Bignose

you can't? http://en.wikipedia.org/wiki/Quadratic_equation

the first step is to rearrange the equation at hand: [math]c\frac{d^{2}y}{dx^2}=\frac{d^{2}y}{dt^2}[/math] (I'm going to glom together a and b as c = a/b) and note that the left hand side is only differentiated with respect to x. and the right hand side is differentiated with respect to t. This suggests a solution of the form y(x,t) = X(x)T(t). That is, the final solution is the product of two functions, each of only 1 variable. Now, if you let ' represent differentiation with respect to the only variable of the function (i.e. X' is differentiation with respect to x, and T' is with respect to t), the equation can be written: cX''T = XT'' or cX''/X = T''/T now, since the left hand side is ONLY a function of x, and since the right hand side is ONLY a function of t, we know that the only way this is so is if both sides are equal to a constant. cX''/X = k and T''/T = k Now you have two ODEs you should be able to solve, and when you get each of X(x) and T(t) the final solution is y(x,t) = X(x)T(t). You should be able to check out any book on PDEs from the library as a reference for this procedure of breaking PDEs down to ODEs. It only works for certain cases of PDEs, but it is the standard procedure for these separable-like ones.

we have a pretty good idea: http://www.soest.hawaii.edu/GG/ASK/earths_core.html Again, people have studied this question for quite some time. Before just throwing out an idea, and posting it to the forum, may I suggest you do a little research? In this case, the link above was the very first Google link. There are many more. Including references to scientific papers. Given what we know about the core of the Earth, it is very very very highly unlikely that it is a white dwarf.

Think about the ratio of the mass of an average meteor to the mass of the average planet, and then re-think this. -OR- to put it more clearly, the amount of different elements that a meteor could bring to a planet is almost infinitesimal. Please try to answer all of Klaynos' questions. If you firmly believe in your idea, you should develop it enough so as to be able to answer all questions fully to the satisfaction of the questioners. This is how science works -- you get reviewed and asked questions by other people. If you don't answer questions, your idea gains no traction.

Periodic means some function f obeys [math]f(x) = f(x \pm nm)[/math] for any integer n and some value m. The function has the same value when you increase or decrease the input by nm. Arctan isn't periodic, though. Sine and cosine are, though: [math]\sin (x) = \sin (x \pm 2 \pi n )[/math]

[math]A_{ij} = \frac{\partial x_i}{\partial y_j}[/math] where x and y are components of the basis vectors in the two different coordinate systems. This is basically the definition of a tensor. I recommend Synge and Schild Tensor Calculus for much more info.

I didn't realize that the police also enforced the laws of thermodynamics. I thought they had enough to do investigating all the robberies and speeders and corporate fraud and escorting famous people and riots and so on. Who knew? "Officer, if you promise to let me off with a warning, I promise that my entropy will only increase from here on out!"

yes -- follow this example. Plug 2 in for x and you should see that x=2 does not lead to an equality.

ajb, This is an incredibly important and insightful point. Well said.

surely this program has help files?

Is there a question here or something you want to discuss? Or are you just posting just to post? Because this looks like a random cut and paste job, which makes me suspect that someone is gearing up to do some spamming or similar.

There is a concept of a pseudo-inverse. However, it does not have a unique solution. More info here: http://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse

because [math]ab \neq \left(\frac{a+b}{2}\right)^2[/math] except in special cases.

You've really stumbled upon some good philosophical questions here. You may care to partake in some readings on the topic of Philosophy of Science. There are readings on questions like "does it really matter if what we perceive and what reality is is different?" In short, the answer really is no, because if something is unmeasurable, then it doesn't really matter if it is there or not -- its effects are unmeasurable after all.

Well your two expressions aren't equal. -2 + 6 = 4. Whereas 2 + (-6) = 2 - 6 = -4. the + (-6) is because you are adding a negative 6.

Yeah, that just emphasizes how tricky this is. I still look at what you wrote there, and my brain still thinks "another five 2's...." even though I have read your clarification. Must be very, very clear talking about these things.

Interesting choice -- rather than thinking of ways to perhaps better help others understand your math statements and what they mean, you decide to start name-calling. Rather than attacking, why don't you take some time and try to explain it better -- using terms and symbols everyone else in mathematics and physics have already agreed upon. Or, if you insist on using new terms, defining them very clearly. If you choose to attempt to publish your work, peer-review is a very significant part of the process. And, you're work will be criticized. If you can't take the heat from an Internet forum, you are not ready to try to publish.

Not on a fair random number generator (like a fair die) it isn't. The results of past rolls or trials have zero influence on future rolls or trials. On a fair die, the chances of rolling five 2's in a row are the same whether you've previously just rolled one 2, two 2's, seven hundred seventy-seven 2's. This isn't a "paradox" as much as it is you have to be very careful with how you word the question. What are the chances of rolling five 2's in a row on a fair six sided die? [math]\frac{1}{6^5}[/math] I've just rolled four 2's , what are the chances of rolling another five 2's in a row? Again, [math]\frac{1}{6^5}[/math] I've just rolled four 2's, what are the chances of rolling another one, resulting in five in a row? [math]\frac{1}{6}[/math] Because the fact that you have already rolled the die, has no influence on future events. The above is why you have to be very careful with the way statements or words are phrased. You get very different results with very similar-sounding statements.

ok, then, good luck with this. I'll pay you $14,000,000.00 when you get this all to work. Fortunately, in my system $1 corresponds to what you may commonly refer to "a speck of dust". But, don't worry, these units all make sense to me. Now if you'll forgive me, I'm going to retire to bed now. I have to get up early tomorrow and ask my boss for a raise -- I'm going to ask for an extra parsec per hogshead, and I know I deserve it!

ok, if 'x' is any measurement of space, then it has units of length. d/dt has units of inverse time. units of length do not equal units of inverse time. So, your equation is dimensionally incorrect. Anything gotten from it is meaningless then. Not to mention that you never answered my question about what exactly you are taking the derivative with respect to time, too. edited for spelling

Unless your 'x' here is an operator, this isn't even an equation. Because you don't even have what you are taking the derivative with respect to time with on the right hand side.

The question as formed also ignores the fact that different people learn and respond to different media. Some people are visual learners, some people are audio learners. Some people are better reading something themselves, and some people are better having something read to them. Etc. If possible, the best bet is to address all the different types at the same time, so that all types are paid attention to.

I've been reading more about these platform independent-viruses lately, most of them written in java to date. Definitely something to watch for in the future, and something for linux and MacOS users to be aware of.

And, to be fair, science welcomes this critique. The vast, vast majority of what we know today will be shown to be at least incomplete if not wrong some day. There will always be improvements and refinements. Where scientists start getting annoyed is when someone comes along and attempts to claim their model or idea is as good as or better than existing ones without doing the necessary ground work. Without showing that their model makes predictions as good or better than the current models, science does not accept these kinds of claims. Coupled with the knowledge that the current models are the current models because they have been shown to be the best at making accurate predictions, it may seem "dogmatic" to cite the current theory, but there are literally thousands of papers of evidence for it, that if someone would put some time in the library, could be easily found.

DJ, I'm going to write it one more time, despite the fact that it has been written many times over in this thread. I am not the ones making claims. You are. In order to back up those claims, you need to provide evidence that the model you support makes predictions that are equivalent to the model in use today. That is all. If predictions from two models are the same, then the models can be considered equivalent. If one model predicts results more accurately, or predicts more results, then it is considered better. That is all. So, again, my question at hand is: How has progress in using the Gryzinski model to make all the same predictions to similar accuracy QM does coming along? If your goal is for both models to be considered as equivalent, then you need to show that both models make the same predictions. A great number of predictions have been made using QM, with experimental backing to show how accurate those predictions are. Can your model do the same?