Bignose

but the second series is raised to the 2n+1 power, not the n power. This has to be addressed, too.

I've read enough scientific papers, and especially older ones, that I have seen it both ways. It was disconcerting, but in the end, dimensional analysis showed what the author meant. Believe me, I then scratched in my own sets of brackets into the equation to make it clear next time I read it. Back in the day, when it wasn't easy to typeset equations unless they were all in the same line, there were occasionally ambiguous terms printed.

One advantage to having bills in your name is the opportunity to build a decent credit rating. I assume after University, you'll be getting a full time job and buying a car or home, etc. Creditors like to see a history of paying bills on time every time, it makes them more willing to loan you money and at a lower interest rate. Of course, the flip side is that if you screwed by people ditching you and you can't pay, like a lot of things in life, that credit rating can go down a lot faster than it goes up.

How does this "prove" whether the y in the OP's question is in the numerator or denominator?

no, you can't. you can't "prove" (no matter how big a font you use) a convention. You decide on a convention, and stick to it. The question as asked depends on what convention one uses.

Why not write pi in base pi? 10. There's a pattern for ya. Now, writing 2 in base 10.... that's the tricky one now.

No. If the number is "close to zero" but not actually zero, then 1 over that number is not infinite. It may be very, very large. But it is NOT infinite.

Indeed: to build on uncool's comment here, please take a look at M. Breidenbach (1969). "Observed Behavior of Highly Inelastic Electron-Proton Scattering". Physical Review Letters 23 (16): 935–939, as a start. In Breidenbach's results, he reported observing three point-like bodies inside a proton. And then take a look at some of the many papers that cite this one. Since 1969, I suspect that the experimental evidence for quarks has gotten significantly stronger. Nonetheless, there was experimental evidence 42 years ago. That is hardly "only having lots of people believe in them." Or, lots of people believe in them since there is a ton of evidence for their existence.

No, Xitten has it right. "~" should be read as " is distributed as" and N means normal. [math]X \sim N(\mu , \sigma^2)[/math] in words means X is distributed normally with mean [math]\mu[/math] and variance [math]\sigma^2[/math].

note that if indeed it says [math]\sim N (\mu , \sigma^2)[/math] then the 9 is the variance not the standard deviation, the latter being the square root of the former, of course.

biggest problem with this... how to solve for unknowns: [math] 14 - x = 9 + 2 [/math] You got a - on the left hand side, and a plus on the RHS. What value of x solves this?

Considering the wide number of possible operations, I think that this would be incredibly unwieldy very quickly. Also, how would you denote the addition of a negative number? In my mind, a real beauty of math is that the different operations are equal to the same thing. [math]-e^{i \pi} = 0.5 + 0.25 + 0.125 + 0.125 = 3\int_0^1 x^2 dx[/math]. In your system, they wouldn't be exactly equal because of the different notation appended to the end.

"Rocking the boat" happens all the time. Go to most any scientific conference -- scientists present things no one else has ever seen before all the time. What doesn't happen is that the presenters just stand up and start telling a story. They present something new, and then provide evidence in the form of simulation or experiment or both to show why they think what they think. Presenting new things is pretty much the whole reason conferences exist, actually. But, scientists present new ideas that follow the scientific method. That's what makes them scientists instead of fiction writers.

OK, so what experiment would you do to validate or invalidate this idea? Your story tries to explain current experimental results -- so what experimental results would you need to validate or invalidate your story here?

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There isn't a "right" or "wrong" here -- it depends on convention. The problem is that you've got an ambiguity in the expression as typed. Is it: (48/2)*(9+3) or is it 48/(2*(9+3)) ? I.e is the 48 to be divided by the (9+3) term or multiplied? This ambiguity needs to be answered. Most conventions do everything in the brackets first. Then do exponentiation, then division and multiplication, then addition and subtraction, each from left to right. But that is just a convention, it isn't the "right" or only way to do it. There have been many conventions used over the years -- with the biggest one being to use brackets to remove as much ambiguity as possible.

Here's a suggestion: post the equation just using a variable for what you call the "slope". Say k. i.e. [math]c(x) = c_0 + kx[/math]. Then, make predictions with your model for various values of k near what you expect it to be. And show some results. Most equations are manipulated in symbolic form until the very end when the values are then put in. You don't need the exact value of your slope to make predictions with the model or post equations. Show us something instead of just story telling about how good it is.

Well, then, if you don't have it today, why so sure that your model is so great? Why the self-aggrandizing when you don't even have a complete model? How can you be so sure?

Great, please post it in all its [math]r[/math] and [math]\theta[/math] glory. And graphs of the predictions it makes compared to measurements and the predictions current theory makes, please. Show us exactly how good your model really is.

My theory is: I have an invisible troll that lives in my attic leaving no trace of its presence who can solve complex differential equations in its head. Do you believe this? If you don't, have you disproven it? -or- You have the role of science incorrect. Science does not have to treat every idea as valid until completely disproven. What science does is be very skeptical of every new idea until evidence supporting the new idea is presented. And, when overturning an idea that already has evidence, there has to be even stronger evidence that the new idea is better. So, let's see it. Let's see some evidence. Let's see your equation's predictions and how well they agree to the measurements. Please show the predictions from the current theory, and how your predictions are superior to the current ones. Do this, and everyone on this forum will be reading with eyes wide open. Do it not, and expect more skepticism. It really is that simple.

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I agree with this, and that above puts my own strategy into words. A well written negative review usually means something. Along those lines, you may want to go back to the books you disagreed with the average on, and find the reviews that match your personal feelings. Then, see what books those people who matched your thoughts liked or disliked. In other words -- review the reviewers to find the ones that match your personality. Also, reading the sample chapters and table of contents goes a long way. Or, Phi has got a good idea, too. Most libraries will do an interlibrary loan for a nominal fee. My city library charges a mere $1 to got any book in most any library in the country. My school library does it for free. Get the book for several weeks and decide for yourself.

Its ok. It is just that this is a discussion forum, and unless there is something to discuss, posting something pretty much misses the point. If you want to post something just to have it on the web, there are plenty of sites where you can start your own blog or website. But if you want to post something to have a discussion about, then this is a good place.

Ah, my memory isn't perfect. Usually, we set the constant to be negative, and it is often convenient to make it a square, too. So, let us let [math]k=-\beta^2[/math]. Then you get [math]X'' + \beta^2 X = 0[/math] and [math]T'' + \beta^2 T =0[/math] The solution of these is: [math]X(x) = C_1 \cos \beta x + C_2 \sin \beta x[/math] and similar for T. When you apply the BCs, you should get an infinite number of solutions because cos and sin are periodic. I pulled out my copy of Strauss' Partial Differential Equations An Introduction to refresh my memory on these, but again most any text on PDEs will cover this technique. I believe it also goes by the name of separation of variables.

This scaling can be described using the 'regular' 3 dimensions of space. The 'scale' of something is a function of your distance from it and the size of that something. I don't see a need to create a 4th dimension when what you are describing can be adequately described using the commonly defined 3 dimensions. OK, can you post this mathematical link?