studiot

What happens if you move the origin? ie use the substitution h = (z-1) Edit What aspect of complex analysis are you studying? I am guessing you are starting contour integration and Cauchy's Theorem? You need to carefully distinguish between a path in the complex plane and a function of a complex variable, which is what I described earlier. A path is a line or series of connected lines (curved or straight) in the complex plane. A contour is a piecewise smooth path. That is it is composed of a finite number of smooth paths. I assume you have done line integrals in real analysis?

Would you consider a man who wants to exclude knowledge from all other disciplines in his work wise or foolish?

Chemical engineers do not in general build instruments, they build or operate chemical plant and factories. All instruments are based on some scientific principle, usually physics or chemistry so a chemist or physicist will normally be part of the team that develops and manufactures chemical instrumentation and there are many companies in the field. The team will normally comprise experts from various disciplines. You will need to be strong in analytical and physical chemistry and possibly chemical microbiology for this career, rather than the cookery side. It is also good that your course teaches the other subjects you mentioned. It is important for one team expert to be able to have an understanding of what another needs and is talkng about. go well

This is a misconception. Watts are a unit of power, not energy. Power already incorporates time so watts per hour is meaningless. The unit of energy is the Joule. 1 Joule per second = 1 watt So 3600 Joules per hour = 1 watt. In electricity the quantity we call current also incorporates time so current time voltage = power amps times volts = watts So yes 4 x 0.5 = 2 x 1 = 2 watts. But see what EdEarl has said about your load and supplies. Note that most supplies set the voltage and the current is determined by the load. You cannot have a power supply that sets both at the same time. Does this help?

OK I have sketched my understanding of what you have told me so far and confirmed. Elementary wave AB has no beginning and no end. It passes through A and then through B and then continues on. Approaching A we have no information to allocate any marker so assume none. At impact with A the wave acquires an A marker. This remains until the instant of impact with the forward surface of B. I have labelled this SS. At this instant the B marker is substituted in the entire wave in section SS. I have drawn the wave with finite physical size since you have said this is so. The second two sketches show alternative impacts on B at section SS. The first section shows full impact so two points, C and D in the impact footprint impact at the same time (since I have drawn a plane surface perpendicular to the wave for convenience). The second shows the wave striking the surface only partially, with C impacting but D remaining in that section of the wave that hits nothing. But you have repeatedly stated two things. At the instant of C's impact the A marker is replaced by the B marker C and D are a finite distance apart That leads to the conclusion of instantaneous communication between C and D.

I'm sorry I should have said it depends on f(z) as well as the domain. This is because functions like sin(z) will pass go several times for some domains and not at all for others. There is a visual method of determining by inspection for common cases, but a bit long winded for a forum. Pages 130 - 133 of Complex Analysis by Stewart and Tall : Cambridge University Press does the job.

But that will surely depend upon the function, not the domain you pick it from. Say for instance f(z) maps to a single point in the vw plane. How many circuits of the origin is this?

Are you asking about winding number? A function of a complex variable requires two complex planes, not one. It is convention to designate these planes xy and vw. The xy plane or some subset of it (eg your circle or disk) is the domain and the vw plane is the co-domain or range of the mapping.

Reading back over this topic, I note someone identified diagrams as mathematic. I disagree. Diagrams are a discipline in themselves, which Mathematics, along with many other disciplines, makes good use of. Indeed so. However, looking at it from a fresh perspective, I would say you can't exclude Physics (and other sciences) from Mathematics. Applications provide a whole point, motivation, raison d'etre or what you will for all but a few diehard purists.

As a matter of interest how would we do that, say such a battery existed?

I think Mike has a valid point here that there is more to Science than mathematics, although I consider it extremely restrictive to exclude mathematics. It is a question of striking the right balance. I also like the example of the drunken man and the lamp post. In post#111 of another thread I offered the quick off the cuff example that IMHO has relevence here. http://www.scienceforums.net/index.php?app=core&module=search&do=user_activity&mid=74263 Note the emboldened part that offers a technical (scientific) issue that cannot be described by mathematics.

I didn't see any need for any timing device (like a 555) in your description. There are various contactless switches you can use which would be entirely independent of the main open/shut drive and controller. Messing with that may also invalidate the guarantee or service contract on the door. The other advantage of contactless circuit would be that it could be low voltage for safety. I don't know where you are, but I assume the States from your wording so look for proximity switch, 'magnetic switch' , hall effect switch, infrared switch, or mercury tilt switch at firms like Mouser or Digikey. The mercury tilt switch is good for an up and over door because it can be attached to the door and set to switch at almost any angle from vertical. It is a one part switch. All the other types I mentioned are two part. That is one part on the door and one part fixed on the ceiling, wall or floor. You should easily be able to get a cheap module that is ready made. Yes you could also use an infra red or light beam but they are less reliable and things can get in their way easily. go well

No you did not directly answer the question, this ‘answer’ avoids the issue. I’m sure you know that a ‘direct line’ refers to a geodesic in general relativity, not a straight one in the cartesian sense. So what? It is still the direct line from A to B. However the above implies that you accept general relativity. Do you also accept special relativity? Since we are accepting relativity into our model does relativity or TEW have primacy in any conflict of analysis? You found it necessary to introduce ‘rays’ when pushed about dimensions. Whether they are straight or slightly bent by general relativity is moot. However the gravitational warping of space in relativity theory is insufficient to create closed loop orbits in an atom that you claimed existed for TEWs to guide electrons around the nucleus. These are most definitely not ‘rays’. You still have not offered any answer or explanation to my question about these. Talking of atoms and mass, let us dissect the following response Firstly why must the ray either hit or miss B entirely? Why cannot there be partial coverage/ overlap? I can play a hosepipe on a wall corner so some of the stream hits the face squarely on and some passes along the face of the sidewall meeting at the corner. The dimensions of the stream are much less than that of the wall. Secondly since you have eschewed quantum mechanics in your propositions, you are not entitled to use any of the results from it. If you wish to claim there is a ‘smallest mass’ then you must introduce some other theory to account for it. In an earlier post I raised the issue of granularity. You replied that it was a good point but have not taken it further. Waves and wave theory are the theories of continuum mechanics, as is relativity. Quantum mechanics is a theory of granularity. I have asked you repeatedly not to keep saying, words to the effect ‘because Dr Little says’ It is only legitimate in this forum and thread to state what you think in comment of his words, not offer them as gospel, and that is what I am asking. Not to play some sort of Simon Says child’s game. Yet in your last post you divided up my post into four chunks and replied in effect “This is the policy statement from Little HQ" to each. I cannot really see the advantage of designating a wave at all. All it provides is a transmission medium for the ‘markers’, which do all the real work. Every time I want to look at properties inherent in or peculiar to waves you say I can’t do that particular aspect. Waves need an external agent to form rays or guided or focused forms, otherwise they spread into the available space (of whatever dimension). The difficulty with markers is the necessity of instantaneous communication across any distance This, in my view, presents a great difficulty for your theory. The transmission medium aspect could just as easily be accomplished by a stream or flux of ‘EM = elementary particles’, which has the advantage of not requiring external focusing agents. Or alternatively why not do away with the wave altogether and just have ‘markers’ flying about?

Noting Imatfaal response about a lost thread just now reminds me of the situation this morning when I logged in. There were about twenty 'users' with names from the alphabet soup kitchen, but not a single moderator at that time. There were also several pages of spam threads in "View New Content" I wonder if it is possible for moderators to activate a toggle so that when the last one logs off / on no new users can join / an or new threads (not posts) be started? I am sure that the current blizzard of spam is discouraging genuine users an I for one would would happy to put up with this small inconvenience for what would behopefully a temporary period.

It should be noted that hydrogen oxide has by far the greatest effect simply because its atmospheric concentration is so much higher than other greenhouse gasses.

Why is it suprising that I wish to take your axioms, or propositions and test them logically against each other? And why do you not answer a direct question whenever it is inconvenient? If the ray or wave or call it what you will has more than one single dimension then some part of it must, by definition, be off the direct line between A and B. If all parts of the ray or wave carry the marker from A then there must be parts that do not strike B. What marker do they carry an infinitesimal time after the ray has struck B? I am not trying to say your theory contracticts any conventional theory. But I am trying to get you to present it in a manner that does not contradict itself. A while back in this thread I said I cannot accept something just because you say so. I can accept even less appeal to someone not involved in this thread ie Dr Little. I don't care what he pronounces from on high, since I thought we were rational beings discussing an interesting proposition that you have presented to us. For all that I thank him for the original interesting idea. Surely we can jointly analyse it in the light of cold logic? Edit I don't mind whether TEW waves have one dimension, 3 dimensions or some private dimensions like strings. Whichever you choose, all I ask is that other propositions are logically consistent with that choice. Incidentally why are you against them being longitudinal waves?

God morning. A ray is a one dimensional entity. How do you square this with your statement that TEW waves are three dimensional? If you wish to have TEW waves comprised of vibrating one dimensional rays (shades of string theory?) that is brings its own implications. Unidimensional waves can only be longitudinal since they have no transverse dimensions to vibrate in. This might, however, form the basis of an explanation as to how they can avoid interference in general. The question arises how far apart your points B1 and B2 need to be to be distinguishable? Finally you have not understood my question about the ray approaching A. You have stated that the ray from A to B extends 'backwards' indefinitely from A. By backwards I mean away from B along the line BA produced. You have also stated that rays carying the A marker leave A in all directions. The ray leaving A along the line BA produced is exactly the same as the incoming ray, except for sign. ie it is going the opposite way along the same path. Further it is additional to any of the myriad rays passing through A in the normal manner you have already described. Why do they not destructively interfere?

And how do you obtain the amplitude from this complex number?

Enthalpy, haven't you got your pressure difference back to front ?

What exactly is your question? I am having trouble understanding your point about equilibrium or non equilibrium. I am very pleased that my house is in equilibrium so that it will not fall down around my ears and I am even more pleased that the Severn Bridge is in equilibrium when I cross the Severn so I do not get dumped half a mile out into the estuary. I am just as pleased that my pizza in the oven is in non equilibrium when I put it in, so it heats up for me to eat hot, rahter than cold. Did you by any chance interrupt the lesson or did you ask at the appropriate time?

Thank you for your answers. My purpose was not to challenge but to construct a model of TEW waves. The questions were all intended to further this process. The model is not yet at the stage where I can discuss Young's slits, though I would comment that they depend upon plane waves and you have stated that TEW waves are 3D. Back to the model and the light bulb within walls. Do the waves follow Huygen's principle? Consider the wave travelling from point A on the walls to point B on the bulb and carrying the marker from point A. Since the wave extends beyond B it should pick up a marker from material at B, but it is already carrying a marker from material at A and you say that a wave can carry only one marker. How is this resolved? Since the wave is 3D is must also pass through points C, D etc. In fact I assume the whole wave must carry the marker away from A? If this is the case, consider the situation where the wave front from A and carrying the maker from A reaches B. At this point it apparantly changes marker at B. What about the rest of the wavefront? What maker does it now carry? How fast does this change propagate through the wavefront?. What happens if the wavefront is very large so B and another point on the wavefront are many light years apart? If point C is the same distance from A as is B the wave will arrive at B and C simultaneously. If there is material at C as well as at B how will the wave decide which marker to carry, since it can carry only one? Again since the wave is 3D is must also travel away from A along the path AB of the wave you say is incoming towards A. Do these interfere destructively?

That is useful information. What are you actually studying and at what level. I had thought you were perhaps in the first year of engineering college, so I was trying to pitch my replies to suit this. This is why I my explanations were often in the form of questions, based on what I thought you should already know. It is good to see someone who is sufficiently enthusiastic to read further than the syllabus so I will try help. In post 9 I said that entropy was originally introduced for engineers to calculate energy changes, or to look them up in tables. These changes were for steam machinery. Many properties of entropy and other thermodynamic variables were not realised at first, the full story took half a century to develop. So when they introduced entropy S, all the analysis referred to cyclic processes. This stemmed from the fact that machines work in cycles. You input some heat, generate some steam, output some work, release the waste gasses, input some more heat (and water) to end up with more output work and so on and so on. Now the statement about entropy change always being greater than or equal to zero refers to a cyclic process, where what is known as the working fluid is taken from state A to state B and back again to state A. This is not the melting ice in my example which is simple the transition from state A to state B. Now the entropy change round a reversible cyclic process is zero. For an irreversible cycle the entropy change is always greater than zero (ie positive). So if we melt some ice then refreeze it we have a forward transition A to B and a reverse transition B to A, completing the cycle. This, as I said, is about as near to a reversible process as nature allows so the entropy change around the cycle is zero. (SB - SA) = - (SA - SB) So the entropy change is positive in the forward direction and numerically equal but negative in the reverse. Entropy changes for a simple change from state A to state B can be positive or negative. How are we doing now?

Do they only teach post WWII these days in history? Latin was the dominant language under Pax Roman and for some time afterwards. English became the dominant language under Pax Britannica And yes has continued so under Pax Americana Interestingly English was adopted as the official language of China in the 1950s, making it the official language of more than half the world's population, even if they don't all speak it.

A few calculations will help understanding and promote thinking in a themodynamic way. Concepts are no good to you if you only half understand them or get them wrong and calculations help test and improve your understanding. I asked questions associated with the calculation intended to do exactly this and you have ignored them. The whole point of my example is that it forms a very good platform for discussion of thermodynamic issues as we work through it. For example Instead you offer an incorrect statement, misapplied from somewhere else. In order to freeze the water, q is negative thus entropy is negative. Are you trying to tell me I can't freeze water?

If you can derive the equation you will know that it follows the Hamiltonian approach to mechanics, but introducing the quantum interpretation of momentum. This leads to a differential equation in the variation of a quantity we call [math]\Psi [/math] in space and time. Now, [math]\Psi [/math] is a complex quantity it is not real so has no physical reality. To obtain significance in the real world we multiply [math]\Psi [/math] by its complex conjugate and take the square root. This leads to a real number. If we normalise this by equating the integral over the entire space to 1 we obtain ajb's quantity such that we can interpret it as the probability of finding a particle between x and (x+dx) in one dimension. note [math]|\Psi | = \sqrt {\Psi {\Psi ^*}} [/math]