarrow Y[k] \longrightarrow \boxed{ \text{ IDFT-N } } \longrightarrow y[n]$$

Where sequence $x[n]$ has a length of $N=16$ samples, $X[k]$ is its $N$-point DFT sequence. And $Y[k]$ is related to $X[k]$ as given by $$ Y[k] = \begin{cases} { 2 X[k] ~~~ , ~~~ k = 0,2,...,N-2 \\ 0 ~~~ , ~~~ \text{ otherwise } \\} \end{cases} $$

I will solve this problem using the duality argument. Eventhough it's not necessary, it can reduce the mathematical burden via bypassing explicit computations.

The duality in DFT stems from the fact that the forward and inverse DFT transforms are (almost) identical, designated with the following: ($n$ time , $k$ frequency)

$$ x_t[n] \leftrightarrow X_f[k] \iff X_f[n] \leftrightarrow N x_t[-k] $$

We can use the duality property to observe that if an operation $T$ is performed on the time-domain signals $x[n] \xrightarrow{T} y[n]$ with a corresponding reflection on the frequency domain as $X[k] \xrightarrow{M} Y[k]$, where $M$ is the frequency-domain reflection operator of the time-domain operator $T$ , then the same operation $T$ performed on the freqency domain signals will have the same reflection operator $M$ on the corresponding time domain signals, with a possible scale factor if different sample rates are used on the left and right nodes.

Therefore, to use duality, in the above block diagram, I'll replace the frequency domain relation between $Y[k]$ and $X[k]$ with a time domain relation as:

$$v[n] \longrightarrow \boxed{ \downarrow 2 } \longrightarrow w[n] \longrightarrow \boxed{ \uparrow 2 } \longrightarrow z[n] $$

where in the time domain the operation is compression (downsampling) and expansion (upsampling) whose frequency domain DFT relation is readily available as:

$$ W[k] = 0.5 ( V[k] + V[k+N/2] ) ~~~, k = 0,1,..,N/2-1 $$

where $W[k]$ is $N/2$ point DFT of $N/2$ point compressed sequence $w[n]$, and $V[k]$ is $N$ point DFT of $N$ point sequence $v[n]$. Stated verbally, $W[k]$ is obtained from $V[n]$ by adding its second half onto its first half.

Then $$Z[k] = W[ (k)_{N/2}] ~~~, k = 0,1,2,...,N-1 $$

Where $Z[k]$ is the $N$ point DFT of length $N$ point sequence $z[n]$. Again stated verbally, $Z[k]$ is merely a repetation of $W[k]$ two times. This is signified by the ramge of $k=0,1,2,...,N-1$ and the modulus operator inside the argument of $W[k]$.

Hence we can find the relation between $Z[k]$ and $V[k]$ as : $$Z[k] = 0.5 \left( V[ (k)_{N/2}] + V[ (k)_{N/2} + N/2] \right) $$

This relation in the frequency domain was readily available. I didn't use any derivations to achieve it (eventhough at first it was derived by means of DFT manipulations anyway). Now using the duality property of DFT, I assert that, if te time domain signals are replaced by frequency domain signals then their effect on the time domain will similar to the above frequency domain relation, by simply replacing $k$ with $n$. Note that time reversal not needed, as it will be cancelled, but scaling by $2$ is required. So the result will be:

$$ \boxed{ y[n] = x[ (n)_{N/2}] + x[ (n)_{N/2} + N/2] } $$

where $N=16$, $n=0,1,2,...,15$.

Conclusion. It takes more effort to describe a solution more easily obtained via the duality principle.