number - Were there more than seven prophetesses?

The Bavli, M'gila 14 amud 1, quotes:

Forty-eight prophets and seven prophetesses prophesied for the Jews….

Further along on the page, it questions this:

Were there no more? But it says [in I Sh'muel 1:1] "there was one man from Ramasayim Tzofim", i.e., one of masayim, two hundred, tzofim, seers, who prophesied for the Jews!

And it answers:

There were more. Indeed, the rabbis taught "There were so many prophets for the Jews — twice the number of people who left Egypt [at the Exodus]. But a prophecy needed for posterity was written, and one not needed [for posterity] was not written".

Thus, forty-eight prophets and seven prophetesses prophesied for the Jews and have their messages included in Tanach; many more prophets prophesied for the Jews and do not have their messages included in Tanach.

My question is: Were there prophetesses with messages for the Jews, beyond the seven whose messages were for posterity? Any sources that indicate one way or the other?

(I do not think the answer can be found in D'varim Raba (7:8), which quotes Rabbi Hoshia:

The least [person] in the days of Moshe saw what Yechezkel, a great one among the prophets, did not see — [these were] people with whom the divine immanence spoke face to face, as it says [in D'varim 5:4] "face to face God spoke with you…".

These people — presumably women included — had prophecy, but, unless you can support such a claim, I have no reason to think that it was of the sort that included a message for the Jews, which is what M'gila is discussing ("for the Jews"). I'm asking about message-for-the-Jews prophecy: did women, beyond the seven listed, have that?)

halacha - Ripping garments when hearing Hashem's name?

I've heard in a kabbalah shiur on web yeshiva, if someone says Hashem's name as it's written, either b'shogeg or b'meizid, the person or people that heard must rip their garments as they do when a close relative dies. Where is the source for this, and how is it done?

Also, if someone were to accidentally say Hashem's name as it is written, such as someone becoming religious and learning Hebrew, and the yud in the work sheet is right before a vuv, is this considered b'shogeg pronunciation? is it OK because it's meant to teach them only the letters?

Why does equilibrium constant change when the reaction is multiplied by a number and nothing in the real has been changed?

As far as I know, a large equilibrium constant shows that the a reaction like the one below wants to complete:

$$\ce{B <=> A}$$

If A and B are gases, then K is: $$K_1=\frac{[A]}{[B]}$$

but when I multiply the reaction by 20 , K is $$K_{20}=\frac{[A]^{20}}{[B]^{20}}$$ while the same number of moles of B are consumed. If $\small K_1 = 10$ then $\small K_{20} = $$10^{20}$ so the reaction must be approximately complete. Why does this happen while the reaction materials didn't change?

coordination compounds - What are t2g and eg in CFT?

In the crystal field theory (CFT), when the splitting of the d-orbital occurs, it gets divided into two parts. The upper part with higher energy is the $\mathrm{t_{2g}}$ and the lower part with lower energy is called the $\mathrm{e_g}$ as in:

So can anyone please explain me what is this $\mathrm{t_2}$ or the $\mathrm{e}$ or the $\mathrm{_g}$ below.

Answer

As stated in both the links Geoff and Philipp have kindly commented (1, 2) they are to do with symmetry labels we chemists like to assign to orbitals. Knowing an orbitals symmetry class can lead to a lot of simplifications down the road when you use quantum mechanical calculations and even dictate the reactivity of which orbitals are "allowed" to interact together in reactions.

In this case the $\mathrm{t_2}$ groups three of the metal atom's d-orbitals into a certain class while two of the orbitals belong to the $\mathrm{e}$ class. The $\mathrm{t}$ means triply degenerate while the $\mathrm{e}$ means doubly degenerate (degenerate means have the same energy).

The $\mathrm{g}$ is not about how many energy levels are degenerate rather it is an indication of the answer to a certain operation we can perform on an orbital. It instead relates to how the orbitals behave if we hypothetically were to put a line bisecting the orbitals or "invert" them around a centre point (crudely put "going from one corner to the other". If the phase of the wavefunction (or perhaps more pragmatic) the "colour" of the orbital lobes changes while doing this we label the orbital with a $\mathrm{u}$ if we have no phase change we label it with $\mathrm{g}$. They indicate the orbitals response to an inversion about the centre of symmetry.

We can do lots more of these operations to investigate the symmetry of the orbitals which together lead us to assigning the molecule to a symmetry group. Knowing this is very important for a plethora of reasons.

halacha - Breaking Shabbos to keep future Shabbos(os)?

The reason we allow someone to violate shabbos to save a life is because of the principle "let him void one shabbat so that many future shabbosos will be kept". What are the parameters for this dispensation? Is one allowed to save an avowed atheist? May one violate shabbos for a non-life threatening situation that may lead to additional sabbath observance (in other words can I break shabbos for kiruv purposes)? Why do we not apply this logic to other mitzvot (let him worship idols one time...)?

Answer

Is one allowed to save an avowed atheist?

The Mishna Berura (OC 329:9) writes (my own translation):

A Jew who transgresses averos for his own pleasure, as long as he does not deny the Torah - it seems that we would desecrate Shabbos in order to save him. However if he does so specifically to anger - it is forbidden to save his life even on a weekday, and certainly not on Shabbos.

May one violate shabbos for a non-life threatening situation that may lead to additional sabbath observance (in other words can I break shabbos for kiruv purposes)?

At times we can; Rambam (Mamrim 2:4):

Similarly, if they saw that temporarily it was necessary to nullify a positive commandment or violate a negative commandment in order to bring people at large back to the Jewish faith or to prevent many Jews from transgressing in other matters, they may do what is necessary at that time. To explain by analogy: Just like a doctor may amputate a person's hand or foot so that the person as a whole will live; so, too, at times, the court may rule to temporarily violate some of the commandments so that they will later keep all of them. In this vein, the Sages of the previous generations said: "Desecrate one Sabbath for a person's sake so that he will keep many Sabbaths."

However it seems this dispensation is reserved for Beis Din.

Why do we not apply this logic to other mitzvot (let him worship idols one time...)?

Rabbi Shnuer Zalman of Liadi (author of Shulchan Aruch Harav) explains in Tanya Chapter 24 that the specific averos considered yehareg ve'al ya'avor are a g'zeras hakasuv" (Scriptural decree). He proves this by showing how Shabbos in certain aspects is a more grave offense than sexual offences yet consideration of life overides Shabbos but not sexual prohibtions.

meaning - What is the difference between 捕まえられた and 捕まった?

Consider the following sentences:

A: 私が警察に捕まえられた。

B: 私が警察に捕まった。

Both mean I was caught by the police.

What is the difference between 捕まえられた and 捕まった ?

Answer

Both sentences are correct and the same in meaning, but sentence B is far more common and sounds natural.

For some reason, some Japanese verbs intrinsically have passive meanings, and they are used more commonly than the transitive verb + ～れる/られる version.

See the following question for the list of such verbs.

This question is also related: ところを 見つかる, this was in a highly reputable dictionary

python - How to extract features of individual spikes in non-negative signal?

I have data of non-negative (in the sense there's no signal below baseline) spiking waveforms, which are in the form of a 1D array of numbers:

Spikes that cross some threshold are considered real signal events and I want to be able to measure the properties of individual events such as their amplitude, rise-time, decay-time, duration, and half-width.

The signals are pretty clean so I imagine I don't need some fancy machine learning algorithm. Would a wavelet transform approach give me the results I need? If not, what's the best and simplest approach here?

Answer

Continuous wavelet transforms can provide information and parameters for sparse, piece-wise regular signals. One example related to yours is present in The Continuous Wavelet Transform in MRS, A. Suvichakorn, C. Lemke, A. Schuck, J.-P. Antoine, as exemplified in the following picture.