studiot

Here is the next stage of my reasoning; I have already indicated that A must be 1 or 2. Now consider multiplying E by 4. E is the only digit that does not entail a potential carry digit, so the result of the multiplication of the whole number by 4 has the same last digit as 4E. The result of the multiplication must end in either 1 or 2, since the last digit of 4E = A But there is no number such that the last digit of 4E can be 1 so A must = 2. So 4E ends in 2. There (4x3=12) and (4x8=32) both end in 2 so E is either 3 or 8 Since A = 2; (4A + carry from 4B) can only be 8 or 9, But we are told the leading digit is E so E = 8. Since E = 8 there is no carry on multiplying B by 4, so B must be either 0, 1 or 2

Sorry it's so scruffy, but assuming your stator field is rotating anticlockwise and the instantaneous mag field is as shown; The induced current in the cage wires (shown in section as small circles around the rotor periphery) are given by the right hand rule, crosses into the paper and dots coming out of the paper. The current in a rotor conductor generates a circular field round it, like any current carrying conductor, which reinforces the statorfield on the right and weakens it on the left of the conductor. This is equivalent to a force turning the rotor in the same direction as the stator field rotates. This jiggle in the field is shown in diagram 2.

I'm sorry but you cannot legitmately pick and choose what energies you will include or not include in your energy balance. Work is done on a rising body by the force causing it to rise. The force causing it to rise is not a single force but the resultant of the vector addition of several forces. Some of this work goes into the kinetic energy of vertical motion. (did you remember that?) Some goes into the increased gravitational energy. If the body is not rising there is another force acting, which is the equilibrant to the lifting resultant. Similarly if the body is in level flight the drag will be doing work on the air, leaking kinetic energy away to the air. This KE is maintained by the power of the engine supplying the thrust, which does work on the body. So the engine is continually supplying energy to the body. This energy supply is enough to also power any vertical gain in PE or KE that happens, but the exchange is via the kinetic energy of the body. So there is no energy balance crisis. If the thrust ceases then the body will eventually fall, not rise. It may be possible to temporarily take advantage of the combined lift and drag vectors and upwelling air to glide for a considerable distance. But the glider will eventually return to earth.

No problem with the frictionless model. I wondered if you were thinking of an airfoil mounted on some sort of jet or rocket sled. But remember MigL's four horsemen: Horseman 1 The sled's weight has to be added to the foil's weight. That immediately makes the rising foil different from the non rising one. Horseman 2 You cannot ignore thrust Horseman3 Yes some effort is lost in drag. This energy loss heats the air Horseman4 Whatever is left over becomes lift. HiHo Silver! I'm trying to concentrate on the major parts and keep out the difficult bits.

Sometimes doing an energy balance make things easier, sometimes it makes them more difficult. In the case of flight, energy balances are not as helpful as direct consideration of the forces involved. Much of what you say is correct, but your description of the held down airfoil is lacking. What holds it down? You need to include any hold down forces acting in your analysis. You have shown the 'non-rising' airfoil as moving forwards. How is it driven forwards at the same time as being held down? Address this and you will find the resting place of your misplaced energy. Bouyancy forces act on immersed bodies whether they are moving or not, but they are additional to any lift forces that act due to the motional interaction of the fluid and the body. For most practical airfoils bouyancy forces are small to negligable compared to the weight of the foil, but in hydrofoils they can be significant.

A hypothetically perfect engine is called a carnot engine, and carnot engines cannot produce motion without also producing heat, unless they violate the Second Law. We are happy to disuss and help you resolve your questions, but since we know more physics than you do, how about letting us suggest things? For instance there is nothing wrong with considering your ball thrown into the air as an isolated system, in fact it is an excellent model for many purposes. But then your ball does not posses a jet engine and a fuel tank. The important thing is to know where to draw your boundary around your system. A good choice makes the analyis (relatively) simple. So perhaps you would be kind enough to reiterate your question in plain terms, shorn of all the extra paragraphs you started with.

Another misconception is your use of the term bouyant force. The aerofoil is subject to bouyancy forces, but these are nothing to do with the lift and drag forces generated by airfoil action.

Specifying the whole universe as your isolated system offers more difficulties than it solves. Not least being that we do not know is the universe is finite or infinite. If infinite standard conservation has no meaning. Incidentally you need to be careful saying you understand The First Law (conservation) and then producing statements like this one. I always thought that the large part of the chemical energy went into heat in an engine of any sort.

Indeed it is. Do you know the full principle? In any isolated system total system energy is conserved. So what is your isolated system? You did ask where your thinking was going awry. Incorrectly specifying the system is a very common error.

Why do you think energy must be preserved? Isn't a continual input of energy the job of the engine?

There's invariably more than one method in these things and the real fun comes in seeing how someone else has done it.

Not at all, why do people always assume the worst of others? Being old fashioned I asked because I wanted to know the answer. I think equivalence relations has relevence to the subject of tautologies, but need go no further if you already understand this.

Do you understand the mathematical concept and application of equivalence relations?

Thank you swansont for sorting my spoiler. Robbitybob, It is not necessary to know if all the digits are unique in order to solve this one. You can work on this one from the outside in, like peeling an onion, First A, then E, then B then............................. Thank you commander for a neat problem, I assume you have established a set of simultaneous equations as a method since you mention the general case. +1 will head you off into the right direction (the green) I look forward to more useful and entertaining posts in the future.

Fiveworlds, since both have 5 digits A cannot be greater than 2 ie A = 0 or A = 1 or A = 2 A=0 leads to the trivial solution (00000) x 4 = (00000), there are no other solutions containing zero.

I'm not sure what your prof means but the resting potential of neurons is not 10mV. http://en.wikipedia.org/wiki/Resting_potential#Generation_of_the_resting_potential

No one is accusing you of 'borrowing' anything. You would not be the first to independently discover something already known elsewhere so all credit for that. However I am suprised that since you put that effort into this subject you seem uninterested and defensive when someone else points to what others have also found in the same subject.

Not quite. I'm suggesting that there is a wealth of previous human experience out there and offering some, because it's probably happened before more than once. Don't undervalue theoretical physics, the ability to think logically is valued in all sorts of fields, besides theoretical physics. One of my contemporaries (now a millionaire) was told when he applied to a firm of accounts to start accountancy training "We prefer entrants with a technical background such as yours, we find they make better high level professionals"

Just to clarify a point. You are presenting part of the real zeta function, which is upper schoolboy/entry university stuff. eg Mathematical Analysis : Quadling : Oxford University Press. The series [math]\sum {\frac{1}{{{r^k}}}} [/math] Where is is a positive integer not equal to zero. is convergent for all [math]k > 1[/math] and divergent for all [math]k \le 1[/math]

I did read the next line, as well as the document, and decided that, as written, it was at best ambiguous, but strictly referred to only to the second part of the sentence I quoted and not the first. That is it only referred to "all possible integers that come after 1" as demonstrated in your document. So strictly your statement "all possible powers" includes 1 and so I respectfully suggested you amend it. Note I have not argued for or against your thesis, like Ophiolite, only asked what you want us to disuss about it.

Students (like everyone else) suffer a wide range of personal issues, but one of their biggest problems is the tendency to think they are unique and that whatever it is has never happened to anyone else. This is an observation, not a criticism, and I think it is due to youthful lack of general experience of the world. I originally started the wrong course at the wrong university due to this and the experience certainly affected my career. My brother in law studied Electronic Engineering at Liverpool, where all technical subjects are highly mathematical and theoretical. He came out well and went straight into a large multinational where he thrived. Another friend studied Physics at Liverpool, but left after year 1 because he could not hack the mathematics. He later completed a London External in Physics at Portsmouth, where they are much more hands on than theoretical. He also left and joined a large multinational, where he also thrived. I would suggest that at least part of your question is best dealt with by PM.

1) You should be more careful with your wording since this is not quite true The infinite series [math]\frac{1}{{{2^1}}} + \frac{1}{{{3^1}}} + \frac{1}{{{4^1}}}....................................[/math] is divergent, although it conforms strictly to your above wording., which therefore needs to be changed to exclude exceptions. 2) Since there is speculation in this post I expect it will be moved to the speculations forum where it belongs. 3) Like Ophiolite I am confused as to what aspect of your paper you want to discuss. If you want to connect it to quantum theory then say so, but be aware that your late countryman and genius (Ramanujan) did this many years ago. 4) There is considerable evidence that all creatures except one use the same chemical reactions and colour receptors to detect colours so only those with a neurological abnormality will see red as green or blue.

Only if we return to the topic?

You said Which means they are reflexive or work both ways. Your gave a definition of a bachelor If I can find an unmarried man who is not a bachelor your definition is not a tautology since it is not reflexive. Since I can find an unmarried man (a widower) who is not a bachelor, the relationship is not reflexive and therefore not a tautology. Therefore your definition is not a definition, or it is defective, or your claim that a definition is a tautology is untrue. Suprisingly this refutation of an off-topic example, invokes time (on topic) since time is necessary for a man who was once a bachelor to become married and then widowed.

If you must construct examples please at least make sure that your use of the terms is correct. All (male in modern parlance) bachelors are men, true but Not all unmarried men are bachelors. So where is the tautology?