studiot

I have found some useful further information but need help posting to comply with the wikimedia licence attributing the sources. Please help. http://www.mantleplumes.org/WebpagePDFs/Siberia.pdf https://commons.wikimedia.org/wiki/File:Extent_of_Siberian_traps_german.png https://commons.wikimedia.org/wiki/File:Extent_of_Siberian_traps_german.png#/media/File:Extent_of_Siberian_traps-ru.svg

Hey fellas, I count two questions marks in the OP which makes two questions. So both are right in the question they choose to answer, if they are only going to address one. And both are wrong if they dismiss the other question.

Note Swansont also said entropy can remain the same. That is not the same as entropy increases unconditionally with time.

According to my admittedly coarse scale geology map, this area of the Central Siberian Plateau is a tongue of Qaternery material extending from a much larger area comprising the Yenisei-Irtysh basins., to the west. This is shown in yellow on the map. This tongue is sandwiched between much older formations to the north and south, first Palaeozoic rocks shown blue and purple followed by some Pre-Cambrian, shown brown. This is suggestive of a former syncline. (Youngest rocks in the middle) on a much larger scale than the 10km feature in the OP. http://web.arc.losrios.edu/~borougt/GeologicStructuresDiagrams.htm The rivers run through the Quaternary material, which must be softer than the older rocks and Imatfaal has show to be lower. Not only lower but the Google pictures show that the rivers have cut quite deeply into the plains with the older rocks forming background peaks. The Google maps also show much meandering, typical of low gradients. https://www.google.co.uk/search?q=river+kotuy&biw=1366&bih=679&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiA89Sfn-LRAhUkLMAKHf09DigQ_AUICCgD The point about the ages is that known igneous activity preceded the Quaternary deposition, so the feature in question may be a remnant intrusive dome the radial lines could be old dykes, although the river seems to have cut straight through one (perhaps following an earlier glaciation). I bet there are some lovely rapids there.

A screenshot would be useful to those of us without your special equipment.

No Please read my post#20 very carefully. I am not saying you are right or wrong nor am I proposing alternatives. I am examining it for logical self consistency and consequences. I think this is a good thing to do because there is a danger of 'running away with oneself' when proposing a hypothesis. You have made contradictory statements that the particle and wave are at the same point at the same time and that the wave arrives before the particle. Please clarify this as they cannot both be right. Incidentally your description of wave-particle sounds something like the wavelet or wavicle models. Incidentally it is a mistake to fall into the trap of thinking that light has to be either a wave or a particle. It has some characteristics (but not all) of each, but is actually more complicated than either. Another example of such a physical phenomenon is that of (ordinary) glass. Glass has some characteristics of a solid and some of a liquid but not all of either and is in fact more complicated than either.

My thanks to both wtf and Nedcim for holding an adult discussion about this subject. +1 NedCim, your mathpage link was vastly superior to your previous one and offers some very well presented examples. I note they said exactly what I did That a limit is a number and infinity is not a number. and [math]\mathop {\lim }\limits_{x \to \frac{\pi }{2}} \tan x[/math] does not exist They do offer something of an explanation but Oh dear. Firstly they say that when we say some limit = infinity we mean something other than conventional 'equals' and the reader needs to know the new conventions. Better, I say, to avoid such confusion. They then compound the confusion by introducing two different 'infinities'. (via Gauss' reference to the potential and actual infinities of Archimedes and Eudoxus) Whoops, what's that ? We are only allowed one in the extended real number system. We do not have any rules for two types of infinity. They also discuss something 'becoming infinite or infinity' What's that? Do the rules suddenly change when this happens and what are the rules to know how, if and when it occurs? In particular if you are going to do some algebra on my question you need to prove which set of rules the n's involved obey and when since n 'becomes infinity' in the limiting process. Finally they make the classic mistake of claiming that we never reach a limit. This cannot be true since the definition of continuity at some point, xo requires that the value of a function equals its limit at xo. So to say we can never reach a limit (or that the limit is never included in the set) is stating that we can never reach, say the value of f(x) = x2, a x=2. Sorry I didn't make my last explanation very clear. I will post some background starting from what my sources say was the first formal definition of a limit (Wallis : Arithmetica Infinitorum 1655) going right up to the material you say is hard to find ( Thurston has some vary good pages similar to your Wikipedia article, but without the gloss over the difficult or missing bits)

Not sure why you are replying to me, Mike? I don't recall ever discussing grad, div & curl with you.

Thank you for replying to my question. Do you then agree that the particles arrive after the waves in your hypothesis, not simultaneously as you originally stated? How does this affect your hypothesis?

Isn't referring to 'fluid dynamics' a bit limiting? How about Continuum Mechanics which includes FD and much more besides? I say this because there are many texts at many levels including this in the title.

Nice short input arc that hits the nail. +1

Like Mordred, I feel there may be a germ of an idea in your post. But I also feel there is an implied contradiction in your opening post. It runs like this. Your explanation states "The interference pattern has peaks and valleys of wave energy density which influence the path of the particle between the slits and the detector". This seems to me to be at variance with the statement of simultaneity, " Individual wave-particles can display both their wave and particle nature at that same time", because in order for the peaks and valleys pattern to influence anything it must be present ie it must be there when the 'particle' arrives ie fractionally before the particle. Please explain how this apparent discrepancy is overcome?

Let me just say I find Wiki disingenuous. All the laws? Too many things are undefined or omitted in the gloss over treatment. Without this most of useful mathematics falls apart. Well I'm sorry I can't even quote from your Wiki link here I just had some stupid error message. I've just goT through changing their stupid image types for ordinary letters. So much for standard. Talking of standards, perhaps you would like to write to Professor G H Hardy, Cambridge University and tell him to amend his book, A Course in Pure Mathematics To conform to you standards.

OK so let us try to solve my question using the extended real number system. Would you agree with me that the symbol [math]\infty [/math] must always stand for the same thing, just as say the symbol 9 must always stand for the same real number? So using this terminology [math]\mathop {\lim }\limits_{n \to \infty } {x_n} = \mathop {\lim }\limits_{n \to \infty } {n^2} = \infty [/math] and [math]\mathop {\lim }\limits_{n \to \infty } {y_n} = \mathop {\lim }\limits_{n \to \infty } n = \infty [/math] Substituting [math]\mathop {\lim }\limits_{n \to \infty } \left( {{x_n} - {y_n}} \right) = \mathop {\lim }\limits_{n \to \infty } {x_n} - \mathop {\lim }\limits_{n \to \infty } y = \infty - \infty = [/math] What is the infinite symbol take away the infinite symbol ie what is (the same thing) take away (the same thing) ? And why is it not zero? Because I think the 'limit' should actually be infinity. The penalty you pay for using this extended number system is that normal arithmetic no longer works. You cannot guarantee that sum/product/difference/quotient will yield a sensible result You cannot guarantee the axiom of associativity. Worse. The point/power of convergence is to determine if there are any solutions to differential equations/complex integration/transformations etc and once you let indeterminate elements into your fold you loose this ability. Yes I said somewhere back that some authors do this (Professor Thurston for instance), but associating limits only with convergence gains you far more than it looses.

First statement Yes, of course a sequence can diverge to infinity. But no I do not agree that infinity is a limit. Perhaps you would like to offer a solution to the following proposed limit (or ask Bruce) Let xn = n2 and yn = n Does the limit exist, and if so what is it? [math]\mathop {\lim }\limits_{n \to \infty } \left( {{x_n} - {y_n}} \right) = ?[/math] Second statement. I think you are confusing unbounded and infinite. They have different meanings. An infinite sequence can be unbounded eg 0,1,2,3........ or bounded eg 0,1,0,1,0,1..................

Please note there is no reason to suggest that the basis vectors or axes have to be orthogonal. Calculation convenience often dictates this but skew axes are also sometimes useful as in shear transformations.

Posts 472 and 473 here http://www.scienceforums.net/topic/29763-bannedsuspended-users/page-24#entry968109 I was trying to help other members who are also struggling with elementary limits as many do. Help in such a venture is always appreciated.

Far from being annoyed, perhaps you should read the earlier post questions and replies more thoroughly. I was trying to develop a consistent presentation starting from pretty elementary stuff. I had not even reached the stage of epsilon-delta. I was also avoiding the fact you seem to me to have implied that a 'limit' can never be reached When of course some limits are accessible and some are not. Both of these are in the next stage of the development.

Yes it is an interesting question and not yet fully resolved. You need to study the Continuum Hypothesis from Cantor to Cohen for this. https://www.google.co.uk/?gws_rd=ssl#q=cohen+and+the+continuum+hypothesis

The total interaction force is a combination of the electrostatic (zeta) and the hydrostatic pressure force. Water has a high surface tension, which can affect the latter, which is why surfactants are used. These are also called plasticisers in the concrete and mortar industry. The addition of such a compound may help with your flow and levelling issues.

Perhaps some clarification of terminology is in order. Some authors use the term 'functional analysis' to mean the theory of functions of a (real or complex) variable. That is the word 'functional' is used as an adjective. I think this is the meaning intended here. Unfortunately the word functional is also used in mathematics as a noun with a particular meaning. This meaning was introduced by Kantorovich, Banach and Kerysig A functional is a map from a space of test functions, [math]\Im [/math], (ie functions of interest) to its underlying field. In your case I think the underlying field is the field of Real Numbers, R So a definite integral is such a map from the space of integrable functions to the reals and outputs a real number for each definite integral. Functionals can be non linear or linear. A linear real functional, F, is a map [math]\Im \mapsto R[/math] such that for any two functions, [math]\left( {\varphi \,and\,\psi \in \Im } \right)[/math] and scalars (real numbers) [math]\left( {a\,and\,b \in R} \right)[/math] [math]F\left( {a\varphi \, + b\,\psi } \right) = aF\left( \varphi \right) + bF\left( \psi \right)[/math] Some texts on the subject are Kantorovich Functional Analysis Kreysig Introductory Functional Analysis with Applications Griffel Applied functional Analysis Functional Analysis grew out of Dirac's version of the theory of 'generalised functions' called Distribution Theory.

I take it this question is related to your other one. The sort of proof you are looking for is known as an existence and uniqueness theorem, of which there are several each pertaining to a particular area of mathematics. It looks as though you are studying what is known as the functions of a real variable. Even in this limited area the E&U theorems involve some highly abstract maths which fills large textbooks. A few 'standards' are Hurewicz Dimension Theory Hobson The Theory of Functions of a Real Variable (2 vols) Titchmarsh The Theory of Functions Burkhill A second Course in Mathematical Analysis Graves Theory of Functions of Real Variables Verblunsky An introduction to the Theory of Functions of a Real Variable Littlewood The Elements of the Theory of Real Functions Some of these are rather old.

So if in the series configuration each bulb has 60 volts across it and produces 60 watts and, as you say, has 1 amp current through it, What is its resistance? What will then be the wattage it produces if connected to 240 volts? (assuming it does not blow)

A good idea would have been to post the exact words from your textbook. However if the power is to be the same, by definition, the power rating must be the same ie 4 x 60W (assuming all the new bulbs are the same). Note that the power rating of a mains electric device is only correct at its rated (ie mains) voltage. In the UK both voltage and current are printed on the bulb. Since the bulbs are now in series, what do you think the voltage across each one now is?

Let's consider the power question first, since it doesn't make sense as it stands. "to produce the same amount of power?" "If these lights were to be placed in series" You can't place the same lights in series to produce the same amount of power. Either you place different lights of a different power rating in series to produce the same amount of power as 4 x 60W bulbs in parallel or You place the same lights in series and obtain a different power.