studiot

Whilst English has many words or parts of words that come from Greek, 'pre' and 'post' come from Latin.

I am guessing that English is not your first language, so perhaps you are unsure of the difference between 'pre' and 'post'. 'pre' means before and 'post' means after. You cannot pretension a roof (or anything else) after it is in place, you post tension it. Apart from that, clamping the frame and ground together against seismic forces is an interesting idea.

Hi, Penelope, you haven't said what you field is (or I missed it) so it's difficult to offer specific thoughts. But hey, the world is your oyster, there are so many organisations, apart from straight academe, who would be glad to have you. If later in life you felt like returning there you could do so, some of my best lecturers at University had spent long stints in industry and some of the most unintelligible (though no doubt brilliant) had never been outside the classroom. California, huh, here are a few ideas Become a consultant to the film industry. Work for a dolphinarium Join Greenpeace .Join............

Yup that's what makes the world go round and be a better place. +1

I don't know this book. Has the text said anything about the acceptance criteria or decision rules or whatever? These are an indispensible part of hypothesis testing and your text in green doesn't seem to include them, so I don't see how you can come to any conclusion. As regards one tailed and two tailed tests, it is possible for only one tail of the two tailed test to fall within the considered area for typeII error comsideration.

I assume that you are observing that the terms random and infinity are abstract nouns, which have an existence in their own right, and inquiring if they possess a manifestation as a concrete noun in our material world? Since discussion has concentrated on infinity I will start with random. Sure I can point to a real worls example. Line up a dozen Cobalt 60 atoms and tell me in what order will they disintegrate. As for infinity, there are mathematical ways to handle the ratios of two infinities - it is called L'Hopital's rule and can be found on Google. However this is still abstract thinking. A concrete example is more difficult since we are limited by our own mortality or finiteness. So we are stuck with thought experiments which we could not carry out to the end at infinity. Would you accept the artists 'vanishing point' in perspective drawing as a real world example?

Mondie, you said you didn't want the algebra (you don't need calculus) to derive Bessel so I could only offer a worked example. You can replace my numbers by symbols and work out the squares ( the algebra is little more than expanding (a+b)2 for the general formulae.

This looks like the Greens Function solution by introducing the linear diffusion operator, L [math]L = \frac{\partial }{{\partial t}} - k{\nabla ^2}[/math] Have you considered the boundary conditions, both in time and space?

I did wonder if the clue lay in the word add pressure? This is what you do with partial pressures.

The ideal gas equation can be decomposed into Boyle's Law, Charles' Law and Avogadro's Law, although originally it was assembled as a composite from separate Laws. http://www.chemguide.co.uk/physical/kt/otherlaws.html Note the comment that this is not taught these days.

Thank you sensei, that's often what I do but I would not say I was in error, just that the parser (is that the right word?) was inadequate for the job, or that MathType (advertised on this site) was inadequate or both.

Judging from the comments I see on several forums many find the same problem I do. viz tex/mathjax/mathml, whatever, sometimes works and sometimes doesn't work for no reason apparent to the user. That is very frustrating after a substantial amount of typing work.

Many found Mathjax no improvement when PhysicsForums went to it. I wouldn't waste the time as it is no better.

Relative doesn't necessarily mean there is no absolute. It means that there is a connection between two quantities that can be expressed as an equation. This may be a subtraction, as with velocities and elevations above sea level. It may be a ratio (or division) as in my conker is five times as strong as nigel's new one. It may be a square root as in The increase in radius is the square root relative to the radius. and really any (mathematical) connection you can think of.

Happy termite love table yum

74 downloads of your pdf and no one has challenged it or even commented on it. You have constructed a series of statements without proof. Perhaps you would like to justify and explain what you are talking about since it appears to me to be in direct conflict with conventional wisdom.

http://www.scienceforums.net/topic/85838-why-the-prevalence-of-crackpots-in-physics/

You do not correct the sample mean, only the sample variance. So you always use n-0 to calculate the sample mean. The issue is, as mathematic pointed out, that the mean of a single sampling will probably not match the mean of the whole population exactly. In my example, although the population mean is the most common value amongst the sample means, an individual sample mean equals the population mean in only 1/3 of the possible samples. With only one sample you cannot estimate the variance or standard deviation, unless N = n = 1.

Yes it is mathematically useful in many situations, both classical and quantum. The significance of your first loose definition is that if a function is the same once differentiated (to a constant multiplier) then the solution to a differential equation such as y'' = -ky is an eigenfunction. In other words y is an eigenfunction of this equation. The more general a(x)y''+b(x)y'+c(x)y = -ky Is known as the general eignfunction problem and the area of maths to look up is called Sturm-Liouville theory. S-L theory leads on to adjoint and self adjoint operators as elfmotat has indicated. An important property of eignfunctions is orthogonality which leads them to be linearly independent and forms the basis of useful series solutions. Returning to my first differential equation, this has a familiar general solution y = p*cos(k0.5x) + q*cos(k0.5x) where p and q are constants This may be recognised as the standing wave equation for a stretched string in classical mechanics if the boundary conditions y=0 at x =0 and x=a are added. Using these b. conditions we see that p = 0 and q*sin(k0.5a) = 0 For non trivial solutions since p = 0, q cannot equal 0 and therefore sin(k0.5a) = 0. This happens for the eigenvalue equation sin(k0.5a) = 0, giving the nodes of the standing wave. A similar result can be obtained with complex solutions to the Schrodinger equation in QM

Enthalpy has offered some pretty good comments, to which I would add that Force is measured in Newtons, not kg-metres. Are you thinking of rim or centre drive as it will affect many aspects of the design. In particular Enthalpy has noted the concentration of the mass along the rim, which is fine for rim drive, but the structural requirments for centre drive will require a more massive framework for the 'spokes'. Also the method of drive will be different for centre and rim drive.

Glad you were awake enough to spot the deliberate mistake, now corrected. Hope the rest is helpful, read the attachment in conjunction with the text in the post.

First thing is to get your units straight. You have quoted distances in metric but weight in imperial. Do you know the difference between weight and mass, it is important for rotating bodies. So do you want to work in metric or imperial? Second have you made any effort yourself to solve this question, if so please show where you are stuck.

Take a tip from the Eskimo and build an internal igloo.

Hopefully this is not a real wheel for real passengers, but only an exercise? In which case why is it not in homework help?

OK so what do we actually want to measure when we sample? In other words why do we sample? Well we don't want the actual value for one item. We want a single number that will best represent the whole population. So we want the population average or mean, [math]\mu [/math]. This is given by the formula [math]\mu [/math] = [math]\sum {\frac{{\left( {{X_i}} \right)}}{N}} [/math] That is we add all the individual values, xi up and divide by the number of values in the population. But we also (often) want an idea of the spread of the data. We obtain this as the variance (often reported as the standard deviation, [math]\sigma [/math] or square root of the variance) and given by the formula [math]{\sigma ^2} = \sum {\frac{{\left( {{X_i} - \mu } \right)}}{N}} ^2[/math] That is we add up all the deviations, square, and divide the result by the number of values in the population. But what about the sample? Using upper case letter to denote values from the population, and lower case for values from the sample: If we did the same for only some of the values would be be fairly representing the population mean and variance? Well it turns out that if we took every possible sample of size n < N we find that the average of all the sample means of size n is the same as the population average, [math]\mu [/math], although the sample mean for any particular sample may not be the same as that of the population. But If we take the average variance of all possible samples of size n < N we find is it smaller than the population variance. [math]{\sigma ^2}[/math]. Remembering that we are really interested in the parameter for the population, not the individual sample we find that we can take the sample average as a fair representation of the population average, But, and this is what we want to 'fix' We cannot take the variance of the sample as calculated by the formula [math]{\sigma _s}^2 = \sum {\frac{{\left( {{x_i} - \mu } \right)}}{n}}^2 [/math] as a fair representation of the population variance. Instead of algebra to prove this for all cases the attachment shows a worked example for a very simple case of the population being three numbers {10,20,30} and the sample size being two numbers. So N = 3 and n = 2 It can be seen that the mean of all the sample means is the same as the population mean, but the average variance of all the samples is only half that of the population variance. It can also be seen that bessels correction for this is exactly 2. [math]\frac{n}{{\left( {n - 1} \right)}} = \frac{2}{{\left( {2 - 1} \right)}} = 2[/math] Please also note I have tried to bring out when to use the N or n and when to use (n-1) - we don't use (N-1).