KJW

You may find answers to your questions in the Wikipedia articles 5-HT receptor and Psilocin.

Today I learned about alpha-gal syndrome, a potentially life-threatening allergy to mammalian products such as meat and milk, acquired from tick bites. Specifically, it is an allergy to the epitope of the carbohydrate molecule galactose-alpha-1,3-galactose ("alpha-gal"). According to the Wikipedia article, the alpha-gal molecule is naturally found in the bodies of all mammal species except catarrhines (apes and Old World monkeys), the taxonomic branch that includes humans. Alpha-gal can also be found in the saliva of insects including certain tick species. It is through the saliva of tick bites that humans can become sensitised to alpha-gal, a substance foreign to humans, and therefore become sensitised to mammalian products. Alpha-gal is also present in many manufactured products, including medication and medical products.

I found this YouTube video about "Hyperoperations" which may be of interest. I especially found the "Commutative hyperoperations" at around 16:32 to be interesting.

There are also sesquiterpenes with molecular formula C15H24. A monoterpene has molecular formula C10H16 and consists of two isoprene units (C5H8). Thus, a sesquiterpene consists of three isoprene units, hence the "sesqui" prefix.

Although I'm unfamiliar with the term "sesquation", I am aware of the concept. This is reminiscent of the notion of fractional calculus and the fractional Fourier transform. And the gamma function: [math]\displaystyle \Gamma(z) = \int_{0}^{\infty}\!t^{z-1}\,e^{-t}\,dt[/math] which can be regarded as a fractional form of the factorial function: [math]\displaystyle \Gamma(n) = (n-1)![/math] Interestingly, although there are an infinite number of functions [math]\displaystyle f(x)[/math] that satisfy: [math]\displaystyle f(x+1) = x\,f(x)\ \ \text{for all}\ \ x > 0,\ \ f(1) = 1[/math] the gamma function is the only such function that is logarithmically convex (see Bohr-Mollerup theorem).

If by "present" one means the present defined by the Friedmann-Lemaître-Robertson-Walker (FLRW) metric, while the idea probably doesn't conflict with known physics, it is probably quite meaningless in the sense of having no observable consequences contrasting with the notion of a block universe in which the future pre-exists. In other words, the idea violates Occam's razor.

[math]\overline{\underset{^{\large \sim}}{\partial}}{}^{}_{t} \overline{\mathfrak{T}}{}^{r_\lambda}_{s_\lambda}\ \ \ \underset{^{\large \sim}}{\partial}{}^{}_{k} \mathfrak{T}{}^{i_\lambda}_{j_\lambda}[/math]

It's my understanding that it is due to the dependency mismatch between the time it takes an engine to do anything, which is inversely proportional to the engine speed, and the constant time of deflagration of the fuel-air mixture in the combustion chamber.

This looks intimidating... What sort of beast is it? I should also remark that the mathematics is stock standard mathematics used in general relativity. That you call it "intimidating" is revealing about your understanding of general relativity. I personally regard the mathematics as beautiful, although actually doing the mathematics, especially the index manipulations, can be quite tedious to do manually.

Bear in mind this is "The Sandbox" used for testing how the forum behaves, such as LaTeX code. However, the mathematics itself is about the Lie derivative, a tensorial derivative that is different to the covariant derivative and is independent of the connection.

[math]\displaystyle {\large £}[V{}^{u}] \mathfrak{T}{}^{i_1\ .\ .\ .\ i_p}_{j_1\ .\ .\ .\ j_q} = V{}^{u} \partial{}_{u} \mathfrak{T}{}^{i_1\ .\ .\ .\ i_p}_{j_1\ .\ .\ .\ j_q} - \sum_{\phi = 1}^{p} \partial{}_{u} V{}^{i_\phi}\ \mathfrak{T}{}^{i_1\ .\ .\ .\ i_{\phi - 1}\ u\ i_{\phi + 1}\ .\ .\ .\ i_p}_{j_1\ .\ .\ .\ j_q} + \sum_{\phi = 1}^{q} \partial{}_{j_\phi} V{}^{u}\ \mathfrak{T}{}^{i_1\ .\ .\ .\ i_p}_{j_1\ .\ .\ .\ j_{\phi - 1}\ u\ j_{\phi + 1}\ .\ .\ .\ j_q} +\ w\ \partial{}_{u} V{}^{u}\ \mathfrak{T}{}^{i_1\ .\ .\ .\ i_p}_{j_1\ .\ .\ .\ j_q}[/math] [math]\displaystyle \overline{{\large £} [V{}^{v}] \mathfrak{T}}{}^{r_1\ .\ .\ .\ r_p}_{s_1\ .\ .\ .\ s_q} = {\large £}[V{}^{u}] \mathfrak{T}{}^{i_1\ .\ .\ .\ i_p}_{j_1\ .\ .\ .\ j_q} \left(\prod_{\lambda = 1}^{p} \dfrac{\partial \overline{x}{}^{r_\lambda}}{\partial x{}^{i_\lambda}}\right) \left(\prod_{\lambda = 1}^{q} \dfrac{\partial x{}^{j_\lambda}}{\partial \overline{x}{}^{s_\lambda}}\right) \left|\dfrac{\partial x{}^{j}}{\partial \overline{x}{}^{s}}\right|^w[/math]

A particle's frequency corresponds to its energy, nothing more. To suggest anything more is to peddle woo. An eigenstate is one of the possible states that result from an observation.

I looked at the video but the part I was most interested in was a secret. Even before I watched the video, I was expecting the liquid glass to be a silylating agent. There is nothing new about silylating agents in general. For example, they are used to render laboratory glassware hydrophobic. However, I was curious about the specific silylating agent in this case, which might be quite novel. I anticipate that the silylating agent would be more "glasslike" than typical silylating agents (which have organic groups attached).

I doubt that Newton's laws or Kepler's laws were named by Newton or Kepler after themselves. More likely, they were named by other people somewhat later. Actually, it is quite common for a law to be given the name of someone who is not the person who originally discovered it. From Wikipedia article "Stigler's law of eponymy": Stigler's law of eponymy, proposed by University of Chicago statistics professor Stephen Stigler in 1980, states that no scientific discovery is named after its original discoverer. Examples include Hubble's law, which was derived by Georges Lemaître two years before Edwin Hubble; the Pythagorean theorem, which was known to Babylonian mathematicians and to Indian mathematicians before Pythagoras; and Halley's Comet, which was observed by astronomers since at least 240 BC (although its official designation is due to the first ever mathematical prediction of such astronomical phenomenon in the sky, not to its discovery). Stigler attributed the discovery of Stigler's law to sociologist Robert K. Merton. (From htps://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy)

I assume that. However, it is reasonable to assume that a downvote came from the one antagonistic person who did post in the thread.

some bigotries which very common in this forum. step 1: one demonstrates or proposes an opinion. step 2: a well known member attempts to disagree to that opinion. step3 : there is occuring of existence of many members downvoting that opinion (regardless the reality in that opinion, in fact this is a weakness of opinionating). And this is bigotry, isn't it? I don't understand who is who in the above. In the "Today I Learned in Mathematics" thread, only Genady and studiot were downvoted, and they were presumably by you (as the only person with the motive to downvote these two posters).

[math]R{}_{p}^{\mskip{0.05 cm}·}{}_{t}^{\mskip{0.05 cm}·}{}_{p}^{\mskip{0.05 cm}·}{}^{p}_{\mskip{0.05 cm}·}{}^{t}_{\mskip{0.05 cm}·}{}_{p}^{\mskip{0.05 cm}·}{}_{p}^{\mskip{0.05 cm}·}[/math] [math]R{}_l{}_q{}^r{}_s{}_t{}^g{}^v{}^h{}_x[/math]

That's it!! Just to clarify, the definition says, "for each y in S", which includes x0, whereas y must not be equal to x0.

I think I see it: y has to be not equal to x0.

@Genady, is the mistake you see that subset S requires at least two elements and not merely be non-empty?

[math]\dfrac{\partial \star}{\partial \overline{x}^{\mu}}[/math]

Q: What's the difference between Iran and Vietnam? A: Trump had a plan to get out of Vietnam!

Have you considered ammonia solution? You could also try (if you can obtain it) ethylenediaminetetraacetic acid (EDTA).

I think one thing that says they lean to the right is if they have a national flag in their front lawn. (This probably isn't limited to the US.)

I have to admit that this actually took me by surprise. After taking some time to think about this, I realise that it is ironic that what I said about two different types of axioms, the "deeper stuff" that you said was "not even wrong", appears to be key to my misunderstanding of the notion of completeness. Yes, there are two different types of axioms: one that defines a mathematical universe, and another that constrains that universe. It would seem that I neglected the mathematical universe. That would be because of the way I view mathematics, which is that everything exists unless proven otherwise. That means, for example, I assume the existence of multiplication even if it has not been explicitly defined. My mathematical universe contains multiplication, contains infinity, contains transfinite numbers, contains the axiom of choice, the continuum hypothesis has a definite answer, etc. But of course, that's not how this subject in mathematics is done. The mathematical universe is defined explicitly by the axioms, and notions such as completeness are based on it. So, I actually can see how a system with few axioms can be complete. And I can see that Gödel's incompleteness theorem is not trivial.