SFNQuestions

A regular volcano, no, but what about a SUPER volcano? Wasn't it SUPER volcanoes that contributed to the demise of the dinosaurs due to the increased ash in the atmosphere? If Yellowstone erupted, it would certainly be a problem for crops in the Midwest.

Wrong again. The computer specialist said there was absolutely nothing wrong with my computer whatsoever, no viruses or anything. It shouldn't be that difficult for a website to admit that it may possibly somehow have a technical flaw against adds. Also wrong, I'm simply the only one who's managed to overcome it to tell the tale. How doesn't sitting on ice for hours cause some kind of damage? If I stuck my hand in a bucket of ice for 2 hours, I wouldn't get any tissue damage? How doesn't sitting on ice for hours cause some kind of damage? If I stuck my hand in a bucket of ice for 2 hours, I wouldn't get any tissue damage?

Nope my computer is clean and this is the only website I've ever seen act like this in my entire life.

I don't know if someone from your department was incompetent enough to do this or if its some internet apocalypse, but every time I try to post now an add tries to pop up and take over the entire post, I don't have time to write a title I have to copy and past as quickly as I can. Everything here is super slow, your site probably got hacked. My question is: how can organs be transported on ice if freezing kills cells?

Is there a field of study of or any correlation for the general size of an animal and the minimum size for an ecosystem it needs? Is there an answer in terms of differential equations for systems that involve a complex food chain?

Good to know, thanks. But, who comes up with new species that are discovered? Like if something was discovered in 2017...what language do they decide to derive it from or... what?

Who comes up with the names? How do they come up with them? Is there some root language like Latin and then they stick an extra letter at the end or something like that?

For some unfathomable reason, scientists and journalists claim there's billions of bugs and bacteria that live in the upper atmosphere but don't provide one microscopic reference to any actual species of anything. Does anyone actually know definitely what specific animals actually live in the upper atmosphere or is it all a hoax?

It doesn't seem right, but I could have sworn I remember seeing instances in statistics where a summation was literally just swapped with an integral sign without anything else changing, except adding a dx. Can you really just swap a sum and an integral? I mean, the sum of a linear variable k is a second degree polynomail, and the integral of a continuous variable k would be a 2nd degree polynomial, so maybe there's something to it.

I was thinking, assuming an organism could get oxygen, how would an organism have to adapt to swimming through a very dense liquid, like mercury? If they were made of mostly air and organic fluid like fish already are, they'd have a lot of trouble diving below the surface. But, if say they had bones composed of a dense metal like iron to help them control their level in the water, they would need a lot of energy on a daily basis.

I feel like the answer should be no, because if you could program a model of say a chair that has more information contained in the particles than an actual chair, then you'd be able to program a computer that could use that extra information to program a computer with even more information than the computer that contains it and ad nauseum and paradox, but obviously you can't have an infinite amount of information in a finite space...or can you? I don't think so, but I don't really see anything proving that from being the case. You could argue some conservation law, but information itself isn't dictated by the same rules as an object that you pick up with your hands, so maybe there's some chance.

That's okay, I have done some more testing and found this method is valid. But, thank you for inquiring, it could have just have easily been the case that this was too complicated for me to determine.

Suppose that for solving for the inverse of a function that f(x) can be manipulated into the form of [math]g(f(h(x)))=x[/math]. Then, h(x) is inverted to show [math]g(f(x))=h^{-1}(x)[/math]. Afterwards, the function is reverted to show [math]h(g(f(x)))=x[/math]. Does this correctly show that h(g(x)) is in fact the inverse of f(x)? If not, what can be done in this situation to find the inverse of the original f(x)?

I also see no point in you discussing it further, seeing as how it is no one else's fault besides your own that you made careless assumptions rather than actually trying to help by simply being more cautious in analyzing the problem.

The way I wrote it is as many variables as I have. But, the more general the merrier I suppose, I don't have anything against a more general expression.

Right that's all good stuff, but, I don't need to determine the specific values of the variables, hence why I said "not" to treat them as constants, obviously you can tell just by looking at it that the system is undetermined. My concern, as I said, is the relationship between the variables, not the specific values. But doing some more digging I've found that the method is valid in this specific case, which is perfect because I used that to show the inverse of the trigonometric functions are complex logarithms of radicals. This is more to due with u-substitution than anything else, but with complex functions you might have a z and an x and a y and u and v and so on.

Which is what I said you can't do...so you should be agreeing with me...Do you understand English? Are you using some outdated online translator?

Well, they aren't necessarily constant with respect to the variable you're solving for, you can't always just pretend variables as constants, so it may be okay to always use the quadratic formula in that manner, or there may be exceptions in which case there is no garuntee the formula works. If the intermediate algebra allows for the separation of variables, then it would be valid, but if there is no known method of separating the variables but still pretend the variables are constants to loophole the problem, you will find your solution is completely invalid.

mm nope, sorry, and 0=/=1+1+1

I want to use a quadratic equation that uses not constants, but variables, like 0=xz^2+yz+w. Does the regular formula work for that?

I mean I appreciate you trying to help, but I don't see any indication my question is answered. I'm not referring to a uniqueness theorem as a solution to a functional equation, this is different. And it doesn't need to be limited to functions of a real variable. What I mean is: how can you test different functions against another function to determine if one function can somehow be put into terms of another function at its simplest level? For instance, take the cosine function. For the longest time, no one had any idea about complex exponents, people pre-hand made the assumption that you simply couldn't represent the cosine function in a fundamentally different way as a function of a variable, only to later discover it could be represented as functions of complex variables. That's the mistake I want to avoid. I may have a function or Taylor series that may not look like anything I recognize, but is it its own fundamental combination of operators? Or is it a complicated culmination of pre-existing functions? That's what I want to determine.

How does one determine with 100% certainty that a certain function can't ever possibly be put into terms of elementary functions, or really any arbitrary list of functions? Take the gamma function for instance, [math]\Gamma(x)[/math]. I am fairly confident the gamma function cannot be put into terms of elementary functions, but on the other hand, I've never ever seen anything remotely resembling a proof of that statement or any statement of that nature about any special function. How would I determine it can't be put into terms of other non-special functions or a mix of special functions and elementary functions?

Sorry, what you described does not seem like a definition of functional analysis to me, that is closer to abstract algebra which functional analysis can be a part of to verify properties of an abstraction. If you solve for a functional equation algebraically, it seems as though it is the the same as solving for x a constant, but when solving for an unknown function, you would more than just a constant if those solutions exist, so it would be more useful to know of actual functions containing variables that would satisfy these properties, not just constants. For instance, [math]f(x)^{1/2}=f(x)^2[/math] would show [math]1^{2/3}=f(x)[/math] I suppose a less ideal but relevant question is: how does one know for sure that they've found all conceivable solutions that satisfy a functional equation? For instance, there's the functional equation [math]f(x)=f(1-x)[/math] satisfied by the Riemann Xi function, [math]\xi(x)[/math]. But, it could also be solved by [math]f(x)=c_1+c_2x^2-c_2x[/math] which is much simpler in comparison. However, how would one determine that there isn't an even more complicated function than the Riemann Xi function that would also satisfy this functional equation? How does one know there isn't an unknown complicated function that satisfies [math]f(x)^{1/2}=f(x)^2[/math]? How does one know there isn't an undiscovered operator that provides a solution? Solving for it algebraically certainly doesn't help.

Hello, As I understand, one typically derives properties of functions that satisfy certain functional equations by substituting x for various values like 0, 1, y, -x, x^2 and so on. But what I am wondering is why algebraically solving for the unknown function doesn't work, or at least what it means when you do.