Reading Wikipedia on "Beta Decay" they list the equation of Carbon-14 decaying into N-14. see equation https://en.wikipedia.org/wiki/Beta_decay
I presume the 14 refers to total protons and neutrons. The 6 in C, I believe means six protons. In N, I believe the 7 refers to protons. Where did the seventh proton come from the decay of C-14 into N-14? I understand neutrons can decay into protons, but the math doesn't work for me.
I am working on an app that allows users to enter in recipes. I have access to some data about certain ingredients that the user can select for the recipe, such as if the ingredient is kosher. If all ingredients selected for a recipe are kosher, is the entire recipe kosher? Or are there other rules, such as how the ingredients are prepared or what pot the dish is cooked in, that will make a dish non-kosher even if all the individual ingredients are kosher?
While some recipes will be available to the general public to make themselves, most recipes are used by employees to make dishes that will be for sale.
Note: I'm sorry if this question is really un-informed. I am a non-Jew and am trying to understand kosher rules and just want to make sure I'm doing everything right.
Answer
It is a start. However it must be cooked in Kosher pots & pans. Meat & Dairy, Meat & Fish should not be combined. There are other rules such as Bishul Yisrael, Pas Yisrael, Yayin Nesech that can affect this. Also vegetables and fruits in many instances require checking for insects. Blood spots in an egg can be a problem. Meat and chicken require slaughtering according to Halacha.
If I wear a tallit katan during the day and also to bed, can I wear the same one during the day and also to bed? Or must the one I wear to bed be a different one than the one I wore during the day?
Also, if this changes anything, I'm Sephardic.
There were a lot of great answers here. I gave the checkmark to ento's answer because I felt it most completely explained all aspects of this use of こと. But many of the other answers are excellent, so if you're visiting this question for the first time, please take a few moments to read through all answers. Thanks to everyone for your help with this question.
When learning the phrase "I like X", everyone learns "Xが好きだ". But if X is a pronoun, you sometimes see こと:
あなたが好きだ。 → あなたのことが好きだ。
What purpose does こと serve here? I know that in subordinate clauses, こと can eliminate ambiguity:
彼が好きな人 "a person he likes" or "a person who likes him"
彼のことが好きな人 "a person who likes him"
But in a simple statement such as the first example above, it doesn't seem to change the meaning at all.
My own searches on this problem have yielded the following two theories (neither with anything to back them up):
Is either of these correct?
こと also shows up in many other situations, seemingly without any effect on the meaning:
事件を覚えている。 → 事件のことを覚えている。 I remember the incident.
地球を考えて行動する → 地球のことを考えて行動する take action while considering the
Earthplanet (edited to "the planet" to fulfill the requirement for 考える to be paired with something abstract)
What's going on here?
Answer
I've let my subconscious sleep on this for a while, which has a native Japanese language processor built in, and come to the conclusion that のこと does two seemingly opposite things. I'll illustrate them with my inner images for [noun] and [noun]のこと, and later quote a dictionary to further support my views.
Let's take 事件のこと as an example.
A plain "事件" is a simple dot...
add a little blur/halo around the dot and arrows going toward it and you get "事件のこと":
The little blur/halo adds a "universe of variable traits" (quote from Dave M G's answer) around the subject noun and lifts it to an abstract level (because traits are abstract things).
This "abstracting" aspect becomes apparent when the ensuing verb is about a physical action:
あなたを抱きしめたい。 I want to hug you.
あなたのことを抱きしめたい。 I want to hug all the things that is you. (figuratively)
パンのことが好き, is just fine in this light, if it's meant to be "I like everything about breads," and not "I like to eat breads."
Now to the arrows. I'd like to call these the "focusing" feature of "のこと" (as mentioned in Enno's answer). The "focusing" aspect can be seen clearly when the ensuing verb has directivity in itself.
人を見下す。 Look down on someone.
人のことを見下す。Look down on at someone. (I know it's incorrect, but I hope the spirit gets through.)
With the latter example, there's a bit more emphasis on the action of looking down.
At this point, I took up the dictionary and looked if it has anything to say about it. And these two definitions from Daijirin match up with my observation:
The dictionary makes it seem like these two are mutually exclusive, but I think the two aspects of ..のこと can manifest themselves at the same time, or with one of them more stressed than the other, depending on the abstractedness/directivity/etc. of the verb/noun used in conjunction.
So in summary, のこと in あなたのことが好き serves two purposes: abstracting and focusing.
As for the two theories, theory 2. "こと encompasses more of the object" corresponds to the "abstracting" aspect of こと, which I deem true. Theory 1. "こと adds a layer of indirectness" is also true, because speaking abstractly means indirectness. However, I'm not sure if it's universally "preferred from a Japanese standpoint", perhaps except in the case of expressing emotion (あなたが好きだ!), it's well conceivable that a reserved mode of expression can be preferred by some.
I'll leave the analysis of 地球を考える and 事件を覚えている to sawa's answer =)
The nasi of Shevet Naftali's name was Achira (אחירע), which translates to "my brother is evil." What did Enan (his father) have against his brother, that he should give his son such a name?
Answer
There are four meanings of the name Achira given in our tradition.
Other explanations of the name (by Christian scholars) are "brother of evil , i.e. unlucky" (אחי [מזל] רע), "brother of the shepherd" (אח רעי), and "my brother is [my] friend" ( ַאֲחִי רֵע).
מדרש אגדה (בובר) במדבר פרשת במדבר פרק א
[טו] לנפתלי אחירע בן עיין /עינן/ . שהיתה ארצו שמנה לתבואה, כמו שנאמר ותרעינה באחו (בראשית מא ב), ואומר בין אחים יפריא (הושע יג טו), רע הוא לשון רצון, כדמתרגמינן רצון רעוא, זה היה שבט נפתלי, שהיתה ארצו מוציאה פירות כרצון בעליה, וכן משה רבינו ע"ה [אמר] נפתלי שבע רצון (דברים לג כג):
הדר זקנים על התורה במדבר פרשת נשא פרק ז
מקשים העולם למה נקראו נשיא דן אחיעזר בן עמישדי ונשיא נפתלי אחירע בן עינן. ומתרצים לפי ששבטו של דן יש בהם פסלו של מיכה ופלטם הענן ובקש דן לנפתלי אחיו שיבקש עליו רחמים שלא יהיה הענן פולטו ואמר לו שיהיה לו אחיעזר בן עמישדי פי' שיהיה לו אח לעזרה שיהיה בן עם אל שדי. ונפתלי השיבו אחירע בן עינן בתמי' כלו' אחי רע שיש בו ע"ז יהיה בתוך הענן:
ר' חיים פלטיאל במדבר פרשת במדבר פרק א
וכי יש לך אדם שקורא לבנו אחירע, אלא אל יאמר אדם שכתוב בתורה דבר שלא לצורך כי על שם המעשה נקרא כך כי נשיא דן היה קורא אותו אחי עזר בן עמי שדי ע"ש שבט דן שהיה חוץ לענן וקורא לנפתלי אחיו אחי היה לי לעזר להיות בן עמי שהם במחנה שדי ונשיא נפתלי היה קורא אותו אחירע ועונה לו אחי רע הוא כי פסל מיכה עמו ורוצה לישב בענן.
Texts taken from Bar Ilan Responsa.
אור החיים, במדבר פרק ז
אחירע בן עינן. ירמוז על דרך מאמרם ז''ל (ספרי שם) בפסוק: שבע רצון, מלמד שהיה נפתלי שמח בחלקו בימים בדגים בפרגיות ומלא ברכת ה' ים גינוסר עד כאן. והוא מאמר אחי רע פירוש שחלק אחיו היה בעיניו רע בערך חלקו, והיתה עינו מלאה מחלק שנפל בגורלו.
Text from Daat
Da'at Mikra
(אחירע = אחי (או אלי) הוא רעי (ה' רעי לא אחסר - תהילים כג:א
I was watching a news broadcast on YouTube and when it moved over to the weather report, I noticed that 「今日の天気」was actually written as 「きょうの天気」. Also 「明日の天気」was also written as 「あすの天気」. It wasn't just the weather report but some other parts of the programme such as the main stream headlines, 「きのう」.
Why are these sentences or should I say, just the start of the sentence written in ひらがな and not full 漢字? Does it depend on the news programme? I asked my Japanese friend and he said he didn't know or even realise it.
For reference, I was watching おはよう北海道 (16:15) when I first noticed it.
Thanks
Answer
This is related to the fact that 今日 and 明日 have two readings. According to the July 2008 issue of 放送研究と調査:
放送で，「今年」を「ことし」と表記する理由
「今年」と漢字で書いた場合，「ことし」と読んだらよいのか，「こんねん」と読んだらよいのか，わからなかったり，迷ったりするおそれがある。そのため，放送では「ことし」と，ひらがな書きにすることにしている。同じように「今日（きょう/こんにち）」「明日（あす/みょうにち）」「昨日（きのう/さくじつ）」なども，「きょう」「あす」「きのう」と，ひらがなで表記するようにしている。
EDIT: This is NHK's house rule, so a different media company may have a different rule about this.
Related:
EDIT 2: OK, regarding the code I’ve pasted below, and seeing the FFT plot, I suspect the LPFilters aren’t working since I’m getting $0.5*m(t)*[cos(2 \pi f_c t ( \theta_e)+cos(\theta_e)]$ instead of $0.5*m(t)*cos(\theta_e)$. But I don’t really know why, I’m clueless... I’d filter the output it but I don’t think that’s how it’s supposed to work. EDIT on this: Well I tried filtering and it didn't work at all... makes me wonder if I'm plotting the FFT correctly. But anyway, the signal looks like in the first screenshot, that's for sure.
EDIT: I've tried a different way of implementing it http://read.pudn.com/downloads80/doc/project/307210/CarrierRecoveryUsingaSecondOrderCostasLoop.pdf and I keep getting the same result, despite the author getting it to work properly
Carrier recovery is discussed in Chapter 10 in "Telecommunication Breakdown" by Johnson and Sethares. I've been running the code they provide and I get the same result when I plot "theta" to see how it changes overtime and it looks the same as the screenshot in the book. But I tried to look at the output of the costas loop (which is not discussed nor plotted in the chapter, not sure why) and I don't seem to be getting very good results. Here's the code from the book (made slight modifications to get the output and also replaced the pam() function with pammod() cause I didn't find such function in the book and I don't have the CD-ROM):
N=10000; M=20; Ts=.0001;
time=Ts*(N*M-1); t=0:Ts:time;
m=pammod(randi([0 3],1,N),4);
mup=zeros(1,N*M); mup(1:M:end)=m;
ps=hamming(M);
s=filter(ps,1,mup);
f0=1000; phoff=-1.0;
c=cos(2*pi*f0*t+phoff);
rsc=s.*c;
rlc=(s+1).*c;
fftrlc=fft(rlc);
[mx,imax]=max(abs(fftrlc(1:end/2)));
ssf=(0:length(t))/(Ts*length(t));
freqL=ssf(imax)
phaseL=angle(fftrlc(imax))
%costasr
r=rsc;
fl=500; ff=[0 .01 .02 1]; fa=[1 1 0 0];
h=remez(fl,ff,fa);
mu=.003;
fc=1000;
theta=zeros(1,length(t)); theta(1)=0;
zs=zeros(1,fl+1); zc=zeros(1,fl+1);
output=zeros(1,length(t));
for k=1:length(t)-1
output(k) = 2*r(k)*cos(2*pi*fc*t(k)+theta(k));
zs=[zs(2:fl+1), 2*r(k)*sin(2*pi*fc*t(k)+theta(k))];
zc=[zc(2:fl+1), output(k)];
lpfs=fliplr(h)*zs'; lpfc=fliplr(h)*zc';
theta(k+1)=theta(k)-mu*lpfs*lpfc;
end
So I decided to plot output vs s and this is what I got:
If I understood the theory about Costas loop, if the input is $s(t)=m(t)cos(2\pi f_0 t+\theta_i)$, if the loop worked fine, at the output I should have $0.5*m(t)cos(\theta_i - \theta_o)=0.5*m(t)cos(\theta_e)$ -> for $\theta_e$ ~ 0 -> $0.5*m(t)$ but as you can see, there's something else besides m(t). Why is this happening? I tried plotting the FFT of the rsc and the output, and as you can see, there is some info at around 2000 Hz that shouldn't be there, only the baseband should:
