/sci/ - Science & Math

UNANSWERED QUESTIONS

MATH:
>>15311070
>>15312868
>>15315177
>>15322664
>>15324196
>>15324978
>>15325012

PHYSICS:
>>15325449

CHEM:
>>15312194

STUPID QUESTIONS:
>>15310684
>>15314061
>>15316188
>>15316234
>>15318711
>>15318763
>>15319791
>>15320642
>>15320752
>>15325541
>>15325907

Hey. what are the best resources for studying\preparing for calculus? Fast!

>>15332629
Why did the other one get removed?

>>15332629
Does x mean unknown and y mean known or is there more to it I'm started trying to learn today

https://odysee.com/@hermeneiachannel:8/dr-barry-trower-wifi,-radiation,-bees,:a

If there is so much conclusive evidence proving the harms of low intensity microwave fields used in such things as phones signals or wifi, even as far back as the 1970s then why weren't these safety concerns taken intyo proper account?
The data on immune suppression alone is conclusive evedence of harm.

>>15332727
khan academy
>>15332793
i know this isn't what you asked, but if you want people to take you seriously, you shouldn't link to cranks

>>15332799
Is Khan academy the absolute best? For me it was a bit confusing

>>15332799
>cranks
Barrie was literally commissioned by the met police the guy has as good a set of credentials as anyone you could want to ask on the topic.
The fact you call him a crank says more about you than anything else.

>>15332774
No one seems to know. It wasn't removed, it expired with only 50 posts.

>>15332848
The fact you think he's not a crank says more about you than anything else.

>>15332887
So getting back on topic why do we allow such dangerous technology with proven health effects without a better public understanding of the actual risks involved we are in quite a lot of danger?

Is 1200 IU of vitamin D too much? or is it enough?

Consider [eqn]x^4+1.[/eqn]What's an easy way to factor polynomials that do not have a real root? Meaning how do I decompose this polynomials of degree 4 into two polynomials of degree 2?

>>15333109
you know how [math](x^2 -1) = (x+1)(x-1)[/math]?
likewise, [math](x^2 +1) = (x+i)(x-i)[/math]
try solving it from there

>>15333036
kill yourself before your gangstalkers do

>>15333109
[eqn]
x^4 + 1 \\
= (x^2 + 1)^2 - 2 x^2 \\
= (x^2 + 1)^2 - (\sqrt{2} x)^2 \\
= (x^2 + \sqrt{2} x + 1)(x^2 - \sqrt{2} x + 1) \\
[/eqn]

>>15333103
get a sun lamp, it'll be cheaper and do more

>>15333136
Why is every attempt at discussing the topic here shut down or dismissed?

>>15333109
Haven't you ever heard about Sophie Germain identity?

>>15333136
>>15333156
>>15333381
Okay, I got this. But what's the go-to algorithm for polynomial-decomposition into real factors in general? Is there even such an algorithm?

>>15333428
You take a complex root [math]r[/math] which exists because of the Fundamental Theorem of Algebra.
If [math]r \in \mathbb{R}[/math] then you can factor out the real polynomial [math]x - r[/math]
if [math]r \in \mathbb{C} \setminus \mathbb{R}[/math] then you can factor out the polynomial [math]x^2 + 2 \Re(r) x + |r|^2[/math] instead which is a real polynomial again.
You can repeat this process until all factors are either linear or quadratic.

>>15332629
>stupid
What is the oldest preserved DNA sequence in [math]Homo sapiens[/math] genome?

>>15333658
It's
[eqn]x^2 - 2 \Re(r) x + |r|^2 [/eqn]
of course.

This came up during my studies, and I don't exactly understand it.
[math]
\frac{b^p+1}{n^p+1} * \sum_{k=1}^{n-1} k^p = \frac{b}{n} \sum_{k=1}^{n-1} (\frac{kb}{n})^p
[/math]
Could someone explain how one gets this product? What principles am I forgetting?

I have a hobby that involves using 10% KOH. Sometimes when I use it after I clean up I notice my hands get a little tingly and I suspect it's because I'm getting a little bit on them. Should I be more careful during cleanup and use/throw out gloves? Also, I have a jar of waste that I throw tissues and such in after using the KOH. Should this go to hazardous waste eventually?

>>15333895
>I notice my hands get a little tingly and
rip anon, we hardly knew ye

I want to show the disjointness of n sets where n is a natural number. I decided to do this with induction. Can I start with one set and say: It's one set so it must be disjoint from all other sets (of which there are none). Or do I have to start with (at least) two sets?

>>15334122
nvm I figured out I think

Why most of the schematics that see on the internet about vapor/gas core reactor/rockets use UF4 instead of UF6?

What do you need the uniform boundness for?
Isn't
[eqn]B = \bigcap_{k,l=1}^\infty \left( \bigcup_{n \geq k} f_n^{-1}\left( \left]1 - \frac{1}{l}, 1 + \frac{1}{l}\right[ \right) \right) [/eqn]
always a [math]G_\delta[/math] set?
The sets [math]f_n^{-1}\left( \left]1 - \frac{1}{l}, 1 + \frac{1}{l}\right[ \right)[/math] are open because each [math]f_n[/math] is continuous. So the union of them is open and the intersection goes over all pairs [math]k,l \in \mathbb{N}^2[/math] which is a countable set.

What's the difference between EngD and PhD in engineering? I almost never see the former used but I've been told it's more correct when referring to a person who has a doctorate in engineering.

Am I too stupid for math. I’ve been stuck in calculus for 3 years and have not made any progress, I just don’t understand any of it, it’s so complicated. Even when they’re explaining it I just can’t keep up with all the names and definitions. I probably just have a low iq. I dunno, what do I do?

>>15335109
If you're in the US, it's not you; It's the education system. The only thing I can tell you is watch professors Leonard's videos on calc 1 for the procedure and theory and practice a buttload of problems.

>[math][A \in \text{End}(V) \land A = 0][/math] [math]\implies[/math] [math]V = V_0[/math]
Why is this implication true, I don't get it. Couldn't V be any vector space of dimension greater than 0 and A = 0, since A doesn't have to be an isomorphism. (Assuming V_0 means the zero sub space in V.)

Is the kernel of a linear transformation always the eigenspace to the eigenvalue 0?

>>15334470
>B=⋂k,l=1∞(⋃n≥kf−1n(]1−1l,1+1l[))
Can you maybe elaborate on where you wanted to go with this to prove the statement

>>15335793
Are you including infinite dimensional spaces in your question

>>15335815
I didn't, but now I'm intrigued. Can you tell me separately for the finitely and infinitely dimensional case? (Or just the finite case, that would also be good.)

Every diagonalizable endomorphism A has a partition of unity [eqn]A= \sum_{i = 1}^k \lambda_iP_i[/eqn]where [math]\{\lambda_i\}_{i \in I}[/math] are the (pairwise distinct) eigenvalues of A and [math]\{P_i\}_{i \in I}[/math] are again linear endomorphisms. My question: Can you always choose the [math]\{P_i\}_{i \in I}[/math] to be projections onto the (one-dimensional) bases of the respective eigenspaces?

>>15335901
Forgot to mention: The underlying vector space is finitely dimensional.

>>15335833
In the infinite dimensional case, one has to redefine the what the whole "eigenvalue" buisness even means, because the ability to prove things about a vectors space in infinite dimensions depends highly on what kind of topologies you can theoretically introduce on them.

One has to talk about algebras of operators over that space instead. It is a topic, not tooo difficult, yet difficult enough, that writing it in this thread would be annoying.

The name is abstract Harmonic Analysis and I redommend Gerald B: Foland's "a course in abstract harmonic analysis" the first few chapters (or until you tire of the topic).

Folland is also a great opportunity to up your representation theory game, by studying Chapter 5 (Analysis on compact groups)

Enjoy :)

Given [math]F[/math], the field of constructible numbers, prove whether or not there is an injective group homomorphism from [math]\mathbb{Q} / \mathbb{Z}[/math] to [math]F^{\times}[/math].

I know the answer is that its impossible, but not sure how/why.

For each positive real number [math]r[/math], let [math]n(r)[/math] be the number of solutions [math](a,b)\in\mathbb{Z}^2[/math] for [math]a^2+b^2\leq r^2[/math]. Evaluate [math]\lim_{r \to \infty}\frac{n(r)}{r^2}[/math].

It is 0, right? I mean, [math]n(r)[/math] must be less than [math]r^2[/math] since [math]r^2[/math] represents the entire disk and therefore the denominator grows more rapidly than the numerator

How are you supposed to tell if a molecule is sp3, sp2, sp or not hybridized at all? I know very little about chemistry

>>15336064
Their orbitals |Ψ|^2 are different and their energy is different

I'm interested in the toy system that results from defining small categories within the boundaries of set theory, i.e., showing that each part in the definition of some category is a set, proved from the Zermelo axioms. Obviously, this isn't the way it is supposed to be done, and that's why i acknowledge my interest on this restriction as some kind of toy system or toy example. Hence, a (necessarily small) category, defined inside the language provided by Zermelo theory, must be some ordered tuple but i don't know exactly which sets it should be equipped with besides the set of objects and the set of morphisms. Moreover, the well-known examples of monoid delooping, finite categories like those with 1 or 2 objects and discrete categories leave me clueless because they assume some abstract single point {*} or some abstract identity morphism [math]\text{Id}_{a}[/math] that is never made explicit and therefore i can't begin to think which set use, or from which superset proven from Zermelo axioms take some element as the corresponding categorical concept. What can be done?

>>15336068
But what if you don't know about those? My teacher is expecting me to be able to tell that NH3 is sp3 hybridized just knowing that N has atomic number 7.

>>15336073
I think what your teacher wants to hear, is that sp hybridization is A bond that makes a "rod", that sp2 makes it look like some soft "throwing star" (it is flat, I mean to say) and that sp3 makes a "pyramid" (https://de.wikipedia.org/wiki/Hybridorbital#Beispiele).).

Are you interested in what "hybridization" technically is?

how does 3(3x)^2(4y) equal 108x^2y? i can't understand where the 108 comes from please don't pick on me i have down syndrome

>>15336087
3*3^2*4 = 3*9*4 = 27 * 4 = 108

>>15335907
Interesting, but I have to tackle LA I and II first before moving on to sth more advanced. Can you tell me sth about the finitely dimensional case? On that note, do you have a take on this >>15335901?

>>15336081
Oh yeah, I think you're right because the molecules that I had to decide the hybridization for all had pictures attached with them too.

I'm interested to hear what it technically is though because my reading material just says that you can define a new basis using a linear combination of different atomic wavefunctions and that it's called hybridization.

>>15336105
oh i forgot about the associative property and didn't understand how x could steal ys coefficient damn i'm retarded thank you

>>15336042
>It is 0, right?
No.

https://en.wikipedia.org/wiki/Gauss_circle_problem?useskin=vector

>>15336115
>Interesting, but I have to tackle LA I and II first before moving on to sth more advanced
Sure, enjoy!
>Can you tell me sth about the finitely dimensional case?
No difficulties here: just per Definition "kernel"="0-eigenspace": Av=0=0*v

>>15336120
Exactly, I wanted to make a point that it is nothing but the name for a certain approximation that is comparatively easy to work with and yields very good qualitative and quantitative results

>>15336199
Alright, nice. Then I understand it all. Thank you Anon. I appreciate your help

>>15336042
I wouldn't say. I think it's the ratio of the number of points (a, b) within the square to the number of points on the disk. Both a and b are integers ofc. So the limit should converge to pi, since pi*r^2/r^2 = pi.

How much time needs to elapse between when you first eat something and when you begin farting out the gas created from digesting it.

>>15336218
Your mom

>>15336121
no worries

>>15336195
this is great. Thank you!

>>15336211
I didn't recognize the error term. This is inaccurate. But the other anon linked a wiki resource that say the error term is smaller or equal to [math]|2\sqrt{2} \pi r|[/math], so we have [eqn]\pi \leq \lim_{r \to \infty} \frac{n(r)}{r^2} < \pi + \lim_{r \to \infty} \frac{|2\sqrt{2} \pi r|}{r^2}
= \pi + \lim_{r \to \infty} \frac{|2\sqrt{2} \pi|}{r} = \pi + 0 = \pi[/eqn]and therefore the limit should be pi on account of the squeeze theorem.

>>15336025
Maybe you can show that for all possible group homomorphisms Phi there exists an element a from Q/Z such that a is not 0 and Phi(a) = 0. In this case, it immediately follows that all group homomorphisms are not injective. This would be my first idea on how to try it.

>>15336265
what about consider |1/4|, and |phi(1/4)|?

>>15335907
I should add to my explanation: the main difference in infinite dimensions is that the set of c, such that (A - c*1) does not have an inverse, that is continuous (no nice theories, if it is not continuous, that's way), is then called the spectrum. It has an extra name because not all elements of the spectrum necessarily have a vector v, such that Av = c*v now.

>>15336495
I don't know anything about constructible numbers, anon. I can't tell you anything more, sorry

let's say I have some polynomial of the form
[math]a_nx^n + a_{n-1}x^{n-1}...a_0[/math]
for a concrete example, let's say [math]a=1[/math] and consider a quartic:
[math]x^4+x^3+x^2+x+1[/math]

here's the question: is there some mathematically concise way or notation to express "the family of functions of the above quartic polynomial derived from all of the different possible combinations of the same terms but differing signs of said quartic"?
or in less retarded terms
is there some concise way to express the family of polynomials
[math]x^4+x^3+x^2+x+1[/math]
[math]x^4-x^3+x^2+x+1[/math]
[math]x^4+x^3-x^2+x+1[/math]
[math]\dots[/math]
[math]-x^4+x^3-x^2+x-1[/math]
[math]\dots[/math]
[math]-x^4-x^3-x^2-x-1[/math]

(I want to be able to generalize this to any degree polynomial)

are there any signal processing anons here? I need to extract MDCT coefficients from mp3 files, but I have almost no idea how to do it, and I cannot find anything on the internet. So far I have tried converting mp3 frames to pcm samples and then applying the MDCT function to those pcm samples, but the results seem strange.

>>15337136
to be clear, I came up with a way, by representing the coefficients as binary numbers, for example
[math]x^4+x^3+x^2+x+1 \equiv 11111 \equiv p_{4,31}[/math]
[math]-x^4+x^3-x^2+x-1 \equiv 01010 \equiv p_{4,10}[/math]
and so on, where a negative is 0, a positive is 1, and [math]p_{order, decimal val.}[/math]

but this is only convenient for shrinking it down. It's not very amenable to any kind of analysis or algebraic manipulation.

>>15337163
what class is this for? Undergrad or grad? I'm a signal processing undergrad senior and we haven't touched anything like this yet in class. Seems neat though.

>>15337173
its not for any class, I am just working on a side project that requires extracting MDCT coefficients from mp3 files.

>>15337136
I think you could use Group Theory to describe this. Let [math]G := \{1,-1\}^\mathbb{N}[/math] with termwise multiplication as product.
Now you can define a group action of [math]G[/math] on [math]\mathbb{C}[x][/math].

[eqn] g \cdot \sum_{k=0}^N a_k x^k = \sum_{k=0}^N g_k a_k x^k [/eqn]
where [math]g = (g_0 , g_1 , \ldots)[/math].

The family of of polynomials you posted is then just the orbit under this group operarion [math]G \cdot (x^4 +x^3 + x^2 + x + 1)[/math].

Consider the transcendent field extension K_1(t) = L with t in K_2. What does it mean that the set of polynomials P(t) in L is "algebraically equivalent" to the set of polynomials P(x) in K_1? I came across this phrase and I can't find a formal definition for it.

how can I prove that [math]4n^2+4n+1[/math] is not a multiple of 3 for any integer [math]n[/math]?

>>15337963
nvm, just got it

Can someone familiar with journal articles please help me figure out the main claim and sub-claims of this article? We have a mandatory research skills module in freshman year and it's incredibly frustrating.

I think the main claim is the first two paragraphs of the abstract, but I'm conflicted, because the last two paragraphs also express the same thing.

https://sci-hub.se/10.1016/j.quaint.2016.08.036

>>15337989
This is the first time I've ever read a research paper. I have no clue what I'm doing.

>>15337989
>connection is not secure
post the pdf into the thread

>>15337993
NTA regular DOI https://doi.org/10.1016/j.quaint.2016.08.036
Title
"Plants before farming: The deep history of plant-use and representation in the rock art of Australia's Kimberley region"
researchgate has a pdf
https://www.researchgate.net/publication/312412099_Plants_before_farming_The_deep_history_of_plant-use_and_representation_in_the_rock_art_of_Australia's_Kimberley_region
>>15337989
Try researchgate before sci-hub and other methods such as googling the title in quotes to check if it is otherwise public. Unless you live in a country where nobody cares about piracy.
>main claim and sub-claims of this article
I don't know about your class and the professors notion of what "main" or "sub-claims" are, so I can only go on my notion of the meaning. You should've posted the specific definitions or instructions as well if you wanted hints.
>We have a mandatory research skills module in freshman year and it's incredibly frustrating.
Given how bad the article you linked was written I'm going to have to conclude your professor is a moron, so that probably doesn't help you any. Please clarify what the retard thinks "main" and "sub-claim" mean.

Anyway, to my general reckoning the MAIN claim in THIS article is that rock art should also be taken as evidence in corroborating notions of plant use. Various sub-claims to my reckoning ought follow from this as claims relating to other lines of evidence. I can't fathom how anyone thinks wasting your time on this is useful but oh well.

>>15337993
>>15337989
here fren

>>15338017
We have to learn general research skills with these articles before going to research related to our major.
We were just asked to find the main claim and sub-claims of this article. I think we have to select the sentences from the article that express the main and sub-claims.

>>15338025
>>15338017

Can I use the last two paragraphs of the abstract as the main claim? Without the word instead.

>>15338094
last two sentences*

>>15338025
>We have to learn general research skills with these articles before going to research related to our major.
This paper is what I'd use to explain "this is what not to do when writing a research paper" by example. If this is the gold standard your professor thinks is good writing I don't suppose it's too late to run?
>We were just asked to find the main claim and sub-claims of this article. I think we have to select the sentences from the article that express the main and sub-claims.
Gave you my thoughts >>15338017 but I'll further it with an example of what I mean. Conceptually, let's assume we only have the abstract. The main claims could be any of the following or more,
>>the orthodox notion of agriculture cumulatively and inevitably developing from foragers' gathering practices is increasingly untenable.
or
>>recent archaeological, botanical and genetic research from Asia and Australia show precocious manipulation of plant resources that continue for millennia within a forager ideology and practice without culminating in ‘agriculture’.
or
>>rock art is a primary record of long-term sophisticated physical and symbolic manipulation of plants that fits neither into the simplistic categories of ‘foraging’ or of ‘agriculture’.
or
>>Rather, we have a society in which people actively chose not to pursue orthodox agriculture while according plants a central place in their lives.
All of these are equally possible as the "main claim", in lieu of any detail in the article. To determine which is the more relevant and primary you have to read the whole article. That abstract is a goddamn crime but you can still figure it out by RTFA.

Pro tip: The segments 1-7 SHOULD, though the article author is the worst writer I've ever seen in my life, provide an outline and flow of thoughts. So which of the many claims is the "main claim" ought be self evident. This article is an example of "how not to write research papers" in my opinion but oh well.

>>15338102
This is a mandatory module. I think it was created to get undergrads familiar with research from the first semester.

Thank you fren. It's much clearer now.

Can you help me with the sub-claims as well? I have some written down, but I'm not entirely sure if they're right

Is there an algorithm to determine the minimal polynomial given an algebraic number? For example, consider the algebraic number[eqn]\sum_{k = 1}^n k^{\frac{1}{2}}[/eqn]What would be the minimal polynomial for a given [math]k \in \mathbb{N}[/math]?

>>15338228
Don't you mean for a given n?
Either way you use trial-and-error
For example for n=10 the minimal polynomial is

[eqn]{x}^{16}-96\,{x}^{15}+3928\,{x}^{14}-89568\,{x}^{13}+1243820\,{x}^{12}
-10681440\,{x}^{11}+53150088\,{x}^{10}-105773280\,{x}^{9}-306405418\,{
x}^{8}+2147919840\,{x}^{7}-2872989528\,{x}^{6}-6781142688\,{x}^{5}+
19259216972\,{x}^{4}+1820726496\,{x}^{3}-29925033224\,{x}^{2}+
1545510240\,x+10788246961
[/eqn]

>>15338246
That's what I meant, yes. Wow, it surprises me that there is no algorithm. Do you know of a proof that no such algorithm exists? On that note: Could it the answer be related to the fact that there is no formula for quintic polynomials?

Does a double negative number always equal a positive?

for example at the beginning of the equation -x where -x = -3
-(-3) does that just make it positive 3?

>>15338272
Yes, if the elements are from a ring (or from a field, which is a ring).

>>15338221
>Can you help me with the sub-claims as well? I have some written down, but I'm not entirely sure if they're right
Yes. I will try to refrain from further commenting on the various ways I wish a pox on your professor. Maybe. Taken as something analogous to categories and sets, a "subclaim" is only sensible within the scope of whatever one chooses is "the main claim".

So given claim A, then it is a group comprised of sets whose elements are the evidences following from A and some given set. A[1{ ... }, 2{ ... }, 3{ ... }]. Subclaims necessarily follow from the main claim. That is, "if A is true, then B is true", so "A is true therefore B". If one is going to claim art should represent a piece of evidence, then the subcomponents or subsets of that claim ought follow "assuming A is true" and further claim individual examples are evidence assuming art represents plant usage.

Just don't fuck up and end up thinking "B is true therefore A" https://en.wikipedia.org/wiki/Affirming_the_consequent
Or end up thinking the modus tollens variant (not-B therefore not-A) is somehow a fallacy https://en.wikipedia.org/wiki/Modus_tollens
And if your professor confuses the two I retract my desire to only drown him in minecraft. I've met some very, very bad professors in my time. Can you tell?

>>15338299
>Guy asks about 3rd grade negative rules
>Answers with rings and fields
Does a fedora that large hurt your neck?

>>15338362
if he didn't understand, he would've just asked again

Consider an algebraic field extension K(t) of degree n. Why is it obvious that all polynomials from K(t) are of degree n - 1?

>>15338390
K(t) is a vector space over K with the dimension n.
1, t , t^2 , ... , t^(n-1) are all lineary independent which means they form a basis.

>>15338272
>Does a double negative number always equal a positive?
Assuming a lot of things, like just talking about the real number line, yes. As the negative, as a qualifier "prefix" to a number or whatever, means the inverse of something. e.g. -3 is the inverse of 3, -x is the inverse of x, etc. Since our regular numbers are symmetrical around their origin, or 0, i.e. equidistant from 0 whether positive or inverted.

It would help you to not be confused if you advance further to not think of qualifiers as identical to operators. Granted it would help all the more if we didn't use the same fucking symbol for it, but that's a lost cause. It would help even further if at some point we explicitly told people "subtracting" actually means inverting by some magnitude. (-3) - (-3) is therefore "the inverse of 3 inverted by another inverse of 3", which is why it ends up being 0 and why "negative numbers" are positive when acted upon by the inverse operator (the negative sign).

In this context of course the inverse can also simply be thought of as "the reverse" by some magnitude for simplicity sake. As "the reversal by the magnitude of the inverse of 3" would also be 3. Just detailing these kinds of things so you're comfortable trying to think about it in different ways.

That only works if, and only if, the numbers you're working with are symmetric across some origin point. For the simple number line and most purposes they are symmetric about origin, or axis, or 0. Though if you're clever you will immediately note that "0" cannot be said to have an inverse in the normal sense, except conceptually as an origin point wherein one could "invert" the axis and bla bla wheel theory and irrelevant algebraic structure shit.
>>15338299
>Yes, if the elements are from a ring (or from a field, which is a ring).
Not necessarily (:
>>See also wheel theory
>>15338362 is right though you're just being unhelpful if someone is asking such a simple pragmatic question.

>>15338390
Because t has a degree n minimal polynomial over K, it follows that t^n is in the K-linear span of the lower powers of t

>>15338459
>>15338530
great thanks

>>15338334
good answer.
>>15338221
anon, if you're thinking the main claim is: >>rock art is a primary record of long-term sophisticated physical and symbolic manipulation of plants that fits neither into the simplistic categories of ‘foraging’ or of ‘agriculture’
its not
look more broadly.
the orthodox notion of agriculture cumulatively and inevitably developing from foragers' gathering practices is increasingly untenable.

>>15333685
It's wrong

>>15338390
the other day i thought of a different answer to this, i'd like a more skilled algebraist to comment on my idea:
let f(x) denote the minimal polynomial of t (hence has degree n)
then if g(x) is a polynomial of degree >= n, we can divide g by f to get
g(x) = f(x)h(x) + r(x)
evaluated at t then, g(t) = 0 + r(t)
where r(t) is of degree strictly less than n
and as far as i can tell this would hold in a more general setting than polynomials over a field? although we've not been concerned much with algebraic extensions of rings

>>15339315
some further thoughts on this:
the kernel of the evaluation morphism [math]ev_a:k[x]\rightarrow k[t] [/math] is generated by f (do we really need the fact that k[x] is a pid for this?), so by the first isomorphism theorem [math]k[x]/\langle f(x) \rangle \simeq k[t][/math]
now as in my above post if g(x) = f(x)h(x) + r(x), then g(x) is in the coset identified with r(x)

so my stupid question is:
given a commutative ring R, and an R-algebra A such that there is an "algebraic" element t in A (that is, there exists a nonzero polynomial f(x) in R[x] s.t. f(t) = 0). Is there a unique minimal polynomial for t? (without any guarantee that R[x] is a PID) My guess is no, but it's too late at night to think of counterexamples.
But if R is a PID, then everything is fine and the above isomorphism still holds right?

>>15339392
Worthless

I have two full time terms of CS left to get a CS degree, same goes for math (pure). I used my (federal) student loans to finance the expansion of an agriculture business I started, and it’s been going well enough that I have no interest in waging, but I still find myself, at times, longing to work on something more interesting. What would you advise? I’m interested in math, CS, finance and ecology but really don’t like someone telling me what to do. Self study doesn’t quite scratch the itch I’m seeking to satisfy.

How long does the rabies virus survive outside the body in saliva?

If you touch X object with saliva (dry or wet) reasonable to say you have rabies in your hands????

>>15339466
Depends on the specific conditions, but generally not more than a few hours.

>>15338334
Thanks for helping, anon. Really appreciate it!
>I've met some very, very bad professors in my time
Haters

>>15339427
Try out a minor, it'll give you that scratch but at the same time allow you to maintain your business

>>15332629
I fell for the chemistry meme /sci/
I am set to start a PhD in chemistry at an elite school next fall but I am wondering what is the point?
Will there be any jobs for synthetic chemists in 6 years?

>>15339543
Should echo what >>15338727 mentioned I was repeatedly saying "if" but in case it was not explicit enough I was not endeavoring to do your homework for you. Quite intentionally. I don't even know if the other anons notion is right or not.

>>15339554
A minor? What do you mean? I’m two terms away from graduating with either a Math or CS degree, my minor requirements are fulfilled in both. My problem is that I don’t see a need to complete the degree, but still want to do interesting work.

Why do I feel so well rested when I decide to sleep several hours later than my normal sleep schedule? I do that sometimes to try and get my sleep schedule back to normal and I always notice how good I feel when I wake up. But if I'm going to sleep and waking up at a consistent time I don't usually feel as great.

>>15339906
>get my sleep schedule back to normal
try not kissing boomer ass once in a while

What is the average distance between two points in a circle?

>>15340073
The distance between two points [math](x,y)[/math] and [math](x',y')[/math] with respect to the norm [math]\|.\|[/math] is [math]\|(x - x',y - y') \|[/math].
To average it out you will need to specifiy a probability distribution for the points. If you use the uniform distribution when you get it as an integral over a 4-dimensional set
[eqn] \frac{1}{\pi^2 R^4} \int_{\underset{x'^2 + y'^2 \leq R^2}{x^2 + y^2 \leq R^2}} \|(x - x',y - y') \| d(x,y,x',y')[/eqn]
Assuming the radius of the circle is [math]R[/math]. Hope this helped.

>>15339392
some clarification: by a minimal polynomial for t, I mean a polynomial that generates the kernel of the evaluation morphism (or equivalently other polynomials with t as a root factors through the minimal polynomial).
And the last line should have read ''.. if R[x] is a PID..'', ofc this happens iff R is a field, so that part of the question is redundant.

Now I have found some sort of a counterexample, consider the [math]\mathbb{Z}[/math]-algebra [math]\mathbb{Z}/4\mathbb{Z}[/math] and t = 2 in [math]\mathbb{Z}/4\mathbb{Z}[/math], the minimal polynomial is x-2, but [math]f(x) = x^2[/math] also has 2 as a root and does not factor through x-2. Now this is a rather shitty counterexample, we really don't think of [math]\mathbb{Z}/4\mathbb{Z}[/math] as an extension ring of [math]\mathbb{Z}[/math].

So my new stupid question is:
given a commutative ring R and an R-algebra A such that the structure morphism [math]\phi:R\rightarrow A[/math] given by [math]r\mapsto r\cdot 1_A[/math] is injective (so A a proper ring extension of R)
if there is an "algebraic" element [math]t\in A[/math] (that is, there is a polynomial [math]f(x)\in R[x][/math] s.t. [math]f(t) = 0[/math]), is the kernel of the evaluation morphism [math]ev_t:R[x]\rightarrow R[t] [/math] (defined by [math]f(x)\mapsto f(t)[/math] ofc) generated by a single element of R[x]?
What if [math]R = \mathbb{Z}[/math]? (nicest ring short of a field)
Again my guess is no, but I'm struggling to find a counterexample.

>>15339404
don't be rude anon, I'd really like an answer to my question

Is qualia still on-topic for /sci/?

why does electrocution cause your skeleton to become visible?

>>15338264
bump

If we assume that a regular n-gon is constructible, how would we show that a 2n-gon is too constructible?

>>15340881
Construct the bisectors of all sides and the circumcircle then intersect them.

>>15338264
For the n=10 case you know that

[eqn]\sum_{k=1}^{10} \sqrt{k} \in \mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5},\sqrt{7})[/eqn]
So it makes sense to expect the minimal polynomial to have the degree 2^4 = 16.

For n = 20
[eqn]\sum_{k=1}^{20} \sqrt{k} \in \mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5},\sqrt{7},\sqrt{11},\sqrt{13},\sqrt{17},\sqrt{19})[/eqn]
So the minimal polynomail should have degree 2^8 = 256. Maple does indeed give me one but it already takes an eternity to calculate it.

But for general n you would need to have a formula that tells you how many prime numbers there are up to n to even guess the degree much less calculate it explicitely.

>>15340930
Great explanation, thank you. However, I don't think it proves that there can't be a more efficient algorithm other than trial and error. As I see it, it only shows that such an algorithm has to somehow incorporate an additional algorithm for the search of prime numbers. But those exist, ofc.

>>15340447
can anyone help or give direction?

I'm fucking retarded. I have that [math] \sum_{k=0}^p {p \choose k}x_{p-k}=p^n [/math], where [math]x_p=S_{n,p}[/math] is the number of surjective mappings from the set [math] \{1,2,\dots,n\} [/math] to the set [math] \{1,2,\dots, p\} [/math]. How do I show that [math] S_{n,p}=x_p=\sum_{k=0}^p (-1)^k {p \choose k} (p-k)^n [/math]. The first part of the problem was proving the first identity, and you're supposed to deduce the second identity from it, so I don't think surjectivity should enter into the argument at any point. It should just be a proof by induction using basic algebra, but I can't figure it out. Help a fren out.

>>15339246
If that's the case, what's the right answer? There's a whole proof in the book I'm studying(Apostol Vol. I) that relies on this, so where do I find the Errata and corrected proof?

>>15340598
It doesn't.

The skeleton lighting up like a neon sign is a visual
gag holdover from the early days of cartoons and films
(1920s-1930s). What physically happens to
people in an electrocution are the following:
>loss of consciousness and bodily control
>body tensing up/contracting, especially hands
>entry and/or exit wounds from the grounding of electricity
>second or even third-degree burns
>body smoking or even self-igniting
>death...lots of it

Check out some Liveleak videos for visual examples.

am I wrong in saying that the nodal analysis for the V- path here is just [math]\frac{V_--V_1}{R_3}[/math] + [math]\frac{V_-}{R_2 + R_4}[/math]? I'm a little confused how the extra branch on the output with R4 affects the feedback path and by extension the inverting input of the op amp, if at all.

can someone help me with this? It's an exercise where you have to find the sequence in which functions are ordered by asymptotic growth rate (from slower to fastest) but I don't understand why the right answer is D

>>15341534
The Order of Growth rules tell you that [math]\Theta(n^c) < \Theta(c^{\log{n}}) < \Theta(n^{\log{n}}) < \Theta(c^n)[/math].

The only function that isn't so obvious is showing that [math]\Theta(n^c) < \Theta({n \choose c}) < \Theta(c^{\log{n}})[/math]. But if you write out the terms you should be able to see it grows as *roughly* [math]n^c[/math].

>>15341346
>Liveleak
F

>>15341373
>I'm a little confused how the extra branch on the output with R4 affects the feedback pat
It doesn't. Current gets divided, but that's irrelevant here.
Vout gets voltage divided by R2 and R1. The output of the divider is V-, which is set to equal V+. To solve for Vout, you have to invert the voltage divider equation.

>>15339427
>but really don’t like someone telling me what to do.
>Self study doesn’t quite scratch the itch I’m seeking to satisfy.
well, pick one, because knowledge doesn't come as a suppository

>>15341312
I'm not sure what a 'right answer' would be. There is a statement that is wrong. Are you looking for a way to simplify either the left- or right-hand-side?

>>15332629
>Complete the following reactions with the correct reagents
I am a tard taking orgo so these questions seem virtually impossible. What are some strategies and tips for solving these style problems?

>>15341832
forgot attachment

>>15341823
This is the whole theorem in context.

>>15341151
Do you know about binomial inversion?

3^{-2x} - 3^{-x} = 2
There's something I'm missing here on how to solve this, tried factoring out 3^{-x} but I'm feeling kinda really dum, shouldn't be as hard.

>>15333685
Oh. Just a typo then. In your original post you wrote [math]\frac{b^p+1}{n^p+1}[/math] instead of [math]\frac{b^{p+1}}{n^{p+1}}[/math]. You instead have your equality immediately once you move [math]\frac{b^p}{n^p}[/math] inside the sum.
>>15341854
Notice that [math]3^{-2x} = (3^{-x})^2[/math]

>>15341854
[math]3^{-2x} - 3^{-x} = 2[/math]
Good job.

>>15341854
Let [math]y = 3^{-x}[/math], so [math]y^2 - y = 2[/math] and solve the quadratic.

Are there lava monsters in the earth's mantle?

pic related. I wasn't interested in getting lectured about nofap. I feel like it's healthy, fun, and free. I just wanted to know if there was an app that filters my search history and stuff. Something that leaves the useful content and gets rid of the unuseful content. I would like to be able to hand my phone, laptop, or desktop to someone else and porn doesn't show up in the search or history, but all of the other normal, useful stuff remains. Is there not an app for this?

I could have used incognito or something, but it's too late. Now all of the useful stuff is mixed with less than useful stuff.

thanks folks.

>>15342082
You could have a separate guest account for other people to use

>>15342219
Or better yet, a separate account for masturbatory purposes.

I wanna do something with phenol red, but I've heard that I MUST use gloves. Is phenol red so dangerous?

I'm getting confused right now because I'm quoting too many politicians: If I quote a politician, let's say Merkel, and I find that part of what she said in an online article of the Frankfurter Allgemeine Zeitung, with that article being written by a guy named Müller:

Do I quote "(Merkel, 2015)" or "(Müller, 2015)"? I am quoting in verbatim. It would make sense to quote "Merkel", but what do I put in the reference list then? It has to be Müller's article, right? So I would have to go by Müller (2015)... bla.
It also doesn't feel right to do "Merkel, cited in Müller" in this occasion, this is reserved for when I found an academic quote in another source, right? And since I'm talking about narratives and discourses, it can't be that I go with this because I really hardly ever see discourses being quoted like this

is it possible to get into med school after being out of college for years and having no connections? I thought you needed academic letters of recommendation with all the test scores and stuff

>>15332727
James Stewart's Calculus Vol. 1

>>15341835
remember carbonyls are the most versatile functional group

>>15341832
>>15341835
bare minimum, you need to know how to read bond line structures, otherwise the rest of this post will not make sense to you.
next, you need to be able to recognize the functional groups. you can see in b) that the molecule starts with an ester and ends with an ether. ochem is all about changes in functional groups; once you know which ones you're dealing with, recall what reactions use esters, and what reactions form ethers, to start piecing together a series of reactions.
another important thing to look out for is a change in the number of carbons in the molecule, since only a handful of reagents are capable of adding or removing them. for a) I could immediately tell the reagent you're looking for is a Grignard because the product has a new C-C bond. Grignards form tertiary alcohols (an OH bonded to a C bonded to three other C's) when reacted with ketones. your starting compound is not a ketone but a secondary alcohol. so you need to turn the secondary alcohol into a ketone before you can use a Grignard reagent to turn it into a tertiary alcohol.
the rest of the problem solving process is just a matter of learning all of the reactions of each functional group and remembering them with practice. good luck.

Trying to wrap my head around multivariate differentiation. Let [math]\varphi: \mathbb{R}^d \to \mathbb{R}^k[/math] be [math]C^\infty[/math]. Define [math]F: \mathbb{R}^d \times \mathbb{R}^d \to \mathbb{R}^k[/math] by [math]F(x,u) = d \varphi (x) \cdot u[/math], where [math]d \varphi (x): \mathbb{R}^d \to \mathbb{R}^k[/math] is the derivative of [math]\varphi[/math] at [math]x[/math]. How to show that [math]F[/math] is [math]C^\infty[/math]?

are hands supposed to be squeaky clean or smooth after washing? I always hated liquid soaps due to smooth/greasy feeling, but apparently squeaky is "le bad" according to jewgle. so which one is it and what feeling is left behind surgical soaps?

>>15345216
The k-th component of F is [math] \sum_i u^i \partial_i \phi^k(x) [/math] and it's enough to show that all these components are smooth.

>>15345376
Thanks, I think that's all I needed to hear. I can make sense of this problem now.

hey, don't know if this is the place to ask but figured you guys might know. if 2 people play a game where they wanna roll a 2 or 5, taking turns, whats the odds player 1 wins?

>>15346042
Call the odds that player 1 wins p

p = (1/3) + (2/3)*(2/3)*p
(5/9) p = 1/3
p = 3/5

>>15346064
thank you for the reply but do you mind explaining this to me?
I get that 1/3+2/3*2/3*p is just 5/9*p, but how do you go from 5/9 p = 1/3 = p =3/5?
thanks again for the help.

I decided to read some chapters in the napkin but because I skipped some I don't know the notation used here (specifically the [math]K((X))[/math] part).
Any ideas?
For context [math]K[[X]][/math] is the set of generating function with coefficients in the field [math]X[/math] and based on the stuff below [math]K((X))[/math] is probably the set (field?) of laurent series with coefficients from [math]X[/math].

It is not needed for reading further but I would like to know what it means, just out of curiosity, without having to skip through the earlier chapters.

Does someone have a good reference for an approach to Hodge theory or complex geometry using functional analysis?

>>15346406
You know how to construct the rationals from the integers?
You can do the exact same construction with any commutative ring to get a field called the fraction field. K((X)) is just the fraction field you get from K[[X]].

>>15346430
Oh yeah I get it now. And apparently K((X)), the fraction field of K[[X]], is also the laurent series (which is a pretty nice). Thanks!

Whats the lim of g(x) when x tends to 4 and g is a function with the properties like:
|g(x) + 5| <= 3(4 - x)^2 for x in the intervals of [3 , 5]

>>15343838
Merkel said "..." (Mueller, 2015)
it seems to me

>>15346557
-5

How was i supposed to know that:
1. It was Ni+2 there?
2. It would make a hybridization of sp2d (which i've never heard of in my entire fucking life, what the hell?)?
3. The electron from the last 3d orbital would stay in that sub-level?
4. That hybridization with orbitals outside the valence shell were possible? (I mean, how does that make sense?)

My professor sucks and every time i ask him something, he tells me to study more and goes to jack off or something. Please, i just want to understand this shit. None of the material i read tackles this.

Why people with adhd like myself (Yes, I'm egotistic how could you tell) that are highly irritable, disagreeable, impulsive, neurotic or/and prone to anger tend to be confused for schizophrenics, autists or people with borderline (even when they clearly don't fit critteria; they are just uber insufferable even when right)? Is it solely because of choice of medication (aka HOW DARE they prescribe that fuck which pisses me off amphetamine (disregard that said person doesn't even like to take it), he needs to be forced to take antipsychotics or antidepressants so hopefully they suffer/find it unpleasant)? Because I feel like that's the main reason behind this bias even tho all people with neurological disorders are treated like children that can't decide for themselves (autist being treated like downies, schizos/bipolar/adhdtards forced to take their medication so they shut the fuck up)

>>15346633
1. The complex has 4x CN- ions, and an overall charge of -2, meaning the Ni must be +2 to balance charges
2. Ligand field theory (picrel). A metal center with four ligands is either gonna be tetrahedral or square planar (i.e. px, py, and dxy orbitals)
3. I don't get your question, but likely as a result of the hybridization changing energy levels enough to overcome Hund's rule
4. 3d and 4p/s orbitals are all valence shell, review how the Aufbau principle works

Hybridization is a bit of a shaky concept in inorganic chemistry, and I'm not sure why your prof is wasting your time with it. You basically have to unlearn the handwavy "rules" you learned in Ochem, and re-learn them from the perspective of point group symmetry.

What is the best way to know someone is gaslighting you in the moment?

Is there a closed formula for number of surjections on finite sets?

>>15347536
The number of surjections from [math]\{1,2,\dots,m\}[/math] to [math]\{1,2,\dots,n\}[/math] with [math]m \geq n[/math] is [math]\sum_{k=0}^n (-1)^k \binom{n}{k}(n-k}^m[/math].
This follows from inclusion-exclusion, counting first all [math]n^m[/math]functions, removing the ones that miss at least one point, adding back the ones that miss 2, ...

If T is a linear operator on a real vector space of odd dimension, then [math]T^2 + I[/math] is non zero, as [math]det(T^2) \ge 0[/math] whereas [math]det(I) = -1[/math].

How would you prove this without using determinants?

What does it mean, when people say you cant solve the navier-stokes-equation? What does it mean when people say you can approximate the solution with numerical analysis? What is a numerical analysis?

>>15347806
whoops, meant to write [math]det(-I) = -1[/math] of course

ln = natural logarithm (log base e)
e = 2.7182
How would I determine x for:
lnx + x = 5
I know trial and error will get me an answer close to 3.65 but what is the mathematical way of finding x?
I have just started Calculus
Thank you in advance.

>>15347941
Start with a guess like
[math]x_0 := 3.65 [/math]
then just iterate
[eqn]x_{k+1} = \frac{x_k(6 - \log(x_k))}{1+x_k}[/eqn]

The solution of the equation will be the limit [math]x = \lim_{k \to \infty} x_k[/math].

>>15347806
Hint: Consider T as a linear operator on the complexification of the vector space and use the fact that [math] T^2 + I = (T + i)(T - i) [/math]

>>15347807
>you cant solve the navier-stokes-equation?
That's wrong
>What does it mean when people say you can approximate the solution with numerical analysis? What is a numerical analysis?
https://en.wikipedia.org/wiki/Numerical_analysis

>>15347807
They are a set of linked 3-dimension differential equations. There are no known closed-form solutions to the general equations, only for certain simple situations. So we can't write down an equation for the answer using analytic functions given all the input parameters and geometry. All we can do is solve the equations using computer algorithms to find approximate solutions.

For example if we could solve Navier-Stokes then we would improve our understanding turbulence and hypersonic flight by several orders of magnitude. However all we can do at the moment is throw supercomputers at the problem.

What symbol is this? Approximately greater than?

>>15348049
The Latex symbol is \gtrsim but its meaning depends on the context.

the set of all binary strings may be enumerated in lexicographic order: 0, 1, 00, 01, 10, 11, 000, 001 ... and so on

is there a closed form formula (by which I mean any reasonable math-y expression, as opposed to an algorithm or computer code) for the n-th string in this enumeration?

the set of all binary strings may be enumerated in lexicographic order: 0, 1, 00, 01, 10, 11, 000, 001 ... and so on

is there a closed form formula (by which I mean any reasonable math-y expression, as opposed to an algorithm or computer code) for the n-th string in this enumeration?

>>15348224
Well if n starts from 0 then add 2 to n then remove the most significant bit (first digit in binary string)

All things being equal, if I bend a first class lever and adjust the fulcrum accordingly will the forces still be the same?

>>15348444
yes, the torque is just the cross product of the force and the displacement (from the axis of rotation) to the point where its being applied

>>15347941
Use a root-finding algorithm such as Newton's method or Halley's method. There is no closed-form solution in terms of elementary functions. There *is* a closed-form expression in terms of Lambert's W function: ln(x)+x=5 => xe^x=e^5 => x=W(e^5). But W is invariably evaluated using root-finding.

So why is the Big Bang justified? Couldn't there have easily have been a Big Gang Bang where the Chaos of eons beginning blacked the Cosmos of becoming? Equally logically possible is the Time Pussy Dilation where spacetime bends to let out the biracial baby of both Chaos and Cosmos.

when a photon is absorbed and then re-emitted from an electron in an atom, does it always re-emit from the same position where it was absorbed, or can it appear from anywhere in the electron cloud?

I'm assuming if it can be from anywhere, the reflected angle is still the same regardless, it can't alter it's direction because then the atom would need to somehow create energy in alternate directions and deal with energy it just gained in directions it isn't using

>>15350235
>delay close

>>15350235
Spontaneous emission of the photon is completely random. It can be in any direction.

>>15350331
it's not random

>>15350363
Yes it is, I have no idea why you would think otherwise unless you are thinking about stimulated emission which occurs in things like lasers.

Help, how did they get 87% for the first question? Obviously this answer gives the answer for 2nd question as 13%, but I don't get what they did to get 87%.

>Limit the total number of figures and tables to no more than 8, place secondary figures and tables, pictorial figures, and over-sized tables in Supplementary Material
so no more than 8 in manuscript WITH supplementary material?

>>15350768
Have you never heard of an appendix before?

>>15350755
[eqn] F(13) - F(7) = F(10 + 1.5 \cdot 2) - F(10 - 1.5 \cdot 2) = \Phi(1.5) - \Phi(-1.5) = \frac{1}{\sqrt{2 \pi}} \int_{-1.5}^{1.5} e^{-t^2/2} dt \approx 86.6\%[/eqn]
You have to use numerical integration to approximate the integral as it has no closed form solution.

>>15350769
rude

>>15350771
Or you can just look at the table they've provided in the question

>>15350771
>>15350774
Thank you, I was wondering what bounds they used and why, seeing the integral there I realize that 7 and 13 is +-1.5 std from 10.

>>15350771
Do you happen to know if ti-84 can calculate error functions or am I just gonna have to integrate like you did? It worked with integrals but shortcuts are always welcome

Finally dis its . I cut my axillary artery. Bow I willl be at peace

I just started reading this book on reflection and coxeter groups by James E. Humphreys and I just wanted some clarification on this passage where he lists some examples for reflection groups. Since he doesn't unambiguously define [math]A_{n-1}[/math] anywhere, I figured it's just [math]S_n[/math] acting on the [math](n-1)-[/math]dimensional Euclidean space as described, since anything else wouldn't really make sense. But I just wanted to be sure.

>T=n1+2n2+3n3+4n4...
in this equation 1 is exponent of 1n, right?
2 is exponent of 2n and 3 is exponent of 3n, right?

>>15351156
it's gibberish unless you write it in latex or a picture.

>if you flip a coin 100 times and it lands on heads 99 that means the probability of getting heads is .99
Why do statards believe this?

i noticed that in some papers in zoology (ecology) "survival rate" is not the same as "Sr" but how do they differ? "Sr" probably means exactly "limited annual survial rate" so if i understand it correctly, if Sr =0.9 then 90% of population survives to the next year

Scientifically speaking, what's the reason we can close our eyes and mouth but not our ears?

What is [math] \epsilon_{jki}\delta_{ii}A_k [/math]?

Just thought some of you guys might get a kick out of this. Yes this was a real published research paper.

>>15332629
This reality makes me incredibly uncomfortable as if it was just me all along, just playing with myself. Can I get rid of this feeling without seeing a shrink? Please don't troll me or anything.

>>15353479
More details

>>15353509
Not like it even matters at this point, if I was truly a valued member of society there wouldn't be this many control mechanisms put in place just to force me to be here in this society

This is ridiculous, all of it is

I think my TA hates me. He's responsible for taking bi-weekly sign-offs on workshop tutorials, which adds up to 20% of the grade.
He was pretty active on the group chat and told us that the next signoff would be held on a day we had exams. He texted the group chat at 11:50, so I privately texted him at 11:55 (WhatsApp) and told him that we had a test at that time. This guy throws a temper tantrum on the group chat the next day and tells us that some individual texted him at midnight on a public holiday and he would block the numbers of anyone who continues to do so. I think he blocked me or deleted my message because it wasn't read. No one else told him and he found out at the last moment that we had an exam. Informs us 2 hours before the exam that the signoff would be conducted one hour before the exam.
No one shows up, so he changes the time to after the exam and doesn't show up.

Should I apologize the next time we meet, or just ignore it?

My assignment is to dectect this shape, what do? I know something something sbout frequency transform, line detection etc and that's it, wtf do I do next? I know I'm supposed to use machine learning, but I know near nothing about it. Can someone give me some starting point?

does anyone know if its possible to strike the air so hard you can briefly set it on fire? i wanna know if this sort of thing can happen in a logical manner cause i wanna use it as an ability for my fantasy OC

I have to find the lagrangian of this system, but I'm not quite sure about which generalized coordinates should I choose, any suggestion? The rod is rolling (without slipping) over fixed disc.

>>15354015
or if its possible to move something so fast you manage to set it on fire like a match using air friction

>>15353895
why would you apologize? This is his own doing

>>15354042
okay is there a fucking way to make fire out of thin air?

>>15354056
at mach 25ish (atmospheric reentry speeds) the air starts to ionize

>>15354056
fire requires a source, heat and oxygen. you only have two of those.

>>15332629
Good Morning /Sci/entists!

>Why I am asking
I built a better version of Kurumi MaidCard which will have no dependency on Pastebin, because Pastebin jannied MiniMaid.

I built a new MiniMaid which can be posted in 4Chan posts as four java classes. Just save them in the same directory and compile them and now you have MiniMaid and you can open Maid Cards with it to get Kurumi MaidCard so you can make them too.

I want to release it /sci/ instead of /g/ because it is an example of Applied Computational Maidposting which fits better here than on what is basically a consumer electronics board.

>question I want answered
What is the /sci/ equivalent of posting a dra/g/on maid board block?

Thank you /sci/entists for reading my post.

>>15354218
Forgot to link this.

>>>/g/92803592

If you want more details you can read them there.

A world-class expert in my field is visiting my university for a seminar soon and faculty and grads are given the opportunity to have one-on-one meetings with him if they want. I kind of want to reserve a time slot because he's sort of working on the same thing as me (PhD student) but I'm a bit nervous over getting mogged by him and basically wasting everyone's time because we're too intellectually apart to have a meaningful discussion. How does that sort of thing usually works? Any unspoken rules I should keep in mind? Has any anon had experiences with meeting big profs at seminars?

>>15332629
What's the best job for a 95 IQ brainlet now that the gpts are going to be doing what I would've been doing in the past? I'm the brainlet BTW.

Is it worth doing a physics phd if you've already got a masters?

>29
>skinnyfat
>doctors say i'm "healthy" yet i've been saying to them that I am having general chest pains but alot in picrel
>got 2nd, 3rd, and 4th opinions
How do I convince a doctor to do all the tests for heart disease on me?

>>15354661
For what purpose? If you are looking at a job and the employer says to you: "If you get a PhD in this or that field we can give you your dream job" then yes.
If you are in a general sense trying to improve your labour market position then probably not.
If you think you maybe want to enter academia then probably not.
If you are not sure what to do with your life and think it can't be such a bad idea to get a PhD then absolutely not.

>>15354598
I've never heard of such a thing as students reserving time-slots to talk privately with a guest to the university.

is grant money from GRFP "not designated for education expenses"? does the $ in "scholarship" in my 1098 Box 5 not go to paying tuition? one of you had to do this recently unless you waited last minute

>>15354218
>What is the /sci/ equivalent of posting a dra/g/on maid board block?

>>15332727
Professor leonard on youtube.
Khan academy was very badly explained IMO.

>>15354036
I haven't considered the problem deeply or anything but to me it seems like the best coordinate here would probably be the angle of the point of contact

For an entrance exam I'm studying for there is a section on implication in logic. You're given a syllogism and then have to tick whichever answer applies. There is only ever ONE correct answer.

So here is what I got stuck on.
All dogs are animals.
All animals are made up of cells.

The potential answers are:
A: Some Dogs are not made up of cells.
B: All things made up of cells are dogs.
C: Some things made up of cells are dogs.
D: All Dogs are made up of cells.
E: None of the answers above.

I consider both C and D true statements that necessarily follow from the syllogism. If all dogs are animals and all animals are made up of cells, then all dogs must be made up of cells, right? Well, no. Apparently according to the simulation, only C must follow necessarily.

So I looked up the guide in the learn material and it states that whenever A is B and B is C, the only statements that necessarily follow are that Some C are A and that some A are C.
Why? I don't get it. I even drew it up like a retard. It would only make sense to say that "some dogs are made up of cells" if the original syllogism stated "some dogs are animals".

>>15356483
Which one is strictly necessary?
>Why? I don't get it.
1. There are things that possibly follow
2. There are things that necessarily follow
3. There are things that contingently follow.
If you are being asked which one necessarily follows, then you can exclude things that merely possibly follow or what is contingent, etc.
In your case your answer is figuring out the first two. You're being asked what necessarily follows. I'm pretty sure you can immediately figure out which one is the wrong answer.

>>15356483
>So I looked up the guide in the learn material and it states that whenever A is B and B is C, the only statements that necessarily follow are that Some C are A and that some A are C.
I shouldn't have skipped over this. You appear to have a general example of one POSSIBLE configuration of a 3 tiered syllogism. The question is not the general example, clearly, as it states "all C are A" and "all B are A". Your general example is "SOME C are A".

You really need to pay attention to the words. Carefully. "some" and "all" have completely different results.

>>15356644
Correction: "all C are B, all B are A". My bad.

>>15355863
Bump, please help

>>15356606
But both necessarily follow. Some dogs are made up of cells is just the weaker claim of the two.

pic related is how it's explained in the book. How are System 1 and System 2 any different?

B in system 1 is equivalent to C in System 3. C in system 1 is equivalent to A in system 3.
So if the statement All C are B is a valid solution for system 1, then why is the statement All A are C not a valid solution for system 3?
If I would write the syllogism for system 1 in the same terms as system 3 it would say "All B are C." and "All A are B."

Premise 1 and Premise 2 just swap places but I don't see how the order of the premises would make a difference. Like how does the premise
"All animals are made up of cells"
and
"All dog are animals."
allow me to conclude "All dogs are made up of cells."
but when I swap the order to
"All dogs are animals."
and
"All animals are made up of cells."
I can now only conclude "Some dogs are made up of cells."

I get understand that statement forms such as "p && q || r" are ambiguous and require parentheses but are statement forms composes entirely of and connectives or or connectives ambiguous? Like do I need parentheses for the following statement forms:
p && q && r
p || q || r

>>15356857
>Premise 1 and Premise 2 just swap places but I don't see how the order of the premises would make a difference.
Pay attention to the circles and visually what you can strictly infer from them. Set notation probably could help here as well
System 1
"all A are B, all C are A"
B{A[C]}
The valid solutions follow from the circles or set. All of C is contained within B. Some of B is C.
System 2
"all A are B, all A are C"
B∩C = {A}
Some C are B, some B are C.
>So if the statement All C are B is a valid solution for system 1, then why is the statement All A are C not a valid solution for system 3?
Someone fucked up is why. "some C are A, some A are C" would be a 3-ring venn diagram where A overlaps B and C but exists outside of C. Hence, some of C would be A and some of A would be C. Nested like it is, the sketch is wrong.
>But both necessarily follow.
Ignore "system 3". Only one answer necessarily follows. Follow system 1.

>>15356918
No, these expressions are unambiguous even without parentheses.
&& as well as || are "associative" just like, for example +, and "a + b + c" does not require parentheses either.
Expressions like that can be given a formal mathematical meaning; for example "a + b" could denote an element in an Abelian group, and "a && b" could denote an element in a Boolean algebra.
Intuitevly, they are of course associative because the meaning of "p && (q && r)" and "(p && q) && r" are both, self-evidently, "all of p, q, and r are true".
I suppose you could also write down the truth tables for "p && (q && r)" and "(p && q) && r".

Aight, so i got a pretty big science 101 question. I should have asked this in my first college physics class but i didn't so now i'm gonna look like a moron. Like, i've got a pretty good idea of how black holes work and i don't know this simple fucking thing.

So, if we're all in the big bang, if the big bang is all of the stuff in the universe moving from being ultra compact to spreading out, how do we know where its center is? Or don't we?

>>15357242
There is no center. The Big Bang was not an explosion from some focal point, it is the expansion of space itself which is why no matter which direction we look in we see everything moving away from us at the same speed.

>>15356857
Holy fucking hell WHY do they NOT just fucking USE SET THEORY NOTATION FOR FUCK SAKE.

Some resources
https://en.wikipedia.org/wiki/Syllogism
rules https://wikieducator.org/Rules_and_Fallacies_for_Categorical_Syllogisms

>So if the statement All C are B is a valid solution for system 1, then why is the statement All A are C not a valid solution for system 3?
Hoo boy here we go. First understand per the wiki about particulars vs universals. Also see image uploaded here.
For reference:
System 1 = AAA-1 "Barbara"
https://en.wikipedia.org/wiki/File:Modus_Barbara_(Euler).svg
System 2 = AAI-3 "Darapti"
https://en.wikipedia.org/wiki/File:Modus_Darapti_(Euler).svg
System 3 = AAI-1 "Barbari"
https://en.wikipedia.org/wiki/File:Modus_Barbari_(Euler).svg

All C are B is valid for system 1 as they're all "universals". Even if any term had no instances (elements), it would still be true.
For system 1, consider it like nested sets. B{A[C()]} all the relations are true. "carries no existential import" (fuck you aristotle).
1. All A are B
A is clearly a subset of B
2. all C are A
C is a subset of A
3. All C are B
C is clearly nested in A which is clearly nested in B.

Notice how sets make it all sane again?

In system 3, it is supposed to be (and is failing to be) modus barbari. They are not nested sets, as one is actually stating "some element A exists in set B". Therein lies the problem. To demonstrate,
Set mockup: C{B[A]}
1. All A are B
True as A is clearly an element of B
2. All B are C
True as B is a subset of C.
3. All A are C
This does not follow. "A" is an element, and all of "A" may not exist within "C" merely because one PARTICULAR instance of A exists within B. "A" could be a member of many other sets, such as Z{A} and so on.

Do it my way, you instantly can intuit the problem. Do it Aristotle's retarded way with those retarded euler diagrams and, well, yeah. (1/2)

>>15356483
(2/2) from >>15357250

Now let's set this up the sane way instead of the retarded way.

1. All dogs are animals.
2. All animals are made up of cells.
3. ???
A: Some Dogs are not made up of cells.
B: All things made up of cells are dogs.
C: Some things made up of cells are dogs.
D: All Dogs are made up of cells.
E: None of the answers above.

You are given 3 systems to find the right answer. The premises in system 1 are in the wrong order, as are those in system 2 and its diagram. We're stuck with ugly system 3 since we want to go from A to B to C.

The only valid answer is therefore going to "some C are A", or "some A are C". To avoid the aforementioned existential fallacy.

Assuming I didn't fuck up in my insomniac state and get any of the orders wrong in my explanation from before, hopefully the right answer is now immediately apparent. Use system 3.

>>15357250
>>15356857
I feel I need to further clarify my example for system 3 just in case. Keep in mind my "set theoryish mockup" is WITHIN the logic given by the systems you are using, since you specifically asked "why does this work in system 1 but not 3".

I should've specified in system 1's example "All set A are set B" and so on, and for system 3 I should've specified in conclusion "all element A are in set C". An element was chosen to analogize your request to demonstrate why you can't make a universal statement about a particular in system 3. In that, by doing so, you are not only saying "it exists" you are saying "it ONLY exists IN HERE". That's doubly bad.

Let [math]X = \{0,1\}^\mathbb{N}[/math]. We equip the space of regular probability measures [math]\mathcal{P}(X)[/math] with the weak-* topology, where by definition [math]\mu_n \to \mu[/math] iff for every continuous function [math]f \in C(X)[/math] there holds [math]\int_X f d \mu_n \to \int_X f d \mu[/math].

I'm reading some text where it seems that, as far as the author's concerned, [math]\mu_n \to \mu[/math] in the weak-* sense iff for every cylinder set [math]C \subset X[/math] there holds [math]\mu_n (C) \to \mu (C)[/math]. By "cylinder set" I mean finite intersections of sets of the form [math]\{x \in X \mid x(n_0) = b_0\}[/math] for some given [math]n_0, b_0[/math].

Is this really equivalent to weak-* convergence? How come?

This proof feels wrong but I'm not sure why.

>>15358916
Theorem 1.17 is right here:

>>15354036
I'm with the other anon on point of contact. If the rod doesn't slip then it is always tangent to the disc, center of mass position and gravitational energy can be computed from the geometry. Kinetic energy seems harder, you'll have to consider rotation of the entire rod about the disc center plus pivoting of the rod about the point of contact, but it seems tractable.

>>15358916
I don't know what you are doing with the whole `degree p' thing (is f a polynomial?) but you can just use a change of variables [math]x\mapsto -x[/math] in your [math]\int_{-b}^0 f(x)\, dx[/math].

>>15358916
This proof is correct, but only for even degree monomials. We want to prove the integration formula for all even functions (how about [math]\cos(x)[/math]?), so we can't assume a specific formula for [math]f(x)[/math]. Instead, do as >>15358942 suggested.

>>15358932
I (the other anon) actually did the calculation for some reason.
I'm pretty sure the kinetic energy takes the nice form [math]\dot{\alpha}^2(\iota + \alpha^2)/2[/math]. (Where [math]\iota[/math] the moment of inertia of the rod)
The angular velocity of the rod is (more or less) obviously just the angular velocity of the point of contact.
And when you parametrize the position of the center of mass in terms of [math]\alpha[/math] it turns out the norm of the derivative is exactly [math]|\alpha|[/math].

In this proof, why does it say x must be a multiple of p(x)?

In probability, is there a term for how the odds of a single nonzero outcome happening approaches 1 given unlimited trials?

>>15359038
I'm not sure, can you give more context?

>>15359038
Murphy's Law.

>>15359039
I assumed it was the Law of Large Numbers or Law of Averages, but turns out those don't necessarily describe this.
>>15359044
Murphy's Law actually used in statistics? I thought it was more of a colloquial term.

>>15359025
>suppose that I consists of all multiples of some polynomial p(x)
>x in I

>>15359038
Infinite monkey theorem

>>15359069
Thanks anon. I thought it'd be named something more pretentious.

>>15359059
Oh, I thought that meant that I had all multiples in p(x) and then some.

>>15357250
>>15357292
>>15357311
Thanks for the explanation and the effort is appreciate, however I want to specifically respond to this:
>You are given 3 systems to find the right answer.

The book contains a total of 19 systems. My inclusion of system 2 wasn't really to imply that I have to choose from those 3 systems, it was just to demonstrate how the book explains it and I still intuitively disagree with why "All dogs are made up of cells" isn't a valid solution. I genuinely think that there must be some mistake there because clearly something THIS counterintuitive requires an explanation IN THE FUCKING BOOK. It makes no sense to just gloss over it. I almost feel like system 3 was supposed to be about some A being B and all B being C and someone just accidentally inserted an "all" in there during print.

>>15354036
Kinetic energy = centre-of-mass + rotational, so:
[math]L = 1/2\dot{\theta}^2\(mr^2+I) -mgr\sin{\theta}[/math]
where [math]\theta[/math] is the angle above the circle's horizontal for the COM, [math]I[/math] is the rod's moment of inertia.

>>15354036
Kinetic energy = COM+rotational
so:
[math]L = (1/2)\dot{\theta}^2(mr^2+I) - mg\sin{\theta}[/math]
where [math]theta[/math] is the angle above the circle's horizontal for the rod's COM and [math]I[/math] is the rod's moment of inertia.

>>15359136
>The book contains a total of 19 systems. My inclusion of system 2 wasn't really to imply that I have to choose from those 3 systems, it was just to demonstrate how the book explains it and I still intuitively disagree with why "All dogs are made up of cells" isn't a valid solution. I genuinely think that there must be some mistake there because clearly something THIS counterintuitive requires an explanation IN THE FUCKING BOOK. It makes no sense to just gloss over it. I almost feel like system 3 was supposed to be about some A being B and all B being C and someone just accidentally inserted an "all" in there during print.
Oh, my bad, I had assumed you were given some sort of simple or more narrow set to work with. In that case, you are going to have to go and identify which pattern of the syllogism applies given the two premises given. It may have in fact been pure coincidence that babari was the correct pattern to answer that specific question, assuming I didn't fuck up.

Anyway the main thrust of my attempt to help clarify was that you can represent such systems with very simple notation that intuitively demonstrates the logic of any particular syllogism. In that it is also self evident, representing the structures as you would in set notation and set theory, why you can or can't do things a certain way. Such as from babari trying to say "all" of "a particular" or "all" of "some thing" exists within two categories.

If the book does not provide notation to work through and make it easy to figure out which syllogism applies, I highly recommend using set theory or propositional calculus or both. Especially because the language used and visualizations used get very confusing, because they do not intuitively show you why you can or can't do things a certain way.

If you want more help please ask. Just please be sure to also provide the fuller context of what help you need and why, so I don't waste time having guessed wrong.

>>15354036
>>15358993
Just stepped through the calculation myself. Set the disc center as [math](0,0)[/math], disc radius [math]R[/math], finite length rod mass [math]M[/math], [math]\alpha[/math] is zero for a flat, balanced rod, CCW positive. Kinetic energy was
[math]\frac{1}{2}MR^2\dot{\alpha}^2\alpha^2+\frac{1}{2}M\frac{L^2+12R^2\alpha^2}{12}\dot{\alpha}^2[/math].

I recognize the first term as the CoM rotation energy modulated by an [math]\alpha^2[/math] term. If we have a really long rod that can somehow wrap all the way around the disc, the CoM has a greater distance from the origin and a higher rotational energy the more times it winds around the disc. Also, at [math]\alpha=0[/math], the kinetic energy is indeed zero; if you visualize it in your head, the CoM momentarily has no velocity when the rod passes through the zero position.

As for the second term, the rotational energy term, first convince yourself that the angular velocity of the rod with respect to its point of contact with the disc (ignore all translational motion) is indeed [math]\dot{\alpha}[/math]. The point of contact is also the pivot about which we calculate the energy. The moment of inertia needs to be computed about that pivot, just use the parallel axis theorem with [math]R\alpha[/math] as the displacement from the CoM, employing the no-slip condition. Indeed with [math]\alpha=0[/math], we get the MoI for the rod about its center [math]\frac{1}{12}ML^2[/math], as it is balanced on its center at zero rotation angle.

These solutions >>15359139 >>15359166 are oversimplifications of the problem.

>>15354008
Well, what is the computer allowed to calculate? When you say you're supposed to use machine learning, are you able to apply image segmentation like Mask R-CNN? Or do you have to do image processing? If this is for some CSCI course, I doubt you are expected to learn the mathematics necessary for the latter like the Discrete Fourier Transform you mentioned. What you're allowed to do will determine the approach you take.

>>15359136
>>15359224

The problem is that the premises are equivocating “animal.” The taxonomy narrator breaks “animals” up into its subgroups, one of which is “dog.” The biology narrator is breaking up cells into all the examples of things made up of cells, including “animals”. “Dogs” are not a part of “things that are made up of cells” the way “dogs” are a part of the things made up of “animals,” even if the premise “all dogs are animals” is tossed into the mix, because the “animals” superset treats “dogs” differently than the “cell” superset treats “dogs.” Why? Because the supersets of “animals” and “cells” are separate in the premises, and it is only the equivocation of the word “animal” that is making you conflate them.

This is paradoxical to you because you are adding the information that, of course, dogs are made up of cells, but the syllogism does not imply that; you added that.
Your venn diagrams are therefore wrongly applied.
This should be a big circle of "animals" with "dogs" inside, and another big circle of "cells" with "animals" inside, and a faint line connecting the word "animals" that you are equivocating.

The confusion here is that you are adding information -- that the "animals" is the same -- that the premises do not contain.

I personally would not even say that any of the answers were correct until the equivocation was addressed.

>>15359606
This was already dealt with via very simple examples analogizing the particular to an element and whether or not one is attempting to claim some particular is exclusively a member of a subset or not.
>>15357250
>>15357292
In any event as noted the universal is the correct answer e.g. where it's got the same (lack of) existential import.

>>15359643
Goddamnit. I meant the particular "some" not the "universal of that particular". I keep forgetting it is not obvious to a casual observer that my statement there requires you understand I'm making nested statements.

>>15359643
I don't mean to be persnickety, but no it was not. Your (exhaustingly) rigorous definition did not show the fallacy of equivocation at the heart of the question.

If someone is not aware of the fallacies, then they cannot apply the symbolism correctly to begin with. The question deceptively equivocated "animal," and the resultant added information is not something that the symbolism could parse, since the one applying the symbols would not see the equivocation of "animal" any better after giving both "animals" the same letter.

>>15359666
I am sorry, then, for I do not understand what meaning you intend by that equivocation if NOT the existential fallacy already dealt with. Since any equivocation would make itself evident by the consequence of its existential import, e.g. "element exists in these nested sets". If they are all universal, as with barbara, there's no problem from an equivocation as there's no existential import of "some particular" being exclusive to the nested universals.

Also it wasn't really all that rigorous at all, I was trying to keep it as simple and brief as possible to give an idea of how one could approach better understanding what the (horseshit) diagrams are trying to convey and why things don't work one way vs. another.

>>15359424
This shit somehow got me really confused about rigid body dynamics.
If we just have some rod flying around in a plane, the the total kinetic energy should indeed just be [math](M\dot{x}^2 + I\dot{alpha}^2/2[/math] right?
(Where x the position of and I the moment of inertia about the center of mass)
In that case I don't see how my solution (>>15358993) can be different from yours, besides forgetting about the mass and radius.
Stating the angular velocity of a rigid body wrt some reference frame does not really make sense as far as I can tell, though you seem to do that.

>>15359767
[math](M\dot{x}^2 + I\dot{\alpha}^2)/2[/math]

>>15359767
Yeah in fact I distinctly remember programming this simulation using that "decomposition" for the energy, and it seems to capture the energy just fine.

>>15359767
The energy written in >>15359785 is certainly the expression for a rod that is free to move and spin in space, I don't disagree with that. However, when we include the kinetic energy in the Lagrangian as per the original question, we have to bake the constraints (rod touches the disc at only one point, no slipping) into the formula. I don't yet see any contradiction between your and my ideas, save for the simpler formula with [math]\theta[/math] not yet capturing the constrained motion that the formula with [math]\alpha[/math] does.

>>15359843
Cool simulation, what language was this created in?

I have a question regarding error propagation.

I am calculating the density of a cylinder, and so am measuring its mass, diameter, and height. Of course, the volume of a cylinder is [math] V = \pi r^2 [/math] so I need to divide the diameter by 2. My question is, when I perform the error propagation calculations, do I use the value I measured, the diameter, or do I use the value I used, the radius? Its the difference between using [math]\sigma_V = V \sqrt{\left(\frac{\sigma_{diameter}}{diameter} \right)^2+\left(\frac{\sigma_{height}}{height} \right)^2 } [/math] or [math] \sigma_V = V \sqrt{\left(\frac{\sigma_{diameter}}{radius} \right)^2+\left(\frac{\sigma_{height}}{height} \right)^2 } [/math]

Also, I am assuming that we take out anything from uncertainty calculations that don't interact with another variable or are fixed constants, ie [math]\pi[/math] or [math] r^2 [/math]

>>15359930
Oh, I see, yeah I never actually studied Lagrangian mechanics formally, but I remember something about the constraints showing up as partial derivatives or something.
It's... javascript. WebGL seemed easier to wrangle than OpenGL or Vulkan, otherwise I wouldn't touch it.

>>15359994
At least from a mathematical standpoint they are different. If we look at the diameter/radius terms, we have
[math]V^2\left(\frac{\sigma_d^2}{d}\right)^2=\frac{1}{16}\pi^2 d^2h^2\sigma_d^2=\frac{1}{4}\pi^2 r^2h^2\sigma_d^2[/math]

whereas
[math]V^2\left(\frac{\sigma_r^2}{r}\right)^2=\pi^2 r^2h^2\sigma_r^2[/math].

Now, if [math]\sigma_r=\frac{1}{2}\sigma_d[/math], these terms would be equivalent, but this is not probably not the case in your experiment. If you have only one ruler or caliper or whatever, then [math]\sigma_r=\sigma_d[/math], so it actually matters. The difference comes in the magnitude of what you are measuring; measuring the radius to be [math]15.2\pm0.5\text{ cm}[/math] is qualitatively different from measuring the diameter to be [math]30.4\pm0.5\text{ cm}[/math] in that uncertainty is a larger fraction of the former measurement than in the latter. This is reflected in the contribution being quartered when using the diameter. I'm not sure what your last question / statement about "taking things out from uncertainty calculations" is saying.

>>15360000
Checked. Yeah, by writing the energy with constraints, the equations of motion are obtained by calculating [math]\frac{\partial L}{\partial q}[/math] and [math]\frac{\partial L}{\partial \dot{q}}[/math], the partial derivatives of the Lagrangian with respect to generalized coordinates ([math]\alpha[/math] and [math]\dot{\alpha}[/math] in the problem), and automagically satisfy the constraints.

As for numerical simulation and visualization, I haven't delved into it very much as it's not really needed in my line of study. Still something I would like to get into however. Any recommended starting points? Just pick something to sim and roll with it?

>>15360233
Oops.


"Now, if [math]\sigma_r=\frac{1}{2}\sigma_d[/math], these terms would be equivalent, but this is probably not the case in your experiment. If you have only one ruler or caliper or whatever, then [math]\sigma_r=\sigma_d[/math], so it actually matters."

>>15360233
If you don't actually care about ODE methods or things like that, just pick up Octave or Sage or some other framework and go crazy.
If what you're trying to visualize isn't cutting edge math, expect little trouble in return for a lot pretty pictures.
Something I've been enjoying recently are geodesics. I have an Octave script now that finds them on a vanishing set of any reasonably nice function of R3.
Oddly appropriate considering these could just be understood as motion of a particle constrained to a surface!
You can get the general ODE in that case very straightforwardly with computer algebra; https://math.stackexchange.com/questions/111577 gives you the second fundamental form, and Lee's Riemannian Geometry Lemma 8.5 gives the geodesic equation in terms of that.

>>15360248
>>15360233
So Im still a bit confused. should my uncertainty formula be one of the two I posted here>>15359994
or do I need to do something different? I know that my uncertainty is with respect to the diameter, not the radius, so how do I change my error propagation formula accordingly?

bumpt

Why every algebraist in my department is either gay, trans or a woman?

>>15332629
I have a question about AI. If AI is really the great filter, then why have we never made contact with or detected any artificial intelligences?

>>15365185
Don't ask why, just think of the possibilities

>>15354218
fuck off eli

So, i did the exercise with the method on the left, got the correct result but my prof. did it like in the right.
I asked if my way was okay. She said it was wrong and that you had to convert all of the variables of "x" to "u", including the limit statement. I asked why. She said basically the same thing but in different words and said that if i got the right answer but with the wrong method, she'd consider it wrong in the exam.
Why is this method wrong?

My laptop says input is 2.1 amp at 19 volt, but the stock charger that came with it (new) has an output of only 1.58 amp. (Works fine.)

But this goes against what I've read about output amp needing to meet or exceed the appliance's input requirement. Supposedly too low amp can overheat the charger or destroy the appliance.

So what's going on?

>>15365619
She did a change of variable, you did a substitution. Your method is 100% correct but if the question explicitly asked you to use a certain method then yeah you'd lose marks.

Prepare yourself for a retarded question. Why is this matrix not orthogonal? The columns vectors are all orthogonal. Do they need to be normal vectors as well or am I missing something?

>>15365921
They need to be orthonormal, which makes "orthogonal" a bit of an odd name, even if they are alternatively called orthonormal.
Otherwise you won't end up with the key property that the inverse is the transpose

>>15365939
Thank you anon

>>15348049
>~<
≥_≤
°∆°

>>15333895
KOH is corrosive, not a poison. If you've washed your hands with water and they're fine, then they're fine. If you routinely get it on your hands and start damaging your skin, wear gloves and be more careful.

10% KOH tissues dangerous aren't unless you expect the garbage man to literally touch them for some reason. They won't harm the environment. You can flush them down the toilet if you prefer. You don't need to stash them up in a huge pile and dispose of them in one go either.

Trying to make a convolution loop wherein I only use two for loops for any two matrices of any size. I am not allowed to use numpy's convolve function

Why doesn't this code work?

>>15366102
You're supposed to loop over the two arrays so why is the first loop using y? So it's no surprise your code to then generate the values for y[] is also wrong.

why isn't this 1/0 at n =0

>>15366985
0! = 1

>>15367015
math is retarded

>>15367030
(n - 1)! = n! / n
so
2! = 3! / 3 = 6 / 3 = 2
1! = 2! / 2 = 2 / 2 = 1
0! = 1! / 1 = 1 / 1 = 1

maybe it's not math that is retarded.

Guys in stupid. How do I convert watts per meter-kelvin to watts per centimeter-celsius?

>>15367233
I would think its just a matter of dimensional analysis. See pic related. That gets you to watts per centimeter-kelvin at least. Now if you have the numbers you are feeding into this, ie you know the temperature in kelvin, you can just convert that to Celsius by adding 273.15 to it before doing the calculation. If you have only a number that incorporates all the units without multiplying their constituents together, Im actually not sure. I dont think regular unit conversion works with temperature conversions. Its not like "every degree kelvin has 273.15 degrees celsius in it" because its just an offset rather than a multiplier, and honestly I dont know how you would deal with that part off the top of my head.

>>15367233
>>15367284
The offset can be ignored in this case, since the interpretation of thermal conductivity W/m.K isn't "W/m per number of kelvins" but "W/m per temperature difference, measured in kelvins". So all you need to do for that is scale by 9/5 to get temperature difference in Celsius, with the offset cancelling out.

>>15367055
Now do that for [math] (0-1)! [/math]

>>15367030
>>15367055
>>15367320
All of you are retarded, 1 is the identity for multiplication - the definition of 0! = 1 is intuitive

>>15332629
would you bleed out faster if you have high blood pressure?

>Find the constant of motion for a problem with helicoid symmetry: [math]V(\theta-kz)[/math]
I was able to solve similar problems with a given potential, but I feel totally lost now that I've been given a potential as a general function.

>>15368080
I'm supposed to solve it using Noether's theorem btw

>>15367233
Divide by 100. Kelvin and Celcius are the same thing if you're dealing with temperature differences. If you aren't, you have to use Kelvin, because "per °C" doesn't make any sense for something which is proportional to absolute temperature.

>>15367316
>scale by 9/5
Not unless Fahrenheit is involved somehow.

How do I show that in R3 any subset of the xy-plane has measure zero without using contradiction?

What if someone injects rabies into my food?

>>15368102
Jacobi's transformation theorem or just covering it by cubes of arbitrary volume.

164,385,000 - men in the US
4.5% of men are gays/bi
4.5%*164,685,000 = 7,397,235 - number of gays in the US
>https://news.gallup.com/poll/389792/lgbt-identification-ticks-up.aspx
925,800 - men that have HIV
692,200 + 61,800 = 754,000 - number of gays that have HIV
96,300 - hetero men that have HIV
>https://www.cdc.gov/hiv/pdf/library/reports/surveillance/cdc-hiv-surveillance-supplemental-report-vol-26-1.pdf

Now, the following conditional probability

[math] P(\text{guy has HIV}|\text{he is gay}) = \frac{P(\text{guy is gay and has HIV})}{P(\text{he is gay})} = {\frac{754,000}{164,385,000} \over \frac{7,397,325}{164,385,000}} =0.1019 [/math]

also

[math] P(\text{guy has HIV}|\text{he is hetero}) = \frac{96,300}{164,385,000} = 0.0130 [/math]

conversely

[math] P(\text{guy is gay}|\text{he has HIV}) = \frac{P(\text{guy has HIV}|\text{he is gay)} \cdot P(\text{guy is gay)} }{P(\text{guy has HIV)}} = 0.1019 \cdot \frac{7,397,325}{925,800} = 0.8142 [/math]

Does this look correct?

>>15368160
Your second calculation doesn't use #{hetero men} in the denominator.

>>15368160
women can get HIV

>>15368198
Ah yes, makes sense
[math] P = \frac{96,300}{0955 \cdot 164,685,000} = 0.0006 [/math]

>>15368201
Right, but I just used the numbers for men

What is the order of the subgroup of [math]A_5[/math] generated by the two 3-cycles [math](123)[/math] and [math](145)[/math]?

is there any course/book you guys would recommend for self-teaching undergrad level Linear Algebra?
All the courses at my university are really geared towards engineers so it doesn't need to be anything proof heavy or whatever, just concepts and exercises. My advisor is asking me to take a grad level Lin. Algebra course next semester but I never took the undergrad version, so I'd like to familiarize myself with it
again, all geared towards engineers

>>15368736
>engineers
khan academy

>>15368083
Do you know how to use Noether's theorem to show that the z-component of angular momentum is conserved if V is only a function of angle? Do pretty much the exact same thing

New thread, please

Suppose I have a graph G = (V, E) which has a perfect matching and an integer k. How do I prove that showing there is a subset S ⊆ V of k vertices such that every vertex in V - S is connected to some vertex in S is NP-complete? I also don't know what reduction to use.

What is the relation between integrals and bivectors?
My gut keeps telling me there's some cool relation between the two, like effectively taking integrals with simple matrix multiplication, but I can't figure out what