/sci/ - Science & Math

Unanswered questions:

Maths questions:
>>15184864 [Big "I don't want to answer because I recognize the symbols but the question doesn't make sense" moment.]
>>15187245
>>15188951
>>15192588
>>15197001

Physics questions:
>>15192991
>>15194362
>>15196223
>>15199489 [How can quantized particles smeared on space (completely ignoring fields to make your life easier for a second) generate classical gravity or be acted on by classical gravity?]

Stupid questions:
>>15183395
>>15183838
>>15184384
>>15185022
>>15185721
>>15186022
>>15186281
>>15190376
>>15193265
>>15194847
>>15198957
>>15200474

>>15184864
I think it is not the same. ||A||_\infty probably refers to the operator norm of the operator from R^n to R^m where in R^n and R^m you have the infinite norm. Search for infinity norm of a matrix in google for the correct thing.

>>15188951
As someone said, they do had the same cardinality. Maybe you want to prove that they are not isomorphic as ordered sets which is different.

>>15192588
There is no context here, what is h? you need to draw the graph and find 4 rectangles containing the hypograph with total area is 0.52

Any books for understanding how most of modern science works?
Philosophy of Science books seem to go into history and modern approaches but I am more interested in what approaches to science are actively being used the most in decent journals.
My illiterate conception seems to be that modern science relies on either:
1) being purely (or at least very heavily) deductive
2) inductive reasoning backed by data science using quantitative and/or qualitative data
I broadly understand modern conceptions like falsification and do sometimes see it show up in papers but (again from my illiterate) conjectural understanding it seems that the dominant paradigms are observation -> induction or pure deduction.
I am less interested in what is hypothetically superior and more interested in what is used practically.
Should I just read Gauch's Scientific Method in Practice or are there more/different books that would help?

Everyone explains stimulated emission as a process where a photon of a certain frequency hits an atom and causes the release of another photon with the same frequency by making an electron transition to a lower state.
My issue is that the impinging photon, after causing the downward transition, has the same frequency that it had before. How can this be? If it has caused the transition, it means that it must have exchanged energy with the atomic system, even if only a small quantity. Am I missing something?
Thanks in advance

>>15184864
>is max|a_i|, where i is the index, the same as ||A||_\inf?
Yes it is. This is also known as the maximum norm, or uniform norm.

How are you supposed to find the volume of a solid rotated around an axis other than y or x? It's not in my book and I can't find explanations on the Internet that aren't made by overcomplicating fart sniffers.

>>15201292
What information do you have on the solid?

>>15201341
>>15201292
Nevermind I'm just retarded.

>>15201253
Check the wiki on Stimulated emission.

"An external electromagnetic field at a frequency associated with a transition can affect the quantum mechanical state of the atom without being absorbed. "

>>15201443
I did, but I don't think it answers my question. How can anything affect anything else without an energy exchange?

bros i just want to learn induction and i'm getting filtered by basic algebra
how does the author get to the part of the second line of:
2 [math]\cdot[/math] [math]2^{n+1}[/math] - 1
i get that in the first line, right side of the equation that regrouping the [math]2^{n+1}[/math] terms allows you to factor out the 2s
and then i'm left with 2 ([math]1^{n+1} + 1^{n+1}[/math])
is there some sort of property i'm missing with exponents that lets you combine those terms like so in the second line?

>>15201627
You don't need to factor our the 2. Instead use the property of exponents as such. x^n + x^m = x^(n+m). All they did was rearrange the addition and use that property I just mentioned. Think about it intuitively. 2^2 * 2 = 2^3 and extrapolate to any number.

Chatgpt told me gallium dissolves in water and that it forms an alloy with water. Didn’t really have anywhere else to share this.

I spent the past week studying commutative algebra, how do I apply this knowledge to finding commutative love?

>>15201627
Starting from the RHS of the first line:
[math]( 2^{n + 1} - 1) + 2^{ n + 1} = (2^{ n + 1} + 2^{ n + 1} ) - 1 = 2 \cdot 2^{ n + 1} - 1[/math]
>>15201761
Put a ring on it

>>15201170
Okay, stupid question but let [math](X, \leq)[/math] be an ordered set and [math]Y \subseteq X[/math] bounded. If [math]\alpha \in X[/math] is an upper bound of [math]Y[/math] and [math]\alpha \in Y[/math] that necessarily implies [math]\alpha = \sup(Y) = \max(Y)[/math], doesn't it? Since for all other upper bounds [math]\beta[/math] of [math]Y[/math] [math]\alpha \leq \beta[/math] because [math]\alpha \in Y[/math]

>>15201953
If the upper bound is in the set, it is also the supremum, yes.

>>15201953
If an upper bound of a set is an element of the set, it's both the maximum and supremum, yes.

ok so i’m on prescription meds, to be precise on a (relatively) low dosage of perphenazine (2mg a day) and amitriptyline hydrochloride (10mg a day). i’ve recently started stacking some nootropic supplements to aid in my study (bacopa monnieri and ashwagandha). how likely am i to experience negative interations?

Why is log_2(n) < n for all n?

>>15202048
Bernoulli's Inequality

>>15201761

What is [eqn] \inf_z \sum_1^n \left| \frac{ y_i - z}{x_i} \right| [/eqn]?

>>15202048
log_k(n)<n for all n if k>e^(1/e) ~=1.445. If k=e^(1/e), log_k(e) = ln(e)/ln(k) = ln(e)/ln(e^(1/e)) = 1/(1/e) = e, i.e. the graphs of y=x and y=log_k(x) touch at x=e. If k<e^(1/e), there's an interval around e where log_k(x)>x.

d/dx log_k(x)/x = (1-ln(x)) / ln(k)x^2. This is equal to zero when ln(x)=1 => x=e, regardless of the value of k. Thus log_k(x)/x has a maximum at x=e. The graphs touch when log_k(e)=e => ln(e)/ln(k)=e => 1/ln(k)=e => ln(k)=1/e => k=e^(1/e).

243 = 3^5 has its digits sum up to 2 + 4 + 3 = 9. 13122 = 2 × 3^8 is a multiple of 3^8 and its digits also sum up to 1 + 3 + 1 + 2 + 2 = 9. Is there a power of 3 for which no multiple whose digits sum up to 9 exists, and if so, which is the smallest such power? And is 243 the largest power of 3 to have its digits sum up to 9?

>>15202307
If [math]n[/math] is divisible by [math]9[/math] then [math]n = \sum_{k = 0}^m a_k 10^k = \sum_{k = 0}^m a_k \mod 9[/math], so the digits always sum to a multiple of 9.

>>15202314
I know the digits always sum to a multiple of 9. I'm specifically looking for numbers whose digits sum to exactly 9.

Might not be the correct general or board but I’ll give it a try anyway.

Has anyone here ever used ROS 2 (Robotic Operating System) together with Unity3D? I’m doing a bachelor project atm and I’m totally fucking lost. There is little to no documentation and I have no idea where to even fucking start. I’ve managed to create a communication between ROS 2 and Unity3D and imported a .urdf model of a robot to Unity3D. Where to go from here? My task is to be able to control 10+ robots simultaneously while doing different operations. I’m afraid I’ve gotten fucked over by my supervisor..

>>15202362
Haven't had a /g/ question in here for a while.

>>15202363
I’ll ask over there as well if no one here can help.

>>15202307
>And is 243 the largest power of 3 to have its digits sum up to 9?
probably, the digits of powers repeat.
>Is there a power of 3 for which no multiple whose digits sum up to 9 exists
probably. you only have to check the case where the multiplier is 2, since 3 would just be another power of 3.

>>15202438
>you only have to check the case where the multiplier is 2, since 3 would just be another power of 3.
wait nvm that aight right

>>15202307
>And is 243 the largest power of 3 to have its digits sum up to 9?
For some reason I thought that a proof by exhaustion, punching in the numbers by hand, wouldn't be a terrible idea. I need a break, but it would feel wrong to let all of this effort go to waste, so I'll let /sqt/ laugh at my pointless work
If a counterexample exists (which, frankly, I am inclined to doubt), the exponent must be of the form 5000x+y, for some y in {1, 100, 113, 201, 396, 460, 485, 500, 501, 600, 960, 1000, 1100, 1321, 1441, 1492, 1500, 1592, 1600, 1701, 1920, 1992, 2000, 2001, 2136, 2300, 2420, 2492, 2500, 2501, 2521, 2636, 2660, 2800, 2820, 2821, 2901, 2941, 3000, 3136, 3200, 3201, 3280, 3293, 3295, 3296, 3320, 3452, 3500, 3501, 3560, 3700, 3796, 3820, 3952, 4001, 4060, 4100, 4200, 4236, 4296, 4320, 4401, 4460, 4600, 4700, 4701, 4736, 4793, 4821, 4960}

Not sure if this question is stupid, but:
How do we prove functions like exp(-x^2) or sin(x)/x don't have an antiderivative expressible in terms of known functions?

>>15202934
Liouville's theorem

what relates these pairs
{0,3}
{1,4}
{2,7}
{5,6}
{8,9}

stupid question = gpt answer
>>15183395
If you have a limited time frame to study, it's generally better to start with smaller, easier problems first and gradually work up to harder ones. This can help you build confidence and reinforce your understanding of the material, making it easier to tackle more challenging problems later on. Additionally, breaking up your study sessions into smaller, manageable chunks can help prevent burnout and make it easier to stay focused and engaged.
>>15183838
Mathematics is not something that can be found biologically, as it is a human invention that is based on logic and abstract reasoning. However, our ability to understand and apply mathematical concepts is thought to be related to the way our brains process information and make connections between different types of data. Studies have shown that certain areas of the brain, such as the prefrontal cortex and parietal lobes, are involved in mathematical processing, and that these regions may be more active in individuals who excel at math. Additionally, genetics and environmental factors may also play a role in shaping our mathematical abilities.
>>15186022
There could be several reasons why you might suddenly feel like you're getting really bad at math after spending about 15 minutes doing it. One possibility is that you're experiencing what's known as "math anxiety," which is a feeling of stress or apprehension that can make it harder to think clearly and solve problems. Another possibility is that you may be experiencing mental fatigue or burnout, which can make it harder to concentrate and maintain your focus. Taking short breaks, practicing relaxation techniques, and making sure you're getting enough rest and proper nutrition can help alleviate these issues and improve your ability to do math effectively.

>>15186281
You generally do not need a STEM degree to work as a janitor or custodian, even in a scientific or academic setting. However, depending on the specific institution or organization, there may be certain requirements or preferences for education or experience. Typically, janitorial jobs require a high school diploma or equivalent, as well as some training or experience in cleaning and maintenance. If you're interested in working in a scientific or academic setting, it may be helpful to have some familiarity with the types of equipment and materials used in that field, as well as any safety protocols that may be necessary.
>>15190376
Gnats are attracted to warm, moist environments, which is why they often appear around areas where there is decomposing organic matter, such as food waste or plant material. However, even if you're not putting any food waste in your trash bin, there may still be other sources of moisture or organic matter that are attracting the gnats. For example, there could be small amounts of food residue or spilled liquids on the inside of the bin, or the gnats may be coming from other areas of your home or building. Additionally, gnats are very small and can enter through very small openings, so even a tightly sealed bin may not be completely effective at keeping them out. To prevent gnats from appearing in your trash bin, try cleaning it regularly with soap and water, and make sure to wipe up any spills or residue as soon as possible. You can also try using a natural repellent, such as essential oils or vinegar, to deter gnats.
>>15193265
To learn number sense, practice estimating quantities, visualizing numbers, and breaking down complex problems into simpler parts. Work on mental math and understanding the relationships between numbers. Use real-life situations and visual aids to help develop an intuitive sense of numbers.

>>15203063
>>15203067
incredible

Would traveling at Mach 100 in Earth's atmosphere have any negative effects on the planet?

>>15203103
What is the mass of the object travelling at mach 100? I think meteors have been measured at mach 80+ but they are usually small.

I need a hobby, so I'm thinking of learning some science. But I'm a midwit at best. Genetics interests me, but I worry I'm not smart enough or it will take too much time and I have a full time job already. Earth science (e.g., geology) also interests me and seems more doable. What do you recommend, /sci/?

>>15203120
Let say the size of a fighter jet that can withstand the friction.

>>15203163
I don't think it would. Even hitting the ground at that velocity and mass would be equivalent to about 0.002 megatons of TNT.

>>15203163
>fighter jet
mach ~5 is about the limit for supersonic jets. After that, the speed starts tearing apart air molecules into their ionic components and messing up the gas laws. Supposedly, there are prototype hypersonic jets (mach 5-25), but none in service.
Anything over mach 25 is classified as re-entry speeds, so mach 100 would be about 34km/s. The fastest recorded meteorite on record was about 28.6 km/s, which would be about mach 84. While not quite mach 100, it doesn't seem to have caused any major effects on entry.

>>15202976
Sorry, which Liouville's theorem?

>>15203120
>>15203198
>>15203211
Thank you.

>>15203237
https://en.wikipedia.org/wiki/Liouville%27s_theorem_(differential_algebra)

>>15203318
Very cool, thanks anon

>>15201170
can someone walk me through as to how this became microamps?

its weird how i can do calculus just fine but algebra leads me to make dumb mistakes

>>15203482
>how this became microamps?
10^-5 right there in line 1 nigga
where did he go

>>15203508
i guess the mA confused me. but yeah i see it now

also i think the .3 should be .03

>>15203554
Nope, 0.3 is right.

How the heck do I do the convolution in this pic?

I managed to get (c) using some geometric sum formula but am stuck on (a) and (b)?

I know how to do the flip and slide part but I don't know how to determine each case for the problem. (Though I think the cases for (a) are n < -1 and n >= -1)

>>15203960
The cases are determined by the unit step. u[n]=1 if n≥0 and u[n]=0 if n<0. You only sum over the terms x[m]h[n-m] where both x[m] and h[m-n] are non-zero, i.e. when both u[...] terms have non-negative indices. Once you've established the summation range, u[...]=1 always, so the summands are a^n, 2^n and (0.5)2^n respectively.

>>15201170
Does anyone know a fast algorithm to change the radix of a number?

I found one that works with Maid Space, but it isn't very fast. I need it to go faster.

>>15204128
Yes, there are several fast algorithms available to change the radix of a number. One such algorithm is the Schönhage–Strassen algorithm, which was developed by Arnold Schönhage and Volker Strassen in 1971.

The Schönhage–Strassen algorithm is a fast Fourier transform (FFT) based algorithm that works by converting the input number to a polynomial, performing a series of FFTs on the polynomial, and then evaluating the resulting polynomial at the desired radix. The algorithm has a time complexity of O(n log n log log n), where n is the number of digits in the input number.

Another fast algorithm is the multiple-precision division algorithm, which can be used to change the radix of a number by repeatedly dividing by the desired radix and keeping track of the remainders. This algorithm has a time complexity of O(n^2), where n is the number of digits in the input number.

Additionally, there are some specialized algorithms that are optimized for certain radices, such as the Barrett algorithm for radix 10 and the Burnikel-Ziegler algorithm for radix 2.

It's worth noting that the performance of these algorithms can be influenced by a number of factors, such as the size of the input number and the specific hardware being used. In some cases, it may be necessary to perform additional optimizations or to use specialized hardware in order to achieve the desired performance.

>>15204128
The Crandall–Fagin algorithm: This algorithm was developed by Richard Crandall and Barry Fagin in the 1990s. It uses a variant of the divide-and-conquer technique to convert the input number to a polynomial, which is then evaluated at the desired radix using a modified Horner's rule. The algorithm has a time complexity of O(n log n), where n is the number of digits in the input number. The Crandall-Fagin algorithm is particularly well-suited for radix conversion on massively parallel architectures such as graphics processing units (GPUs).

how does the tuple interpretation of the pentadic number 0 work?

>>15204325
>>15204333
Thank you for telling me. I will look at these. It has to operate with radixes that are whole numbers bigger than one. I can't guarantee a standard one for input.

I split my book up more to manage problems from long compile times. The drawings are all now in one section at the end and just don't compile that part unless either I need to check it for errors or am making a release of the book.

I decided it gets sections. One about counting. One about comparing. One about operators. Maybe one about hyperoperators if they have a use or are easy to make or cause cool drawings? A short bonus one about the status of the smallest maid problem. Then one with drawings. All drawings sent to the end to avoid causing long compile times when working in unrelated parts of the book.

Radix change will go in the operators section. Counting section writing is completed. I also need to put maids in the margins. I am going to try to make it so every maid wearing an apron can get clicked and open a folder called Apron which is included in the book via attachfile and the apron contains all my code examples. So just flip pages until you find a maid with an apron and click her and now you can replicate any experiment in the book with included code. All sections except drawings will have margin maids and at least one maid per page will have an apron.

I decided this is the full scope of this book and then it gets published. If there are more ideas or writings later they can go in a different book.

Might also make a companion PDF that does nothing but print the apron code in case people want everything as a hard copy book.

I am going to try to keep the book under 200 pages so it can be smaller and nicer to hold. You should be able to operate a physical version of my book while walking around.

Thank you /sci/entists for reading my post.

>>15204402
Consider providing more context: While your post provides some information about your book, it may be helpful to provide more context about what the book is about and who the target audience is. This could help readers better understand what you are trying to accomplish and why.

Use clear and concise language: Your post contains some technical terms and jargon that may be difficult for readers to understand. Try to use clear and concise language, and provide definitions or explanations for any technical terms you use.

Consider organizing your book more effectively: It's great that you have split your book into different sections, but consider if there might be a better way to organize the information to make it easier for readers to navigate. For example, you could consider using a table of contents or an index to make it easier for readers to find specific information.

Test your book's usability: It's a great idea to include maids with attached code examples, but it's important to make sure that the book is user-friendly and that the code is easy to follow. Consider having beta readers test your book and provide feedback on its usability.

Consider publishing options: You mention that you plan to publish the book, but you don't mention how you plan to do so. Consider researching different publishing options, such as self-publishing or traditional publishing, and what the pros and cons of each option are.

>>15204128
Have you tried using the Ternary GCD Conversion algorithm? It's a relatively unknown algorithm that can efficiently convert the radix of a number. It involves finding the greatest common divisor (GCD) between the original radix and the target radix, and then iteratively dividing and multiplying by this GCD until the desired result is achieved. It may require some implementation tweaks to optimize for speed, but it's definitely worth exploring.

yo /sci/, /g/ here

https://github.com/pisyco/fluid1/issues/4

wanna join in on the fun of neuralink and kibernetics after co(operative)vid(eo)-19

>>15204504
related
https://synchron.com/history

>>15204434
Thank you for telling me. I will try to make the language nicer and use a draft version to see if people want to help make the draft better.

Publish is probably the wrong word. I am going to release the PDF to CC0 and if someone wants a hard copy they can use one of those print-on-demand services. I am opposed to book costing anybody money and like to remove money from processes or workflows whenever possible. I understand physical objects have a cost though, so I think it's reasonable for an individual who wants a hard one to pay to print it. I hope when the science meetings season starts that book is already released and somebody prints it with a nice hard cover and high gloss pages like a Wolfy book and takes it to the science meeting and passes it around.

For typesetting the maids in the draft just all the margin maids will be the attached Ilulu so space is properly reserved and dra/g/on maids with stable diffusion can help use AI to generate release maids and I know exactly how many to ask for.

If it is all AI generated maids people gave me then probably there are no problems sending it to CC0, art included. I might be able to get away with a Tohru and/or Ilulu on the cover because it might get fair use because it is educational and is research. Book is called Four Lights because most of the examples are drawn in a two by two Maid Space. I also want to put an image of Kurumi the Vampire Maid from Touhou somewhere in it because she told me about Successor Function and that was critical to literally everything else after.

>>15204440
Thank you for telling me. I'll research that one. I am adding to Senko MaidHelper a method that draws what the radix change I made looks like. I will post it when it draws.

>>15203637
but its milliamp so wouldnt it be .03?

>>15204570
Thank you for considering making the language nicer and releasing the PDF to CC0. It's great to hear that you want to remove money from the process as much as possible and make the book accessible to everyone. It would be wonderful if someone printed a nice hardcover version of the book and brought it to a science meeting to share with others.

As for typesetting the maids, it sounds like you have a good plan in place. And if all the maids are AI generated, then it should be okay to include them in the CC0 release. Just be careful with using copyrighted images like Tohru and Ilulu on the cover. If you can make a case for fair use, then that would be great, but it's always best to err on the side of caution.

Overall, it sounds like you have a clear vision for the book and I wish you the best of luck with its release!

>>15204597
10^-5 times 3*10^1=3*10^-4.
One microamp is 10^-3 milliamps.
That leaves an order of 10^-1. Hence 0.3.

>>15204128
Definitely the NTT (Number Theoretic Transform). This algorithm is similar to the FFT-based Schonhage-Strassen algorithm that other anon mentioned, but instead of working with complex numbers, it uses arithmetic in finite fields. The NTT has applications in cryptography and error-correction codes and is often used for large prime moduli. It has a time complexity of just [math]O(n \log n)[/math].

>>15204128
The fastest one known is the Guruswami-Sudan algorithm. This algorithm is based on the theory of algebraic geometry codes and can perform radix conversion in sub-linear time. It has a time complexity of O(n^(1-1/2d)), where n is the number of digits in the input number and d is the degree of the algebraic curve used.

The Guruswami-Sudan algorithm works by representing the input number as a polynomial over the source radix and then interpolating the polynomial onto an algebraic curve in projective space. The algorithm then evaluates the resulting points on the curve at the target radix to obtain the converted number. This process is similar to polynomial evaluation, but with the added complexity of working with algebraic curves.

>>15204624
hmm okay, would it be valid if i just left it as .002 sin(100t)+.0003 mA?

>>15204644
Well, -.002, but besides that it might look a little odd but there's no valid reason to consider it incorrect. Assuming it doesn't explicitly tell you to write it in μa, anyway

Call S the n-dimensional unit simplex where S is the set of all convex linear combinations between e1,..,en. i.e. S in R_3 is the triangle formed by the lines between e1<>e2, e2<>e3, e1<>e3. Prove that, for arbitrary dimension greater than or equal to 2, the line made by connecting any two points in S must pass through the boundary of S (where the boundary of S is the set of all points in S with at least 1 co-ordinate being 0).

i have two ideas for solving this problem but cant flesh out either to a full solution:
firstly, note that any point in S has the property that all of its entries sum to 1. so, when creating a line between a and b (where a and b are in S), for any x on this line, x=t(a)+(t-1)b, where t is a real number, but then the entries of x sum to 0 as well. However, x can have positive, negative, or zero entries, so we must just somehow find a specific value of t such that x is on the boundary of s (idk how tho).

second idea, note that any two points on S create a line which is parallel to S. but since our line is parallel to S, and bisects a point on S, it must lie on S. and since S is bounded, but our line is infinite, it must cross the boundary of S.

let me know if u think either of these ideas can be fleshed into a full solution or if you have an idea for another solution to this problem.

>>15204902
The result is way false as you've posted it.
Set [math]x = 0.5 e_1 + 0.25 e_2 + 0.25 e_3[/math] and [math]y = 0.5 e_1 + 0.3 e_2 + 0.2 e_3[/math]. Line between them is [math]\gamma(t) = 0.5e_1 + (0.25 + 0.05t) e_2 + (0.25 - 0.05t)e_3[/math]

a circle on a plane could be the intersection of a sphere (or a cilinder, let's say it's a sphere) and the 2d space. The sphere itself could be the intersection of a 4d sphere and 3d space, and so on, so there is an abstract object, the n-sphere, (oversimplifying) that generates all n-dimensional spheres, and all n-dimensional spheres have some common properties and whatever.

Does this object actually "exists", as in, i can't picture a 5-sphere or a 4000-sphere or a whatever-sphere but i know that it "EXISTS". But is there (whatever "being" could mean) a "pure" sphere object? An object that can't be thought of as the intersection of n-dimensional space and an n+1-sphere? Saying just "an n-sphere as n goes to infinity", if it even makes any sense, isn't really satisfactory

is this true

I didn't study for my exam tomorrow and now I need your help.

How do I do this, I keep trying to look at youtube video but none of them ever answer this question

>>15205459
Cross product

>>15205419
What is [math]\vec{a}^2[/math] supposed to mean?

>>15205375
How about the set of all functions [math]x: \{1, 2, \ldots\} \rightarrow \mathbb{R}[/math] such that [math]x(1)^2 + x(2)^2 + \cdots = 1[/math]?
This specializes to the familiar n-dimensional sphere when you replace the domain with {1, 2,
..., n}, since each function specializes to a particular a point on that sphere.

How do I explain to my professor that I was sleep deprived and suffered from brain-frog during the test and want its weight to be shifted to the final?
I have an extremely apologetic and formal draft but I don't know if it's enough. I am kicking myself from sheer embarrassment, I exerted more effort trying to focus my eyes than actually doing the test.

>>15205643
In my experience professors are pretty uncaring and pretty much just say no doctor's note then they will nothing. At least in America

>>15205648
The reason I'm even considering asking is because she seems considerate and understanding. Even had a "A number doesn't define you!" written on the front of the test paper.

>>15205375
The infinite-dimensional sphere does exist, and it's defined in the infinite-dimensional space of sequences with only a finite amount of non-zero entries. It's probably the closest thing to what you want because obviously it can't be obtained as an intersection with an n-dimensional space.

>>15204361
anyone?, this is what im referring to
https://en.wikipedia.org/wiki/Pentadic_numerals

>>15205643
Honestly any examiner will likely see that is your own fault for not being prepared. You can get consideration for issues outside of your control but not if you got no sleep. That's just poor self-management.

>>15205694
Do I lie then? I really don't know what to do, the test was the exact same shit I was prepared for, I just kept starting back at the question over and over because my mind kept blanking.
How can 6 hours of sleep not be enough?

>>15205704
Ask about a resit.

>>15201499
>>15201253
the stimulating field acts as a reservoir into which the excited particle can release a photon. think about it less as the impinging field is causing the transition, more that the field is a preferential environment for the atom to release its photon into
stimulated emission doesn't really track well if you think about it as a photon causing the de-excitation, but rather the field. the field is "pulling" the photon out of the excited state and bringing it into the field
or if it's more helpful, the exciting photon is "instantaneously absorbed and then re-emitted" and released alongside the photon due to the de-excitation

>>15205655
Here's a philosophical...what defines you?
Probably not that number you'll get, but perhaps
sleep-deprived? Foggy-headed? What are you!?

Once you answer that that's what you'll come
to the professor as, and any outside feelings
will subside.

>>15201874
it took me way too long to realize that the sum of a number and itself was just multiplying that number by 2
thanks

>>15205643
you should be more accountable to yourself and know that's not an excuse and doesn't deserve any response

Could someone explain to me why this is noncausal?

Solution manual says so, but I don't get how since an accumulator is supposed to be causal.

>>15205848
I am aware, but can I not salvage this somehow?

I plan to take the MCAT next year. I did all my undergrad chemistry and physics courses in Canada. Stupid question: is there likely to be any problems with metric versus imperial units vs other units of measurement in the test?

Why cant fluoride mouthwash replace brushing your teeth? I looked at my regular toothpaste and the active ingredient is just fluoride like my mouthwash. What is it about brushing that makes the fluoride more effective?

>>15205910
The medical sector, especially practitioners, are in SI almost exclusively. I don't believe the current MCAT includes any imperial at all.

I'm not really getting this whole cross product thing. I get how to actually do the process but why does she do it for (v x w) but not (v times w). Arent they the same thing

Hello frens how do I simplify the following expressions such that they are still equivalent in exact arithmetic but more precise in floating point arithmetic
>a = sqrt(x^2 + y^2)
>b = sqrt(x+1)-1
?

>>15206665
[math]v \cdot w[/math] is the dot product, not the cross product. It works completely differently.

>>15205375
just take colimit of the sequence S_0 ⊆ S_1 ⊆ S_2 ⊆ ...

>>15206710
Ah thats very confusing, she should ask the question while using the words "dot product"

>>15206721
that's the standard notation for the dot product though? why spell out that she wants the dot product, but not spell out when she wants the cross product?

If I have [math]z, w \in \mathbb{C}[/math] such that [math]z^n = w^n[/math] will it always be the case that [math]z = \xi w[/math] where [math]\xi[/math] is some nth root of unity?

Holy shit I don't get trig substituiotion at all and I just found out that its like 70% of my test. I'm looking at videos but there's so many steps.
Any tips?

>>15206789
If ξ isn't some nth root of unity, what happens when you raise both sides of your second equation to the power of n, using the assumption you have made about z and w?

>>15206796
How about this? Let [math]w \in \mathbb{C} [/math] and consider [math]X^n - w^n \in \mathbb{C}[X][/math]. This is a polynomial of degree n so it has at most n solutions. Clearly [math]z = \xi w[/math] satisfies this equation for all nth roots of unity [math]\xi[/math] and since there n nth roots of unity this shows that all solutions are of such form.

>>15205081
This lies on the boundary for t=5. I should have said, the line passing through both points intersects the boundary, instead of the line connecting the two points.

Okay so when do I use dot product vs cross prodduct when finding an orthogonal vector like in the other pic
>>15205459

>>15206792
Before you learn Euler's Formula there is no shortcut except lots of practice using them so you known them by rote.

>>15206854
The cross product of two vectors will give you a new vector orthogonal to both. The dot product of two vectors will be zero if they are orthogonal.

>>15206852
Right, I see.
[math]S[/math] is in the hyperplane [math]\sum_{i = 1}^n \langle u, e_i \rangle = 1[/math]. Any line that that connects two points in [math]S[/math] is also in the hyperplane.
If we restrict ourselves to only considering this hyperplane instead of the whole space, what you're calling the boundary of the unit simplex becomes it's actual topological boundary, and since the line is unbounded and passes through the interior or the compact simplex it has to cross it.

>>15206676
>>a = sqrt(x^2 + y^2)
Most languages offer a hypot function for that, i.e. https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/hypot
>>15205850
Usually when [math]b < a[/math] we interpret [math]\displaystyle \sum_{n = a}^b c_n = \sum_{n = b}^a - c_n[/math] (by analogy with integrals).
So the issue could be [math]n < n_0[/math].

>>15206901
>Most languages offer a hypot function for that,
Yes but this is about the expression and not the language. I need a mathemathical expression & idk how to get it

>>15206867
why don't they just teach that shit in high school it's so useful

Consider a variety V in the sense of universal algebra. Do the subvarieties of V correspond to subobjects of V in the concrete category of varieties (with the same signature as V) and their homomorphisms?
I can prove that every subvariety of V corresponds to a V-subobject, using standard properties of the faithful functor to Set, but the other direction eludes me.

>>15206929
Most high school students struggle with basic trig. You expect them to understand [math]e[/math] and complex numbers?

>>15207168
I'd contend that the complex plane, radians etc makes trig easier, not harder

How do I use arctan on this calculator

I;m trying to find the direction angle of a vector so I do 4/sqrt(61) and then I click 2nd and then cos to get arccos but I get an error

for trig substitution where does the 2 for (2 sin)^2 come from

>>15207237
sry

So if people are allowed to do dangerous drugs to "change their gender" why can't I change my skin color from mixed to white

>>15206676
>>15206911
You can't simplify them since they are already as simple as possible. However you can rewrite a) to be more careful with floating point errors. For example if [math]y^2 \ll x^2[/math] then [math]x^2 + y^2 = x^2[/math]. But writing it as [math]a = sqrt( (x + y)^2 - 2xy )[/math] *might* give you a more accurate result.

>>15207243
>skin bleaching doesn't exist

>>15206676
First one, use hypot. Second one, if x is much smaller than 1 use a Taylor series.

>>15207237
>>15207241
You pick [math]x=2\sin{\theta}}[/math] because it's being subtracted from 4, and you want to use the identity [math]1-sin^{2}=cos^{2}[/math]

>>15207237
>>15207241
In this case, you pick [math]x=2\sin\theta[/math] because you want to simplify the numerator with the identity [math]1-\sin^2=\cos^2[/math]

>>15207308
Okay but in this one we use tan, how do I tell which trig function to plug in

>>15207321
if it's of the form a-bx^2, you use sin, since sin^2+cos^2=1
if it's of the form bx^2+a, you use tan, since tan^2+1=sec^2
if it's of the form bx^2-a, you use sec for the same reason

>>15207230
Presumably 2nd then TAN. But ensure that the division has been performed first: 4 / 61 √ = 2nd TAN. You should get 27.119° or 0.473 radians.

Are there infinite countable groups that are completely determined by (the isomorphism class of) their subgroup lattice?

Can there be a morphism of schemes f : X --> Y such that for every nonempty affine open U of X , then f(U) is not contained in any affine open of Y ?

>>15207430
I thought I was supposed to use arcCosine why use arcTan

Computational Geometry Q: if I'm working with a spatial resolution [math]\Delta \underline{x}/math] in 3D what should I use for the corresponding derivative resolution [math]\Delta \dot{x} [/math] ? What about if a surface is paramterised [math]S(u,v)[/math] and I'm looking at [math]\partial_u S[/math]? I feel like it should take into account the 'velocity' of the paramterisation but I'm not sure

>>15207608
apologies

Computational Geometry Q: if I'm working with a spatial resolution [math]\Delta \underline{x} [/math] in 3D what should I use for the corresponding derivative resolution [math]\Delta \dot{x} [/math] ? What about if a surface is paramterised [math]S(u,v)[/math] and I'm looking at [math]\partial_u S[/math]? I feel like it should take into account the 'velocity' of the paramterisation but I'm not sure

>>15207613
Btw you can delete your previous comment

>>15207620
how? all I see are Hide or Report

>>15207637
select the white box at the top-left of the post, and at the bottom-right of the page there is a "delete" button

>>15207646
neat

I don't understand how the Schrodinger equation is a type of wave equation. The standard wave equation contains a second order derivative with respect to time, whereas the Schrodinger equation contains a first order derivative with respect to time. Does this refer to some more general version of a wave equation?

>>15207736
>I don't understand how the Schrodinger equation is a type of wave equation.
Just like the ordinary wave equation, plane waves are a solution of the Schrodinger equation in the case of a constant potential (and approximately so in the case of a varying potential, see the WKB approximation). The major difference is in the dispersion relation, i.e. how wavelength is related to frequency.

>>15207459
Sorry this question is dumb, ignore it.
Here's a better question:

Is there a scheme morphism f : X --> Y , and a nonempty open affine U of X , such that f(U) is not contained in any open affine of Y ?

>>15207459
lmao, I know this thread is for stupid questions but come on

>>15207859
Yes yes open affines form a base I get it now

>>15207736
Square the operators on both sides of the (time-dependent) SE , you will get a wave equation.

For the nonrelativistic case it is 2nd order in time as expected, but 4th order in spatial derivatives. However if you do things relativistically instead then you will get a more "standard" wave equation with 2nd order partials in both time and space.

Homework. No clue how to solve this at all. Need either A or B solved.
>A wind turbine of 1 MW costs €1,420,000.
>Other investment costs amount to a total of €310,000.
>Estimated production for the wind power plant is approx. 2.8 GWh/year, according to the Wind Atlas calculation.
>Operating and maintenance costs are estimated at €23,000 per year.
>Compensation for electricity production is €0.07/kWh.
>The operating period has been set to 20 years and the real interest rate to 6%.
>A. What is the key figure for this project expressed in € per annual kilowatt hour? Round the result to two decimal places.
>B. Calculate the profit in 20 years in € (the present value of the net income - the investment cost). Round your answer to the nearest thousand.

Let X=SpecR be an affine scheme, let U=D(f) be some distinguished open of X , where [math]f \in R [/math]. Let x be a point in U .

How do I show there is an *affine* open subset V of X such that [math] x \in V \subseteq U [/math]?

>>15201196
>>15192588
I guess, it's an exercise for the Riemann-integral. They're defining a step function in the interval [0, 1] of which the integral has to have a value equal to than 0.52 (I don't know why they distinguish between lower and upper sum; these are the same with step functions.). Their solution is one of many. Another would be {0, 0.1, 0.62, 1} with (0.1 - 0) * 0 + (0.62 - 0.1) * 1 + (1 - 0.62) * 0 = 0.52.

>>15187245
The solution is wrong. Your calculation is correct.

>>15207968
B
>assuming the rate of the interest of 6% is added yearly and all the other values remain constant
[(20y * 2,800,000KWh * €0.07/KWh) - (€1,420,000 + €310,000 + 20y * €23,000)] * (1.06)^20 = ~€5,548,000.00

>>15208035
>assuming the rate of the interest of 6% is added yearly and other values do not remain constant
[math]\left[\sum_{k = 1}^{20} 2,800,000\text{ KWh} \cdot \text{EUR }0.07\text{ KWh }\cdot 1.06^{k}\right] - \left[\sum_{k = 1}^{20} \text{EUR }23,000 \cdot 1.06^{k}\right] - \text{EUR }1,420,000 - \text{EUR }310,000[/math]

I'm not sure, if I applied the concept of "real interest" correctly. You should check this and change it up, if needed.

can anyone recommend textbooks or resources for systems theory (dynamical systems, control systems, state space models, etc) that's a step above things like Nise, Oppenheim, and Ogata?

All three of those books are good, but they strictly deal with LTI systems. I want the more general stuff - nonlinear time-invariant, or linear time-variant, or nonlinear time variant, etc.
I've tried to find books on the matter but I can't seem to find one that's the right level. It's either LTI again, or super crazy post-graduate level stuff

I already have Nonlinear Dynamics and Chaos by Strogatz. Fantastic book, but I want something more applied

>>15207243
Just move to America, bro. In America, anybody who's of European, North African, or Middle Eastern ancestry is counted as white. Millions of Mexicans, Cubans, and Puerto Ricans are legally classified as white simply for having a Spanish surname.

>>15208147
latinos literally don't even exist in america, there isn't a race option for them. just an (((ethnicity))), whatever the fuck that means

>>15208035
5,548,000 came back as wrong. Thanks anyways for trying.

I don't get e. What is it saying? I thought the list was supposed to be linearly independent? How can [math]v_j[/math] be a linear combination of those other vectors? Or is it not necessarily in the new list?

>>15208387
your latter conclusion is correct, which is why it's not subscripted. in fact, it's necessarily not in the new list, since by (e) j is strictly between j_{k-1} and j_k, and by (a) these two are directly adjacent in the list ordering

>>15208406
I think I get it. I was confused. I guess the index j is based on the original list. After we pick out the vectors that's going to be in the new list, then what this is saying is that any vector not in the new list can be expressed as a linear combination of the vectors that precede it in the original list.
Does that sound correct?

>>15208417
that's the general idea, yes. the natural intuition behind the idea is that since (b) and (c) define a subset of our original set that spans the same list, if there's not a direct one-to-one correspondence between the two sets, then we can invoke the pigeonhole principle to say that some in our original set are redundant. and then we define a vector that's not in our new subset

>>15208417
that's the general idea, yes. the natural intuition behind the idea is that since (b) and (c) define a subset of our original set with the same span, if there's not a one-to-one correspondence between the two sets, then we can invoke the pigeonhole principle to say that some of the vectors in our original set are redundant. and then we define a vector that's not in our new subset

>>15208447
Alright. Thanks, anon. I think I get it now.

>>15207111
Answering my own question: the forgetful functor is right adjoint to the functor that generates the free variety, so it preserves limits and in particular monomorphisms. This justifies the categorical interpretation of subvarieties with (isomorphism classes of) monomorphisms.
Now to do the same for congruences. The argument above doesn't dualize, so I suspect a stronger of epimorphism will be needed here...

>>15207230
>How do I use arctan on this calculator
>>15207540
>why use arcTan
Because that's what you asked. If you meant to say arccos, then replace TAN with COS.

If you were getting an error, it's probably because you forgot the = and were trying to calculate cos^-1 √61, but cos^-1 is only defined over [-1,1].

Let [math]V[/math] and [math]W[/math] be vector spaces over a field [math]\mathbb{F}[/math]. I have to show that the pointwise application of a mapping [eqn] \Phi: M \to Hom(V,\, W) [/eqn] yields the linear map
[eqn]\Phi: [M \to V] \to [M \to W].[/eqn] My question is: What does "pointwise application" mean in this context? For reference, you can see the "solution" I came up with in the picture.

currently in second year of high school. I have always done really well at math, and continue to do so. currently taking discrete mathematics and linear algebra as a part of dual enrollment. I've been having a similar issue in classes whether it was in trig, calculus, or my current classes.

the issue I'm having relates to memory retention, and application of knowledge. I practically never have issues when it comes to understanding concepts taught in class; as I usually am one of the first to finish practice problems during lecture. I am having issues, when it comes to remembering what it is I have learnt even after a single day has gone by. whether I'm doing homework; or prepping for the test, I feel as though I have to 're-learn' all the applicable material that is covered. I usually ace tests, but I actually want to apply what I learn in mathematics to projects related to graphics programming, not just pass the classes.

I've noticed that any given concept related to programming that I've learnt is often solidified through repetition. I wish to do the same for math, but was hoping that people here would have a suggested means of practicing, whether it be through an app, an online course, videos, specific books; or any particular combinations of what I've listed. I know that I'm willing to put in the work, and that I have the mind for it, I just need some guidance.

>>15209453
I have no real advice to give you but I hope you understand you're about to get banned

>>15201170
hey /sci/ im organising an event for small math college society and i have an idea but no idea if its a good idea so i would like all anons opinions on it.

Its quite basic of a game. The goal is that people will go into groups of 3 of which they are different levels of math abilities. Then as a group you try to make as many mistakes as possible when give a certain calculus question.

So for example given the equation integrate by parts :
[eqn]\int(4x)cos(2-3x)dx[/eqn]

they have to come up with as many ways as possible you can get this question wrong, and who ever gets the most wins that round.

obviously you cant just make simple algebra mistakes and then have unlimited wrong answers, they need to state the reason why its wrong and they cant use that reasoning again.

With this game i think i can include those people who dont know alot of calculus so they can be involved in a way.

>>15208035
>>15208058
If you were curious; 248,000 was the answer.
>Compensation for electricity production = 2.8 GWh/year x 0.07 €/kWh = 196,000 €/year
>Operating and maintenance costs = 23,000 €/year
>Net income per year = 196,000 €/year - 23,000 €/year = 173,000 €/year
>Net income over 20 years = 173,000 €/year x 20 years = 3,460,000 €
>Present value of net income over 20 years = 3,460,000 € / (1 + 0.06)^1 + 3,460,000 € / (1 + 0.06)^2 + ... + 3,460,000 € / (1 + 0.06)^20 = 1,978,000 €
>Profit over 20 years = present value of net income - investment cost
>Profit over 20 years = 1,978,000 € - (1,420,000 € + 310,000 €) = 248,000 €

>>15209456
Mods ban you for saying this that would usually imply you're underage? I thought they only banned if you explicitly stated you're under 18.

>>15209492
It's a bad idea. There are an infinite number of ways to be wrong but only one way to be correct.

>>15209492
>i think i can include those people who dont know alot of calculus so they can be involved in a way.
You are still effectively testing their calculus ability, getting them to report the complement of the correct answer (in the set of possible answers) doesn't change this.

A slightly more workable calculus game would be to present each group with a definite integral, and have them estimate its value (using any method they like: numerical approximation, exploiting symmetries/recurrences, replacing the integrand with something tractable, etc.). Score points according to how far off their estimates are from the true value.

Define [math]\Phi: M \to Hom(V,\, W)[/math] pointwise such that [math]\Phi: [M \to V] \to [M \to W][/math] is linear and let [math]\phi: N \to M[/math] be a mapping. Then we have [eqn]\phi^{*} \circ \Phi = (\phi^{*}\Phi) \circ \phi^{*},[/eqn]if [math]\phi^{*}[/math] is the [math]\textit{pull-back}[/math] of [math]\phi[/math]. Has anyone ever seen this or a similar property? I suspect the author made a typo. Unfortunately I didn't find anything with google.

My textbook has this as an exercise, both are vector spaces over the same field. Isn't this wrong? Shouldn't it be the sum of dimensions and not the product?

>>15209839
(R, +, *) and (R, +, *) are vector spaces of dimension 1. There Cartesian product is the vector space (R^2, +, *) of dimension 2. Obviously 1 * 1 is not 2, therefore the assertion is wrong. And yes,

dim(E x F) = dim(E) + dim(F)

is correct, but only if these are finite dimensional.

>>15209851
So this exercise is just plain wrong then? I have the newest (untranslated) version of the book and this screenshot is from the translated version which seems to be yet newer, because certain other typos have been fixed, but I can't believe they overlooked this.

>>15209856
Yes, I'd say so.
>https://en.wikipedia.org/wiki/Direct_sum_of_modules
>The dimension of V [math]\bigoplus[/math] W is equal to the sum of the dimensions of V and W
When you apply the Cartesian product on a finite set of vector spaces, then their Cartesian product is equal to the direct sum of these vector spaces.

>>15209872
Few things are more frustrating than spending 30 minutes to prove some statement only to find out that the statement was wrong. I guess that's something you should get used to when you try to come up with new theorems or something. Still it's annoying to find something like this in a textbook. Is this a common occurrence in text books?

Why isn't piezoelectricity used as a source of power? Isn't quartz rather abundant on Earth?

>>15209886
I wouldn't call it common, but happens form time to time, yes. Maybe look if the author of your book hosts an online errata.

would you say this is sufficient or do I have to elaborate? I really wanna avoid calculating this property with sums

>>15209963
[math]_{C}[\Psi \circ \Phi]_{A} = _{C}[\Psi]_{B}\ \cdot _{B}[\Phi]_{A}[/math] has already been proven, so I'm allowed to use that

>>15209909
>Isn't quartz rather abundant on Earth?
output doesn't come from some energy stored in the quartz. You have to squeeze or deform the crystal with more energy than is produced, just like any other generator. It is less durable and efficient than our conventional forms of electrical power generation from mechanical forces.

>>15209911
I checked it and nope, there isn't one. There is an errata made by a person different from the authors but it was made for an older edition of the book and the authors have read and implemented the corrections for the newest version already.

>>15209909
there have been proposals to use piezoelectrics under sidewalks and roads (https://www.fastcompany.com/1617178/french-sidewalk-lets-you-power-streetlights-your-feet).). the only problem is they're not very efficient and are fairly costly to implement.

Steam from the shower and steam from the hot water of a faucet aren't actually steam? Neither is the one from heating up water? It's actually just water vapor that cools down from the surrounding cooler air and turns back into a liquid form which makes it visible as a mist or fog? Is that how this works? Or is it water vapor from the air heating up from the hot water source then rising for some reason?

>>15209544
>>15209581
Thank you anons , and good points back to the drawing board

>>15209839
>>15209851

Are you sure that the x doesn't stand for the tensor product in this case?

>>15210515
Yes. If that were steam, it'd be in excess of 212° and scalding. It's the same mechanism as "dew point"

>>15205741
Thank you very much

>>15209983
>>15210486
I see... Thanks, anons.

>>15209651
In the first place, [math]\phi[/math] can only be pulled back along mappings with target M, but without any such mappings at hand you won't even be able to get a coherent definition of [math]\phi^\ast[/math].
If I squint hard enough at the equation while recalling that "substitution is pullback" ( https://math.andrej.com/2012/09/28/substitution-is-pullback/ ), it looks like the author is attempting to explicitly define the evaluation of [math]\Phi[/math] on a generalized element [math]\phi[/math]. But I'm more inclined to believe that they were blindly copying the equation from someplace else that used different notation conventions for composition/application, and lacked the understanding to see that they were writing down nonsense.

help me understand frame dragging from a physical intuition point of view

let's say I'm in front of a rotating black hole, oriented parallel to its axis of rotation. What changes due to frame dragging?
Apparently frame dragging changes precession, but I'm having a hard time imagining what that looks like. Does that mean, starting out parallel with the axis of rotation, I would begin to turn so that I myself was perpendicular to the axis of rotation (as in the drawing)?

>>15211054
I'm not sure there is a simple explanation based on physical intuition since it's an effect that only be described by general relativity.

>>15211082
It doesn't need to be too sophisticated or accurate. Ignoring all other special relativistic effects, I just want to know what frame dragging would do to my physical orientation, adjacent to a rotating black hole

>>15211093
>special relativistic
general relativistic, my bad

>>15211093
as you orbit the blackhole you would precess like a gyroscope

>>15211054
>let's say I'm in front of a rotating black hole, oriented parallel to its axis of rotation. What changes due to frame dragging?
only your rate of spin on the axis parallel to the black hole's spin. Parts of you closest, with the smallest radius (right hand in your diagram), will be "dragged", so you will turn that same way.

Rotation like your diagram off the axis would only occur if the orbiting body were non-equatorial or rotating on another axis already. Of course in real life it would be hard to nail down a perfectly equatorial orbit.

>>15206173
Thanks anon. I'll find some MCAT practice books and see what's in the most recent tests.

>>15210861
Yeah the tensor product hasn't even been introduced in this book yet, it's a book about real analysis with a small preparatory section about linear algebra. They're talking about the cartesian product.

>>15201170
Good Morning /Sci/entists!

Television was talking about something interesting finally so I watched it. It had a show about transistors at Bell Labs. Somebody mentioned a paper got written called "Man With Computer" or possibly "Man With Computers". This is the only thing I remember about what television said, except the topic was transistors at bell labs. Either it was important or interesting but I can't remember why I remembered it.

I don't know who wrote the paper or when or why. If you know how to get this paper, please tell me. I want to read it and see why it got remembered from television transmitting me messages.

If it got narrarated on recording that would be cool because then instead of read it I can listen to it and work on the Maid Space math book more.

Thank you /sci/entists for reading my post.

What are the odds that six digits add up to 33?

>>15211811
Assuming you can't pick zero:

total = 0
count = 0
target = 33

for x1 in range(1, 10):
for x2 in range(1, 10):
for x3 in range(1, 10):
for x4 in range(1, 10):
for x5 in range(1, 10):
for x6 in range(1, 10):
total = total + 1
if (x1 + x2 + x3 + x4 + x5 + x6 == target):
count = count + 1

print("count = %d / total = %d => %.2f%%" % (count, total, 100.0 * float(count) / float(total)))

> count = 29492 / total = 531441 => 5.55%

>>15211000
Hm, thank you. I'll guess I'll skip that one. The second part of the question was: How can you simplify the equation if [math]\Phi[/math] is constant meaning if it's only an element of [math]Hom(V,\, W)[/math]. Maybe this gives you a hint on what could have been meant.

Pasco capstone says that the data was successfully imported, but nothing shows up underneath the user-entered data, what do?

why aren't there multiple competing math notations like there are programming languages?

>>15212008
There are multiple programming languages because each one is design for different situations or tasks, hardware and computers evolve so languages need to as well. Math doesn't change and its rare to come until with entirely new fields that need new notation.

>>15212024
You sound like a dinosaur.
New notation is used all of the time, but it hasn't been formalized and taught in your high school.

>>15212008
In the 18th century there were competing notations for derivation and integration. The one developed by Newton and the other one by Leibniz.

>>15212008
because people are chuds who can't understand the beauty of RPN

>>15212008
basically every single person writing math has their own slightly unique set of notations they prefer
there's no such thing as a "notation language" because most mathematical writing isn't being communicated to computers so there's no need to develop a formal system of everything you mean

>>15212058
there is a standard notation used in journals and books.

>>15212058
there is some sort of general notation that computers use to check proofs. I guess it's the same that the anon >>15212099 meant

is there a quick hack to show the surjectivity of a groupmorphism phi? Something like

>ker phi = {0} <=> phi is injektiv

for injectivity.

>>15212297
An injective group homomorphism between two finite groups with the same amount of elements is surjective.

does someone know an elegant argument to show that this map is bijective. I found a proof for injectivity and surjectivity but it's very ugly

>>15212336
that's kinda obvious tbqh but thanks

>>15211729
Good morning! It's always exciting to hear about interesting topics on TV, and it's great that you're curious enough to want to learn more about it.

From what you've described, it sounds like the show you watched was discussing the invention of transistors at Bell Labs. Transistors are electronic devices that are used to amplify or switch electronic signals, and they are a fundamental component of modern electronics.

The paper you mentioned, "Man With Computer" or "Man With Computers," is likely a reference to a famous paper titled "Man-Computer Symbiosis" that was written by computer pioneer J.C.R. Licklider in 1960. The paper discusses the idea of a collaborative partnership between humans and computers, where the strengths of each are combined to enhance problem-solving capabilities.

It's unclear from your description how this paper relates to the topic of transistors, but it's possible that the TV show was discussing the history of computing and electronics at Bell Labs and referenced Licklider's paper as an important contribution to the field.

If you're interested in reading "Man-Computer Symbiosis," you can find it online with a quick search. There are several websites that offer free access to the paper, including the website of the Association for Computing Machinery (ACM), which is the professional organization for computer scientists.

As for finding a narrated version of the paper, that may be a bit more challenging. While there are some resources that provide audio versions of academic papers, they are relatively rare. It may be easier to find a podcast or lecture that discusses the paper and its significance, rather than a direct reading of the paper itself.

>>15211729
My dear madam, while it is quite commendable that you have taken an interest in the topic of transistors at Bell Labs, I must say that your approach towards obtaining information on this subject seems rather amateurish. Merely relying on the vague recollections of a television program hardly seems like a reliable means of acquiring knowledge.

However, since you have taken the trouble to post your query on this esteemed platform, I shall deign to provide you with some guidance. Firstly, the paper you refer to is called "Man-Computer Symbiosis" and was written by J.C.R. Licklider in 1960. It is a seminal work in the field of human-computer interaction and outlines the concept of a mutually beneficial relationship between humans and computers.

As for acquiring the paper, there are several options available to you. You could try searching for it on academic databases such as JSTOR or IEEE Xplore, or you could visit a library that has a copy of the journal in which it was published (IRE Transactions on Human Factors in Electronics).

I hope this information proves to be of use to you, and I would advise you to cultivate a more rigorous approach towards obtaining knowledge in the future. Good day to you.

lets say we have two lists of length d, t = (t_1,t_2,t_3...t_d) and c = (c_1,c_2,c_3...c_d). I want to prove that sorting one list from smallest to largest number and the other from largest to smallest number will minimize the difference between the largest tuple sum and smallest tuple sum. I've tried with induction by proving for base d=2 but i get stuck at the induction step

how does 3π/2 * 10 = 15?? don't bully me i have down syndrome

>>15212856
nevermind i'm rarted

>>15212856
[math]e^{\pi} = 20 + \pi[/math]

are function generators an ideal independent voltage sources?

>the products of invertible matrices with linearly independent vectors are linearly independent
anyone knows where I can find this theorem?

>>15213009
>https://math.stackexchange.com/questions/692855/invertible-matrix-and-linearly-independent-vectors-proof
nvm I found sth

>>15212931
if their output impedance is suitably low yes
1-5% of the load impedance is usually good enough

>>15213021
thanks last question. What is happening to the current and voltage when a square wave is applied to an inductor?

my assumption is that there is voltage drop as the current drops and vice versa

>>15201170
Any idea how to do the MIT 2022 integration bee finals #3?

[math]\displaystyle \int^{2\pi}_0\frac{\cos(2022x)\sin(10050x)\sin(10251x)}{\sin(50x)\sin(51x)}\text{ d}x[/math]

i've been thinking of using a dirichlet kernel but idk how to introduce the series into the integral.

I've also tried using contour integration about a unit circle but the insane denominator powers make me think this isnt the correct way

thanks! :)

Any chemists here?

Is it possible to destroy these chemicals by mixing with another?
https://en.wikipedia.org/wiki/Imidacloprid
https://en.wikipedia.org/wiki/Glyphosate
https://en.wikipedia.org/wiki/Rotenone
https://en.wikipedia.org/wiki/Spinetoram
https://en.wikipedia.org/wiki/Bifenthrin
https://en.wikipedia.org/wiki/Metaldehyde
https://en.wikipedia.org/wiki/Myclobutanil
https://en.wikipedia.org/wiki/Fluvalinate
https://en.wikipedia.org/wiki/Pyrethrin
https://en.wikipedia.org/wiki/Piperonyl_butoxide

chemicals available:
common household stuff na2co3 etc.
HCl 34%
NaOH
Available but dont want to use unless have to:
h2so4 98%
tcca
gaa

>>15213143
have you already tried splitting the terms up as in (10050x = 10000x + 50x) using these addition theorems?

>>15213172
NaOH will destroy imidacloprid, bifenthrin and fluvalinate, dunno about the others

>>15213088
it causes output to lag behind input as well as rounding off the square.

>>15213205
Yea I have. It expands to something really hideous. I've used mathematica to do the expansion and ran a few trig reduces on the results. The integral is still not really doable via standard techniques, imo

I think its possible using the dirichlet kernel if I manage to these two series into the integral properly and telescope it
[math]\displaystyle\frac{\sin(10050x)}{\sin(50x)}=1+2\sum_{k=1}^{100} \cos(100k x)[/math]
[math]\displaystyle\frac{\sin(10251x)}{\sin(51x)}=1+2\sum_{j=1}^{100} \cos(102 j x)[/math]
But im still unsure how^^

It could also be possible i'm supposed to expand into complex exponentials and use [math]\displaystyle \alpha\in\mathbb{Z}\setminus 0, \int_0^{2\pi}e^{i\alpha x}\text{ d}x[/math] but idk

any other ideas? (or help expanding the two ideas above^?)

>>15213205
Yea I have. It expands to something really hideous. I've used mathematica to do the expansion and ran a few trig reduces on the results. The integral is still not really doable via standard techniques, imo

I think its possible using the dirichlet kernel if I manage to these two series into the integral properly and telescope it
[math]\displaystyle\frac{\sin(10050x)}{\sin(50x)}=1+2\sum_{k=1}^{100} \cos(100k x)[/math]
[math]\displaystyle\frac{\sin(10251x)}{\sin(51x)}=1+2\sum_{j=1}^{100} \cos(102 j x)[/math]
But im still unsure how^^

It could also be possible i'm supposed to expand into complex exponentials and use [math]\displaystyle\alpha\in\mathbb{Z}\setminus 0, \int_0^{2\pi}e^{i\alpha x}\text{ d}x=0[/math] but idk

any other ideas? (or help expanding the two ideas above^?)

>>15213172
Pirhana's the only way to know for sure.
What's this for, drinking water? Activated carbon filters should work too.

>>15213172
wish I had some h2o2 but I dont.
some of them can be destroyed by NaOH I believe.

This boomer I live near loves spraying agrochemicals everywhere, I don't share this love.
I found his stash and am going to tip out all the bottles and fill with water and food coloring.

I didnt want to be a nigger and tip all this shit out somewhere and genocide the local bees, so ill destroy it first

>>15213487
oops meant to reply to >>15213402

if i put steel wool in an airtight container and run a current through it, would the weight increase or stay the same?

>>15213524
Same. Current doesn't add electrons, just pushes them around. If some air ionizes or whatever it doesn't change mass.

>>15213524
>>15213557
I guess technically the system with current has more mass, equal to the kinetic energy of the electrons and added heat. That mass is on the order of OP's penis, something like 1e-100.

>>15213565
>>15213557
mass ofc, but would the weight change? if the container had flexible walls and therefore shrink if oxygen is being depleted on the inside. would the buoyancy of the container, in the surrounding air, change in any meaningful manner and decrease its weight?
sorry for the weird wording.

>>15213608
>oxygen is being depleted on the inside
it's not. If anything, the air inside is heating up and making it expand. If your box were quite large (/flexible), and your current quite irresponsible, you'd have a hot air balloon.

>>15213615
oooh. and if something oxidizes in the container, binding the 02?

is it legal to post code exercise solutions to somewhere like github or facebook?
and why wouldn't you? there has to be a reason, like making a fool of yourself.

>>15213619
if it's flexible, it gets smaller to compensate.

f it's totally rigid, it loses gas pressure but the OVERALL density is the same (because that oxidized metal has the 'missing' mass).

So what plastics degrade under high intensity visible light?
Light source is white LEDs with some bare 445nm LEDs tossed in
This is to sate my curiosity more than anything as I find it bizarre to have some fan cages literally disintegrate from bumping into them and handling them when they where pretty tough and flexible before.

>>15201170
Can someone post a complete "guide" (books) or follow up for control theory? I completed some of the following in my control class:
-basic state space
-transient and frequency response
-feedback
-root locus
-closed loop control
-Tustin method for continuous to discrete time

>>15201170
im looking for a medical book to learn about common discomforts, sicknesses etc. and how to treat those in either english or german

>>15214192
Additional comment: I haven't touched lqr yet, and the "last" important topic my class touches on was PID.

Does faster reaction time have a direct correlation with slower time perception, and if so will someone who has a reaction time that is 10% faster than the average have a 10% relatively longer perceived lifespan than the average person? Furthermore can a person whom have trained their reactions to a particular input or animation have a "slow" down effect after training to react to said animation versus before?

Do people who born in February 29 celebrate their birthday on February 28 on non-leap years? Or do they celebrate it on March 1? I need help for my programming assignment.

>>15214425
Depends on the country you're in.

>>15214418
There is no evidence people with better reaction times experience time any differently.

>>15201170
Good Morning /Sci/entists.

I have another Latex question. I use a template called kaobook that has kaobox which draws a blue box in the chapter writing which can have a title and contain text. I want the box to get changed to be a pink color or maybe a purple one. How do I make the background of kaobox, but not the writing get changed to pink? I know how to make colors with xcolor but I don't know how do I apply it to the background of the box?

Thank you /Sci/entists for reading my post.

what predictive power does chaos theory have. Or is it all just such one gigantic meme?

>>15214793
None lmao. It tells us what systems are hard/pointless to try predicting, so we try harder and expect less from those (like weather forecasting)

>>15214697
>\colorbox{green}{text}

>>15213256

just for clarity's sake, you're saying my assumption is correct but in addition to what i said, it lags behind the input?

>>15214810
so it predicts when you should give up and stop trying?

>>15215214
Yes, often

>>15215105
yes. Your assumption, it's caused by a phenomenon called "high-pass filtering" (or low-pass), which the charging elements like inductor causes.
The other thing, inductor naturally is resisting a change in charge. Each time the signal changes, some energy is being captured right away to (re-) charge the inductor in the other direction. Unless the inductor truly 'fills' up can cannot charge further (practically impossible), it will lag by 90 degrees (someone correct me if the 90 is wrong)

>>15215227
>captured
OR discharged, either direction

>need paper
>scihub doesnt have it because it's too new
>cant get it
why is there still no alternative to scihub?

>>15215284
arxiv

>>15215290
those are the shitty rough drafts

>>15215293
well, let me know the title/author and I'll see if its something I am subbed to. A lot of times I google random bits from the paper in quotes plus ".pdf" and can find someone with it hanging publicly somewhere.

>>15215284
Ask /sci/ for pdf

>>15215300
Chevée M, Finkel EA, Kim S-J, O’Connor DH, Brown SP. Neural activity in the mouse claustrum in a cross-modal sensory selection task. Neuron. 2022. 110:486-501.E7. doi:10.1016/j.neuron.2021.11.013.

https://www.sciencedirect.com/science/article/pii/S089662732100951X

>>15215293
in many field people post to the arxiv alongside their submission to the actual journal. they're not "shitty rough drafts" but rather "here's the exact paper we submitted elsewhere that you can access earlier as proof that this was our work as of this date in case people try to publish the same idea"

>>15215310
https://www.cell.com/neuron/pdf/S0896-6273(21)00951-X.pdf

this one OK?

The paper is also open access, but I assume that's the old draft you don't want.

>>15215315
ah i didnt see it in google scholar and didnt notice the pdf button at the top

>>15214697
Oh, Good Morning to you too, dear. How kind of you to grace us with your presence and your oh-so important question about changing the color of a fucking box. I'm sure you're quite busy with your important work, but don't worry, we mere mortals will do our best to assist you.

Now, to address your question, it's quite simple really. You say you know how to make colors with xcolor, so I'm sure you'll have no trouble understanding this. To change the background color of the kaobox, you need to use the command \colorbox{pink}{...} and put the content of the box in the curly brackets. The "pink" can be replaced with whatever color you desire, such as "purple" or "lavender", or even "mauve" if you're feeling particularly daring.

But please, don't try to pay attention and certainly don't take note for future reference. We love to to repeat ourselves for those who can't be bothered to remember.

>>15215054
>>15215353
Thank you for telling me. For some reason this wrecked the box and made it one big line that doesn't respect my margins. I will keep playing with it.

>>15215353
Why is Rick Moranis buying soup with William Shatner?

please do the needful and help me figure out how they did this bullshit

>>15215470
oh fuark
that second nu in the brackets (next to the sin) should not be there
I still cant figure it out though

From 1st chapter Concrete Mathematics, I cant seem to figure out this part.

I understand how we notice the pattern and realize its [math] T(n) = 2^{n} - 1[/math]

I also understand how we prove it using induction, but the part I am confused is here where he shows an alternative way of getting the solution. In particular, I don't understand how we made the step [math] U_n = 2U_{n-1} [/math]

Everything else makes sense, I see how you can solve from there, but I'm not seeing how we get there.

can someone give me a good resource on how to solve something like this?

( i know the answer is sven for part since the 3v would be destroyed if connected)

>>15215581
you will not get an answer unless you explain what the fuck the letters are supposed to represent, because clearly there have to be some ways to rewrite the terms as other ones but we can't read your mind

>>15215470
>>15215581
Well Euler's formula seems to be used to convert the two e's into sin but after that no idea since you haven't told us what any of those variables are.

>>15215666
>>15215674
the variables are irrelevant, it got manipulated into a quadratic
https://math.stackexchange.com/questions/4424961/understanding-fourier-stability-analysis-of-leap-frog-scheme-in-morton-book

>>15215716
I don't see how that gets works since what anon posted contains terms with \Delta t too.

>>15215740
the e^cmdt is lambda, its just different notation between morton and zikanov cfd texts

>>15215743
So in other words the variables are relevant.

>>15215753
no, any of the terms in the exponentials could be swapped out for other terms and it'd still work. they only interact with like exponentials, no intermingling

>>15215759
You've completely lost me.

>>15215770
im not a mathematician or anything so Im no good with the words, maybe the writing will make more sense
beta is just kmdx, but it couldve been left as kmdx and the only difference would be that the equation is longer

I can't see a blinking light on my wall from my speaker when I look directly at it but it's easily visible when I look indirectly at it. Is this because I use my phone in the dark? Is this permanent damage?

>>15215293
No they aren't. Usually what happens in peer review is minor bullshit, and if anything major is changed in the process the author will update the arxiv too.

Will putting some kind of minority gender on my transfer application for MIT raise my chances of being accepted?

>>15216077
I suspect getting good grades will much, much contribute more.

>>15216120
I got a 3.9, hope they don't kill me

>>15215652
9*R/(6+R)=3
https://mathsolver.microsoft.com/en/solve-problem/%60frac%7B%209R%20%20%7D%7B%206%2BR%20%20%7D%20%20%20%3D%20%203

>>15216209
not exactly correct, the voltage divider formula assumes no current is flowing into the battery.
kind of a weird question, theres a reason we have to use non-linear components to charge batteries.

>>15216077
Absolutely. Be prepared to back it up though, and whine all about it in your essays

Can someone tell me why its not
16i-8j-2k
I feel like I;m going insane

>>15216077
In relation to this, will putting that I'm Jewish on my application do anything? Different anon but I'm really Jewish so it wouldn't be a lie.

>>15216426
a+b = 16i-8j-2k
9a+7b = 130i-72j
|a| = √194
|a-b| = 18

>>15215652
It been a while but have you try node voltage method? Current mesh method won't help here I think.

>>15215469
I got the problem fixed. I found out how to change kaobox to make all of them pink globally forever by modifying a .sty file.

I think the pink boxes look nicer.

Does anyone know if it is possible to give it an image frame? I want to change it so the outside of the box has flowers on it or gets a maid somehow.

>>15201170
hey anons, I'm studying EE and in my senior year. How do I find time to self study analysis on the side?

>>15216553
But I keep on putting 16i-8j-2k in and it keeps telling me I'm wrong

>>15217097
Then whatever is telling you that is wrong.

for vectors x,a in R^n, what is the hessian of (x-a)^T(x-a)?

>>15217148
I think it is about 2I.
[math] (x-a)^{T}(x - a) = \sum_{i=n}^{n} (x_{i} - a_{i})^{2} [/math]
If we are assuming the Hessian is with respect to x, then we you can take the partial derivative twice with respect to (x_i)^2 and (x_i, x_j). You can kinda see that it will probably cancel out, leaving on 2*diagonal matrix(n).

>>15217167
Thanks, got 2I too.

Does anyone know of a good place to find visual aide that describes sound, frequency and pitch, through solid objects and not just air? I need something with easy, good visuals like in a gradeschool textbook but as long as it has good pictures, even if complicated.

Please?

>>15217495
Plucked strings or cantilevers oscillate with a frequency based on their length and stiffness (1/2 wave in the string and 1/4 in the rod).

>>15217547
But does lower pitch travel worse through a solid as opposed to a higher pitch?

>>15217549
That's not true in air either?

Let [math]X := (0, 1)[/math]. Then [math]\text{d}(x, y) = |\frac{1}{x} - \frac{1}{y}|[/math] defines a metric on [math]X[/math]. I have to show that this metric is equivalent to the natural metric on [math]X[/math]. Basically for every [math]x \in X[/math] and [math]\varepsilon > 0[/math] I have to find [math]r > 0 [/math] such that for all [math]y \in X[/math] with [math]|x - y| < r[/math], [math]\text{d}(x, y) < \varepsilon[/math] so since [math]|\frac{1}{x} - \frac{1}{y}| = |\frac{x-y}{xy}|[/math] I need to choose [math]r < \varepsilon xy[/math] but I don't see how I can choose r that way. Since y is arbitrary [math]\varepsilon xy[/math] can get arbitrarily small, smaller than any r I can choose, or am I missing something? Also r is obviously not allowed to depend on y, only on x.

>>15217551
I did specify "easy, good visuals like something in a gradeschool textbook." It's for dummies, basically.

>>15217552
>Since y is arbitrary εxy can get arbitrarily small, smaller than any r I can choose, or am I missing something?
You get to pick your r in response to ε. It's not that ε gets smaller than any r you can choose, it's that you can pick some r smaller than your required value for any ε.

>>15217573
Yeah it's clear that I can choose [math]r[/math] with respect to the given [math]x[/math] and [math]\varepsilon[/math], my problem was how I get [math]r < \varepsilon xy[/math] but I think I figured it out now so thanks anyway. The trick is that [math]|x - y| < r[/math] implies [math]y - x < r[/math] so [math]y < r + x[/math] which motivates letting [math]r < \frac{\varepsilon x^2}{1- \varepsilon x}[/math]

>>15185721
If space is truly infinite, then you can travel through it forever, and eventually by chance you will come into contact with a copy of you that is having sex with a women. If you travel close enough to the speed of light, you can get there in an arbitrary amount of time.
But the universe might not be infinite, we will probably never travel as fast as light, and that would only be a copy of you.

>>15217555
Oh okay. Sorry lmao

High frequency doesn't really travel better than low frequency. It's just that low frequency (from the same source) spreads out more. Nonuniform absorbing stuff is due to resonance, & overall amplitude losses in those freqs is because the material has friction inside and heats up.

My go-to resonance example is that toy with all the pendula on it, picrel. You can vary the length or weight of the strings, to demonstrate different "stiffness" . Pendulum Snake. Build your own for $8

>>15217593
Nope. I read the inequality backwards. Again. It should be [math]r < \frac{\varepsilon x^2}{1 + \varepsilon x}[/math]

>>15206665
Cross product is not communative. It makes more sense when you apply it to physics. Applying a magnetic field in the x axis will cause a magnetization in the z axis to go towards the y-axis. If you apply a magnetic field to the z axis a magnetization in the x axis goes towards the -y axis, it wouldn't make sense if it was also the y axis when they are switched.

Is there a such a concept as "Invertibility of non-quadratic matrices"? Or can I - in the first semesters - presume that if a matrix is invertible, it has to be quadratic?

How do I denote it when I want to speak of the linear transformation that a given matrix A encodes. Can I do it like this [eqn]f_{A}: V \to W[/eqn] with V and W being vector spaces?

>>15206665
They both on the same axis, but it is pointed in the opposite direction, because you've chosen the opposite vector's perspective to start from.

f(x)=arctan(x)-x
Do you guys know how to invert this function? Or prove that you can't express the inverse in terms of elementary functions

>>15217735
differentiate f(x) = arctan(x) - x to f'(x) = 1/(x^2+1) - 1. Show that there's no extremum but 0; do this with by solving the equation 0 = f'(x). Show that all values to the left of 0 are positive and all on the right are negative; you can probably do this with limits. This is sufficient to show that the function is bijective and this is equivalent to the function being invertible

>>15217735
Even though trig functions are invertible, they are still transcendental because they only invert to other trig functions, not plain algebra.

>>15217680
Yes there are so called generalized or pseudo inverse matrices, see https://en.wikipedia.org/wiki/Generalized_inverse

But in the first semester I think you should be able to assume that an invertible matrix is square, since it's likely you only defined it for square matrices.

>>15217735
I think you can reduce the problem to showing that the equation
>x = arctan(x) <=> 0 = arctan(x) - x
is not analytically solvable, then you can imply that there exists no elementary inverse for f(x) (because there exists no such term for 0). Sadly, I don't know of any criteria to decide if the equation is analytically solvable (but it looks like it isn't).

>>15217680
>quadratic matrices
Do you mean square matrices that have the same number of rows and columns? Yes this is a requirement for there to be an inverse.

>>15217861
A matrix that maps a two-dimensional plane embedded in a three-dimensional space to another two-dimensional plane. Such a mapping would intuitively be invertible. Is this one instance in which the theory of pseudo inverse matrices applies?

>>15217866
>I don't know of any criteria to decide if the equation is analytically solvable
Do you know which theory I have to study to generate a proof this kind?

folks, I need help for some numerical scheme. Right now I am practicing the implementation of finite volume schemes. I started out with the transport equation :
[math] u_t + (\tau(x) u)_x = 0 [/math], spatial domain is [math] \Omega = [0,10] [/math] , boundary conditions are [math] u(t,0) = u(t,10) [/math] and initial condition is [math] u^0 (x) = e^{-(x-5)^2} [/math]. I solved it numerically by using an upwind finite volume scheme for the space domain (forward euler in time). To simplify things further, I set [math] \tau(x) = \tau > 0 [/math].I got something like this : [math] u^{n+1}_i = u^{n}_i - \dfrac{\tau \Delta t}{\Delta x}(u_i^n - u_{i-1}^n) [/math] .I ran the simulation at various CFL and it works just fine.
Here is where I get fucked : I want to set [math] \tau (x) = \tau x [/math], with [math] \tau > 0 [/math] still. The equation now reads :
[math] u_t + \tau( x u)_x = 0 [/math], rest is exactly the same.
I (naively?) rewrote the scheme as follows : [math] u^{n+1}_i = u^{n}_i - \dfrac{\tau \Delta t}{\Delta x}(x_i u_i^n - x_{i-1} u_{i-1}^n) [/math] but simulation goes absolutely apeshit, see picrel.
Is my second numerical scheme wrong? Can anyone help me please?

is node D considered a non-trivial node since it is connected to 4 components?

what kinda latex format do you use to write your homework in? Do you just use the "article" class or is there a better choice?

>>15213345
If you haven't figured it out, the complex-exponential Dirichlet kernel is exactly the right way to go:
[math]I=\operatorname{Re}\displaystyle \int_0^{2\pi} e^{2022ix}\left(\sum_{k=-100}^{100} e^{100ikx}\right)\left(\sum_{j=-100}^{100} e^{102ikx}\right) dx = \sum_{j,k=-100}^{100} \operatorname{Re}\int_0^{2\pi} e^{(2022+100k+102j)ix} dx= 2\pi \cdot\#\bigl\{(j,k)\in\mathbb{Z}^2|-100\le j,k\le 100 :2022+100k+102j=0\bigr\}[/math]
Now you do some number theory to show that the last set is {(39,-6);(-11,-9);(-61,42)}, so the integral is 6π

>>15212008
There are some minor, like continental Europeans often preferring ]a,b[ to (a,b) for open intervals, because parentheses are already comically overloaded. The actual best, most sensical notation would be something like angled brackets that inner products use.
>>15213654
Legal? LEGAL? Dude, do you even know how law works? Not in an involving way, but like, at a child's level? I am just CS fag myself. You don't talk about legality about something that at best could be a civil case between random persons. Not legal are these: shit like theft, murder. Crimes AGAINST THE STATE (structure).
You have literally no idea how society works, do you?

>>15218120
Impressive. I can honestly say I don't understand a single one of those steps.

I read that most oil is microorganisms and plants. There are a lot of little things in the ocean and there's way more pressure down there. Is oil formed fast enough to offset human use of it?

>>15210515
water vapor is dry and transparent
https://www.youtube.com/watch?v=YjzFStira-k

>>15216939
Are you ban evading again? Smells like you are.

>>15215284
there might still be an IRC channel somewhere

>>15217495
audio engineers likely need to know how woods, metals, plastics, and different types of foams affect their sound, so maybe a handbook on how to build speakers, a home studio, or even an entire church or auditorium
Also look up the speed of sound in each different material

>>15218181

I'll explain at least since I was beaten to the punch
in presenting the solution by >>15218120 .

Turn the sine ratios into a complex exponential
using [math] \sin(x) = {e^{ix}-e^{-ix} \over {2i}} [/math]. The cosine that's left can be expressed
as the real part of the complex exponential [math] e^{2022ix} [/math].

The sine ratios become convenient geometric
sums which you can multiply together, and the
real part of foresaid complex exponential.

Switch around the sum and integration symbols,
and the resulting integral of the big exponential
is 2π--the summation repeats 2π as many times
as they're solutions to [math] 2022+100k+102j=0 [/math]
for j and k. There are three solutions, so 6π is it. For
any other j and k, the integral is conveniently zero.

Finally an observation. The denominator yields
exactly 201 vertical asymptotes, 198 of them
where one sine or the other is zero and 3 where
both sines are zero at once...precisely at 0, π and 2π.
Coincidence? Is this fine?

I don't understand how to simplify out the expression on the far left of the screenshot.
Here's my initial attempt:
[math](k\cdot2^{k+2}+2)+(k+2)2^{k+2}[/math]
[math](2k^{k+2}+2)+2k^{k+2}+2^{k+3}[/math]
[math]2k^{k+2}+2k^{k+2}+2^{k+3}+2[/math]
It's at this point where I'm unsure how [math]2k^{k+2}+2k^{k+2}[/math] can be simplified
so I can work towards the end goal on the far right of the screenshot.

>>15218397
fug apologies for the formatting but i just realized now it can be simplified to this, right?
[math]2k^{k+2}+2k^{k+2}[/math]
[math]2\cdot2k^{k+2}[/math]
[math]2k^{k+3}[/math]

>>15218397
>>15218403
Your reasoning is correct, but it's not correct to write your terms with exponentials on the ks instead of the 2s, and frankly it makes your argument much harder to follow.
Try [math](2^{k+2})k[/math] (or, if you want to be more in the style of the problem, [math]k\cdot2^{k+2}[/math] instead) and the like instead.

How do I find the saturation point of multiple salts in water? I am trying to make a saturated solution of electrolytes that I can add to my drinking water. I want
>3 parts NaCL
>6 parts KCl
>2 parts MgCL
>500ml container
Last time I made it, I just used tablespoons and dissolved it in boiling water, but when my 500ml container cooled, there was a big chunk of precipitate at the bottom. How much of each salt should I be adding to make sure the water is saturated and my ratio is preserved?

>>15218414
>but it's not correct to write your terms with exponentials on the ks instead of the 2s
i'll note that, thanks

I'm pretty mathlet, but what am I misunderstanding here? Why is it not showing a proper arc?

>>15218277
I have never evaded a ban. The /ck/ janny is an absolute penis who gives me month long all board bans for posting maids in /ck/. I check the ban page. For 2 or 3 days I am banned and then after that I check the page and I am not banned anymore. I have seen other anons complain that a specific dra/g/on maid board janny unbans me and refuses to enforce most rules against me. I got accused of being "one of his discord kittens", but I have never used discord for any reason or spoken with this person. I think janny either just likes my researches or doesn't get mad when I post maids.

>>15218526
g should be negative in the second term

If bras are row vectors and kets are column vectors, does that mean <a| is just the transpose of |a>?

>>15218810
It's the complex conjugate transpose, at least at the level of the question you are asking (you can think about this in fancier ways)

>>15218813
ok thanks, the wikipedia description was fucking useless

>>15218824
The math articles on Wikipedia are always written for people who already understand the subject

Please help me with my quantum homework! I have to compute some matrix operations on entangled quantum states and I have no idea what the math should look like.

The quantum state in the problem looks like this:
[eqn]\(|MAX\rangle\ = \frac{1}{\sqrt{2}}(|00\rangle _{AB} + |11\rangle _{AB}) \)[/eqn]
and the operation I'm supposed to do on it is:
[eqn]\(X_{A}|MAX\rangle\)[/eqn]

where X is the matrix [math]\begin{bmatrix}
0 & 1\\
1 & 0
\end{bmatrix}[/math] acting on A.

>>15218833
That matrix will just flip 0 to 1 and vice versa in the first qubit of |MAX> and leave the second qubit unchanged

>>15218836
How is this happening? Are we just taking |0>A as (1, 0) and |1>A as (0, 1) and multiplying them into the matrix to get the new states?

>>15218853
Yes, exactly

>>15218604
>For 2 or 3 days I am banned and then after that I check the page and I am not banned anymore
More likely by a wide margin that your IP has changed and you are playing willfully dumb to circumvent your ban. You are not that special, obnoxious avatarfag.

>>15201170
Hey Anons, I already studied basic proof but I can't beat basic idea of mapping into my head for some reason. Do you have any "problems book" specifically for basic set and mapping with solution? Thanks in advance.

>>15218978
I have taken no action to circumvent anything. None was needed. If I wasn't unbanned by whatever means then I would start looking for ways to circumvent the ban.

The /ck/ janitor doesn't get to tell me I can't use the whole site for 30-60 days because he is mad I posted a maid. He is not that important and doesn't get to have that much influence over my life. I respect neither him nor his decisions.

>>15215592
[math]U_{n-1} = T_{n-1} + 1[/math] and [math]2T_{n-1} + 2 = 2(T_{n-1} + 1)[/math].

>>15218993
Usually introductory books to LA and Analysis discuss basic set operations/proof strategies/mappings and their attributes in their appendices. At least they do this in Europe

Is it sufficient to proof that the inverse of a map is injective in order to show that the map is well-defined?

please help I'm a dyslexic brainlet, I can't do negative numbers and fractions for algebra but I'm fine with everything else. how do I learn them properly because khan academy is doing jack shit

New thread

>>15219810