studiot

Alan, thank you for sharing this. You seem to have negotiated the proper side of the line in providing enough information in your opening post to justify a link to a much larger paper IMHO. I don't know about the correctness of the hypothesis, I have heard studies of correlations between weather conditions and human (and other life) behaviour and also studies correlating weather conditions with quake activity. So perhaps there are more links to be drawn? An authority who might well be interested is Brian Fagan https://www.google.co.uk/search?q=brian+fagan&hl=en-GB&gbv=2&oq=brian+fagan&gs_l=heirloom-serp.3..0i67j0i7i30l8j0.11781.11781.0.12015.1.1.0.0.0.0.141.141.0j1.1.0....0...1ac.1.34.heirloom-serp..0.1.141.1CHWHcSRVUM

Good analysis sensei +1

I really don't see what that is supposed to mean. You can pass a polynomial of any degree you choose through the points (0,0) and (1,1). This proves that you cannot determine the degree of the polynomial from the values at the points. This is also true of other more general sets of points, but is less easy to see. You have to choose beforehand the polynomial degree you want to fit to a set of data.

Surely you understand that you can't? Here are two examples What polynomial(s) pass(es) through the points (0,0) and (4,4) ? What polynomial(s) pass(es) through the points (0,0) and (2,8) ? Now for the difficult one What polynomial(s) pass(es) through the points (0,0) and (1,1) ?

Of course, but it is now a statistical problem, of curve fitting eg by least squares. Do you know the types of polynomial you can use to fit to a set of data, and do you understand what I meant about spline curves and derivatives? eg Collocating polynomial Minimax polymial Orthogonal polynomials eg Tchebycheff

I didn't say that. I said that you should know that the external impedences are much greater than the winding impedences. So Ohm's Law tells you that most of the applied voltage will be dropped across the these, not the transformer primary. For this to be the other way round your primary impedance has to be much greater than the external ones. This is basic electrical circuit theory. Yes I also thought that your transformer would be very inefficient because 1) For one or two primary turns most of the core material will be external to the primary field. Edit - That was not very well put since the core ring concentrates the field and draws it into itself. What I meant was that the volume of a primary of a few turns is very small compared to the ring core volume. 2) The heavy insulation of the windings increase spacing and reduce flux density.

Since we are using computer the solution of 6 or 10 linear simultaneous equations presents no more difficulty than the solution of two. There are even efficient schemes for partitioning the matrices when the system is too big to fit on the computer in one go. This is often the case in engineering calculations where sets of thousands of such equations have to be solved. However if you have too much data, as you do in your example, your system is overdetermined, so you cannot uniquely find a solution, unless there is linear dependency.

The general first order polynomial has two coefficients. The general second order polynomial has three coefficients. The general third order polynomial has four coefficients. The general fourth order polynomial has five coefficients. The general fifth order polynomial has six coefficients. and so on But straight substitution of the x, y values at the data points you can determine these by solving the set of linear simultaneous equations that produces. I was not wrong. If, as in the question I asked and you did not reply to, you wish to fit derivatives as well then you need more data points, which was why I asked you about cubic splines. In reply to your question My office pc has IE 8, on windows XP. and opened the page, but it was not interactive at all, nor did it offer a 'solution'. The windows10 machine with edge opened the page and displayed the cubic solution, (I assume this was actually correct, I did not check) but retained it when I operated the drop down box and selected other values of polynomial degree to try.

OK Most waves are periodic phenomenon and require a medium in which to propagate. Waves can be combined. Telecommunications waves are actually combinations of two sorts of wave. The signal wave and the carrier wave. We really only want the signal waves and mathematically we can regard the microwave carrier waves as only there to create a medium for the wanted signal to propagate in. Signal waves are generally not periodic and often not even continuous in time. Continuous signals are called analog. Discontinuous signals are called digital. The simplest signal wave was the old Morse code, first on the telegraph wires and then by radio. This was a simple series of on and off pulses. So the first signals were digital. Then came the analog voice signals by telephoen and radio Today we are back to digital signals with mobile phones. Does this help?

If you are jealous of my tailor or my barber I will supply their details for a small large fee.

Don't rely on the timestamps here, they are often inaccurate. It was not a mistake just language difficulties, don't worry about it, no one will complain as you are obviously doing your best to communicate. I did say keep doing this as it will help and an English course will also help if you have time for one. Cheer up and concentrate on trying to put over what you want to say about mathematics.

Firstly you link doesn't work properly in all browsers. Secondly, it doesn't work as expected in Microsoft Edge in Windows10. Your example contains 6 data points, enough to establish six unknown coefficients. Yet your example insists that the data is from a third degree polynomial, whatever degree I ask for. So is this a cubic spline approximation or what?

All of these. Keep asking questions it will help your English. For instance I understand your question above, but it was not good English What sort of difficulty do you mean? What kind of difficulty do you mean? Is good English. Sorry for my spelling mistakes in my posts above I hope you notices I often write form instead of from.

I have the 1989 edition of 'Introductory Functional Analysis with Applications' by Kreysig. You may find the treatment of waves from a functional analysis point of view by 'Applied Functional Analysis' by Griffel of more interest.

I still don't see an answer to my question. Functional analysis is the mathematical study of mathematical spaces and the maps between spaces. As such Fourier analysis is included. Fourier analysis is the mathematics of periodic (wave ) functions. When the fourier sequence is finite the map is form the space of continuous, continuously differentiable functions to itself. When the fourier sequence is infinite the map is from the space of continuous etc functions to a space including discontinuous functions eg square wave or pulse that I mentioned before. I'm sure there is a language difficulty so you sould include more mathematics in your questions. Those responding will have no trouble with this.

I suspect your 'problem' lies here (underlined). If you do not understand IMHO you should be heeding Ed's sensible safety advice.

What does this have to do with functional analysis? Note. 1) Of course you can see the phone signal waves with a device - it is called a phone. 2) The phone signals are pulses not waves.

Yes I agree the logic is flawless. But I don't see it as the problem. Some years backalong, where I live, we had a former leader of the liberal party in our area before he was prominent. I heard him speak passionately putting the point "We don't need the nuclear option now" When he was opposing the development of a new reactor at Hinckly Point, our local nuclear power plant. The replacement reactor was shelved for decades and now we are witnessing one of the biggest fiascos in finanace, politics and engineering about the current attempts to replace the old one. Those who have lived that long have spent the best part of a century watching a similar struggle to not build an even better clean energy device of even greater capacity here in Somerset, but that is another story. It seems to me that, all too often. the bigger the project the less the plain common sense that goes into it.

I seem to remember that the book you mentioned was general chemistry. From university level you need more area specific books for different topics within the subject. With all the modern web resources, perhaps you students don't use books these days but here is a brief bibliography. Chemistry a structural view Stranks et al Cambridge University Press Chenical Binding and Structure Spice Pergamon Solid State Chemistry Smart and Moore Chapman and Hall and the grandady of them all Structural Inorganic Chemistry Wells Oxford University Press

Interesting paragraph. Here is a supposed conversation that took place in 1919 at the conference where Eddington presented the first experimental confirmation of (general) relativity. Physicist, Professor Silberstein, "Professor Eddington you must be one of the three persons in the world who understand general relativity" Eddington "Smiles" Siberstein "Don't be modest, Eddington" Eddington "On the contrary I'm trying to think who the third person might be"

A century or more ago the aether wind may have been a plausible explanation, but since that time there have been so many confirmations of relativity in so many different directions, over so many different distances, large and small, that such an explanation cannot now be supported.

Yup +1

I already offered you this but you don't seem to want to discuss it. Take our Earth with its lines of longitude. 3 dimensions All the lines of longitude end at one point (well 2 actually), a pole. Now open out the surface to become a mercator map. 2 dimensions But all the lines of longitude are still there However they no longer meet but reach the end of the map at different points. Do you want to discuss this further? I mentioned the word manifold, if you understand what this means please say so as this is an example.

Reading post 88 Methinks our learned friend has been drinking too much from his desert still.

I think this discussion has really brought out the limitations of the rigid A or NotA brand of logic. So many of the terms support multiple interpretations and/or suble nuances of meaning. Worse the moment we introduce explanations we introduce more terms to have shades of. The meaning of measureable or observable for instance, I think my examples have shown that even the concept of existence has such range of meaning and cannot be simply described as exists or not exists. Another muse arising from another thread where we were discussing the meaning of singularities. We are all happy with the function y = x2 rising ever more as we increase x and noting that we can never 'get to the other side of that infinity' I don't think anyone would call that a singularity, because we can see that we can never reach it. But consider the function y = 1/mod(x). This has a singularity at x=0 (note I do not say at the origin as is often said and is strictly incorrect) But we can bracket or get to both sides of this curve so we regard this infinity as a disturbance of some sort in our otherwise controlled number line and call it a singularity.