studiot

I'll say FYI the term 'soliton' is a contraction of the full definition 'solitary wave'

There is an alternative way to GPS, which doesn't work everywhere or vry well for real time speed control. There is an inherent time lag required for measurement. Sadly Boris and Co do not have the imagination for it, even though they are enchanted by major capital projects.

Yes this is true some physical science cannot be done mathematically, and we had a really good example of this in homework help just recently. Using such (rational) processes are also used to develop hypotheses which are later discarded if they are later found to be at odds with a mathematical one when such these become available. Both rationally proposed hypothesis and mathematical methods have to pass a further test, that of conformity with observation or they may still be discarded until further work is performed. Markus is offering lots of good, cogent thoughts and advice here. +1

The explanation is not short and simple, however much we might like it to be so. @wtf has offered a much more complete and modern answer than I did. +1 for that. It is not 'wrong' to consider 1 as a prime number, in fact some mathematicians still do so. But there are consequences to taking this view. For a thousand years or more everyone followed the ancient Greeks in allocating prime status to 1. However when complex numbers began to be investigated and accepted some difficulties with desirable algebraic structures began to emerge. This was subsequently generalised to the modern structure of abstract algebra including rings, ideals and so forth which was crystallised during the first half of the 20th century. The results of this structure have proved very useful in laying down the rules for all sorts of later developments including wolfram alpha and other symbolic structures you can ask questions of, coding and cyphers, and much more background theory. All at the 'cost' of excluding 1 from the primes. Eisenstein is the only example in the real numbers (including integers) I could think of. So the only way to get a full explanation is to study modern abstract algebra Did you understand why this theorem would not be allowable in a modern structure ?

Definition If a is a natural number then a isdivisible by 1 (the quotient bing a) and by a (the quotient being 1). Any factor of a other than 1 or a is called a proper factor. Any 'a' which has no proper factors is prime. Eisenstein's theorem. If p is a prime number, and a(x) = a0 + a1x + ...........anxn is any polynomial with integer coefficients such that (i) a0 is not divisible by p2. (ii) a1, a2....a(n-1) are each divisible by p (iii) an is not divisible by p then (x) has no proper factor with integer coefficients. This theorem would not hold if we allowed 1 to be prime.

I really have not the time for those who respond to a genuine offer of some mutually informative discussion by preaching back at them a whole load of nonsense.

Such a view was studied by mid 19th century scientists, in particular Stokes, searching for an aether. After Maxwell the relationship [math]c = \frac{1}{{\sqrt {{\varepsilon _0}{\mu _0}} }}[/math] was found. We have a more sophisticated view today. Also, of course, the aether was never considered as 'space' itself, but something that pervaded all space.

Plants require four things for seeds to grow into plants. Water Carbon dioxide Sunlight A few trace elements, mainly phosphorous. Rocks break down to finer particles by processes of weathering and particularly into their constituent minerals by chemical weathering. Basaltic rocks are most resistant, followed by granites. Volcanic lavas are much more loosely bound and break down more readily and quickly. So all the ingredients are there as soon as some phosphoric material and seed are available. As already noted bird droppings (guano) can supply this, otherwise.

Reading this more thoroughly I think the bottles must all contain white powders, not solutions as I originally thought. So you will have to make you own solutions. So you should add two further actions to your table: Solubility in water and solubility in dilute HCl. Are all the reagents listed going to be soluble in both ?

What have you done so far ? I would start by numbering the bottles A, B ,C, D and E. Then perhaps prepare a reaction table of combining small samples from all pairs of bottles.

This looks like homework to me ??

I think this was explained by someone it your last thread about infinity. I said there are many different types of infinity. Take the set of discrete (note the spelling) integers 0, 1, 2, ... This set is infinite because the sequence does not terminate. No member of the set is infinite, all the discrete integers are finite. The set does not 'contain' infinity ie does not have an infinite member. The set is not an integer, it is well .... a set.

First congratulations for looking at alternative proposals and trying to evaluate them. +1 Thre are many factors in play here so you probably haven't considered all of them. After all the experts tend to only consider a subset of the total facts. However some that you should give consideration to. The Earth is ball shaped not flat. So imagine a plate the size of North America moving. What direction is it moving in, on the curved surface of the ball ? You cannot say that Alaska, Washington and California are all moving bodily in the same direction or in a linear fashion. And what about Maryland on the other side ? What trajectory is it moving in? Yet that is so often what is depicted in the simple sections showing subduction, or else the mind of the viewer wrongly assumes this. Such motion as actually occurs induces sideways motion and rotation along much of the interface. These two facts alone make the task of reconstructing the eventual motion over hundreds of millions of years quite difficult to put it mildly. Much of the rheology of the processes are just our best guesses. Remember also the history of the development of the theories.Plate tectonics grew out of measured inconsistencies in continental drift, which itself had not long been confirmed.

I said intensity not direction. Just stop and think about this for a moment. Suppose there was such a thing as negative intensity of illumination. That would mean that any object or space that possessed this property could be illuminated without result until the illumination was strong enough to overcome this 'negative illumination'. Can you offer any examples of this ?

Have you not heard of absolute zero (of temperature) ? There is no such thing as negative intensity of illumination or intensity of sound, or any term in an equation that is a squared quantity. Just accept that you overreached yourself with that earlier silly statement that all quantities in Physics can be both negative and positive.

The temperature scale does not.

Wave and corpuscular hypotheses are competing interpretations of light. That doesn't make them mutually exclusive, that a significant point of QM. So can you demonstrate that Cop and MW are mutually exclusive ? Otherwise why does it matter that they' compete' ? Seems you understand neither of these imperfect interpretations enough to make these comments.

Markus and Joigus have offered some mathematical insights to uncertainty but it is also useful to know that both the maths and the physics say the same thing. Just as both maths and physics says that distance = speed x time, Maths offers this as an algebraic fact, whilst Physics considers the (physical) meaning of the variables and equations concerned, including the dimensional analysis of those variables and mathematical statements. So in Spectroscopy we observe that the single frequency line spectra are not actually perfectly single frequency, they are slightly blurred. This can be interpreted as the time taken for a system to actually perform the transition that absorbs or emits radiation.

You ae right that there are graphical methods that can solve polynomials, and other equations, to any required degree of accuracy. For polynomials Lills (1867) method is one such. But please get your definition of a polynomial expression. It is of the form anXn + a(n-1)X(n-1)+ a(n-2)X(n-2) ...........a0X + b Where the an, b are coefficients , not all zero Conventionally you would generate an equation by setting this polynomial expression equal to zero. Lills method was originally in French, An English version appears in Theory of Equations, Turnbull, 1939 along with other methods of dealing with polynomials eg that of Horner's reduction of of degree. Lills method is also dealt with at great length by Cremona Graphical Calculus and Reciprocal figures. This also deals with a whole raft of graphical methods. The original 1888 translation book was in Italian but has been translated to English in 1977 by Beare. Finally Ewart (1919) Elements of Graphic Dynamics also deals with this and other useful subjects such as graphical integration and graphical differentiation.

Yes QM is still very much a work in progress/unfinished business. +1

Partial molar quantities can also be represented by partial pressures. The truth is that for extensive properties ( do you understand this term ?) like volume, mass, energy, entropy the partial (or specific) properties are additive. So specific volume, molar volume, specific energy etc are additive. Such properties are all represented by an overbar. Since you are doing this in relation to partial properties are you doing the calculus of this ? I'm sorry, I missed the molar bit first time round.

Thank you. Yes, you are correct the change in Gibbs free energy tell us whether a process (including a chemical reaction) is thermodynamically feasible without outside assistance. (ie spontaneity) But the statement of any form of energy, internal energy, heat energy, specific heat, work etc is meaningless without relating it to to something. There is twice as much energy in 2kg or 2 moles of something as in 1kg or 1 mole. So relating it to the number of moles makes no difference to its significance to this fact. You have correctly identified that delta G has to be negative for a reaction to be able proceed of its own accord, A good answer would include the meaning of the negative sign. A very good answer would include a note as to whether this means the reaction would necessarily proceed or if any other factor might be involved. Does this help ?

Isn't that the Enthalpy ? 'Free energy' includes an entropic contribution.

This is in homework help. So I can't answer the question directly - is this really a homework question or are you actually seeking an explanation ? Also you have asked for the 'thermodynamic meaning' - whatever that is. Thermodynamically, working 'per mole' is a method of quantifying that is very convenient, particularly in Chemistry. In Physics and Engineering quantitative calculations are often carried out 'per kg' or even 'per container full' But in Electrochemistry we obtain the full benefit of working 'per mole' since 1 mole of charge is 1 coulomb of electricity. So per mole units can be directly converted to the Electrochemistry of cells, half cells and even reactions via the Nernst equation, Faraday's Laws etc. Please tell us more about the background to this question.

That's a shame, they have obviously taken them down very recently. I went to the website and copy/pasted the link in from my address bar make my last post. Edit No they are still there try again, though 1 has gone awol. (I see I somehow lost an R) http://www.umsl.edu/~chickosj/c365/lectureNMR2.pdf