DQW

Explain what about them ? They have already been explained. "Thought to be" ? By who ? There is no ordinality (first, second, third, etc) among dimensions. And even if there were, then the second spatial dimension, as well as the third, fourth or fifth, would all be single dimensional. The "second dimension" is not a plane (it is the plane which is a two-dimensional object). It is a dimension like the first, but orthogonal to it and the others. In n-dimensional Euclidean space, all these dimensions are identical and orthogonal. The space in which string theories (as well as GR) work, however, is not Euclidean; and the symmetry between dimensions id broken by their curvatures, which can be specified to not be identical. Indeed, in string theories, the curvatures of the spatial dimensions other than the 3 we can relate to are said to be extremely high. Mathematically speaking, a point is infinitesimal. A line is an infinite set of such points that satisfy certain properties. A point is certainly not imaginary - it is perfectly well-defined. The spot you make with a marker on a white-board has nothing to do with a point, and must not be confused with it. What's a real point ? Do you mean the one that is defined mathematically as a 0-dimensional object, which can be specified in n-dimensional space using n coordinates ? And what doesn't a real point ? Now you are using terminology that you've just cooked up to talk about well-defined mathematical objects. If you are using new terminology, you had better first define what these terms mean. In math, points do not have "markers"; the only thing that can be said about a point is its location with repect to other fixed points, using any of several possible co-ordinate (Cartesian, Spherical, Cylindrical, etc.) systems. A "dot" is not a mathematical object either. So, are you suggesting that a "dot" is a "marker" for a point ? And this "dot/marker" does what ? Have two dimensions like a plane ? And if it does, what does that do ? You do not seem to return to the "dot/marker" after this, so there must be some moral learned from the "dot/marker" having two dimensions. What is the moral and how is it useful ? The latter is true, the former is not a mathematical statement. Please define "expand"...or are you doing that in the next part of this sentence ? Okay, I'll take this as your definition of expansion, but you have not specified where you add another point (at what location/co-ordinates), so it would seem that this is not a required detail for an expansion. How ? I only see a pair of points. Where is the line ? Are you talking about the line made by including all the points that are "between" these two ? The act of expanding to two or three or four (or any integral number of) points does not create a line by itself. You have to do other things too (making the "expansion" virtually irrelevent to the transition from a point to a line). Or are you suggesting that a pair of points (arranged in some specific manner, not yet specified by you) constitutes a line. If you are, then you're mistaken. A line (segment) is a continuum (or a compact, connected space) of points, and hence contains an infinite number of points. Now how did all of this explain the "other dimensions" ? Maybe I just don't understand...

Looks like were talking terminating decimals of length 15 digits or smaller. Identifying repeating chunks should not be too hard. Something like the following should work, I'd think : k=0 while ch=false k = k+1 { for i = k+1 to 15 { If N = N[k] then { P=1 d= i-k for j = i to 15 { P = P*(N[j] - N[j+d]) } If P = 0 then ch=true } } }

Phosphorus - though I think that's restricted, and hence hard to get.

One can, however, evaluate the definite integral numberically. One can also say that [imath]\int x^x dx = bling(x) [/imath], where bling is a function that is equal to this integral.

It's the component of the wind velocity along the direction of interest that you want [imath]c_w cos \theta [/imath]. For a perpendicular wind, there should be no effect, according to this simplistic theory. There may be lower order effects, and also, winds are never in laminar flow, so the provided expression is only an approximation.

Wow YT...I'd better consult you, the next time I buy chemicals. We usually buy stuff from Fishersci or VWR, and you wouldn't get 500g for less than 40 bucks from either.

This is pretty well established. The speed of sound in a wind is greater than the speed of sound in still air by the component of the wind velocity along the direction of propagation. This effect will Doppler Shift the frequency of the sound, just as a moving observer would. [math]f(wind~blowing~toward~you)=f(no~wind) \frac {c+c_w} {c} [/math] [math]f(wind~blowing~away~from~you)=f(no~wind) \frac {c-c_w} {c} [/math]

If by "for gravity to work" you mean "for a pair of particles to influence each other's state" (described by a Lagrangian, say), then I'm not sure how your statement can be true. However, this is not something I'm terribly familiar with, other than knowing that QG was itself abandoned because it was not renormalizable. I think higher than second order corrections led to divergences that no one could make go away (at least, not until LQG came along). In any case, I think QG was abandoned when string theories came along that would be renormalizable, and they predicted a spin 2 massless boson ! Now, however, LQG seems to be quite hot.

Thanks 5614, blike and ophio ! Ophio, as far as pure WC is concerned, everything I know about it will likely fit inside a single page. Of cource I can draw extrapolations from the general mechanical behavior of carbides and similar ceramics with low fracture toughness, but if you want to know whether I have done anything specific with WC, here's my answer. I have looked a little bit into HVOF spray coatings using WC/Co. These are very popular in the aeronautical (and tooling) industry, for their exceptional wear resistance. Embedding the WC particles in a Co matrix (we are talking about a cermet here) greatly improves the fracture toughness (and ductility). In fact, I don't know that pure WC gets used for very much. I have also recently heard something about improving the fracture toughness by making the material nanocrystalline. But I really just came across this once, some time ago, and never followed up, so I'm not even sure if it is done only for WC/Co or even for plain WC. You could try Gooling it, unless of course, this is all old hat to you. I shall too, when I find the time. In any case, if you have a specific question, go ahead and post away. I most likely wouldn't be much help, but there's nothing lost in asking, is there ? Besides, there's might be several members that are experts in carbides, tooling or such.

While that last clause is true, the previous parts are not really accurate. Spin dependent transport is a very active field of study in solid state physics and materials science; especially now, with the applications that spintronic devices have in building sensors, RAM chips and hard drives. Pat: You probably know that electrons have a property called spin, that is responsible for the magnetic behavior of materials. When the spins of neighboring atoms interact with each other, you have ferromagnetism (FM - where all the atomic spins want to point the same way, say up) or anti-ferromagnetism (AFM - where the spins want to be alternatively up and down in a crystal). Now, electrical conduction is a process where the electrons hop from one atom to another (loosely speaking; but this is truer in semiconductors and insulators than in metals). The spin of this particular (valence) electron is forced to be a certain way (either up or down), depending of the spins of all the other valence electrons in that atom. (See Hund's Rules and the Pauli Exclusion Principle). So, when the electron hops from one atom to another, the ease of hopping depends on the spins of the valence electrons in those neighboring atoms. So, for instance, it might only be possible for the electron to hop if the neighboring atom was aligned the same way (ie: the material is ferromagnetic). In other rare cases (look up Superexchange), having an AFM ordering might help with the hopping. This is essentially what spin dependent transport is about. In the context of spintronics, one is particularly interested in a phenomenon called Giant Magnetoresistance (GMR), where just as described above, the resistance of an interface between two materials depends on whether the spins on either side are alined or unaligned. If the spins are lined up the same way (this can be done for a ferromagnet, by appliying a magnetic field) on both sides, the electrons find it easy to jump across, and so the interface has a low resistivity. If the spins are misaligned or anti-aligned, it's very hard for the electrons to be happy after jumping across - so they don't, making the resitance of the interface large. That's briefly what spin dependent transport is about. What follows now is a slight digression, based on something said earlier in this thread. If you said this (as a matter of fact) to a condensed matter physicist, you will evoke the strongest expression of surprise and bewilderment (disbelief, most likely though) that you've seen in a while. There is no existing mechanism by which the spin state (at the Fermi surface or equivalent) determines the polarity of transport. In fact, such a thing would be considered extremely bizarre - especially since no one has observed such a behavior... ...until fairly recently ! One American (Gramila, et al) and one German (von Klitzing, et al) group have each independently measured what is now called "negative coulomb drag" in double quantum well structures in the Quantum Hall regime. Only in this very special phenomenon does the spin state appear to affect the polarity of transport - and to date, there is no good theory that explains this bizarreness !

Hey, I apologize for being a grumpy ol fart. The archaic usage of the term 'screw gauge' (for a 'mic') is a remnant from Imperial terminology that still exists today in the UK and some of its erstwhile colonies, including right here in the US. Try asking some of the older machinists in your shop - they will remember the name.

Please look up "exchange particles"... and note the use of the word 'exchange'.

If you want lab grade ammonium nitrate, that is indeed a good price - unfortunately, that page does not spec purity, so it's hard to make a good judgement. If that's better than 98% purity, I'd say that's not a bad price at all.

Yikes ! What a mess ! Crash/Benson : you are both wrong (as is the person that provided the OP with the quoted ionic equation). Where on earth do you see Calcium in a +1 oxidation state ? It only exhibits the +2 oxidation state in ionic form. In any case, neither of these is what applies to the OP's question. I quote : The question is talking about Calcium metal - not Ca2+ and certainly not a fictitious Ca+. In other words, the question reads : [math]x~Ca + y~Sc^{3+} \longrightarrow~? [/math] To the OP : Solve and balance the above reaction, using the fact that Calcium is more electropositive (more active) than Scandium. If you wish to convince yourself that this is true, look up an activity series table or a table of standard reduction potentials. Simply put, Calcium has a greater tendency to lose its valence electrons than Scandium, so it will simply dump its excess electrons onto Scandium, and make itself happy at the cost of the happiness of Scandium. Incidentally, the mentioned reaction is the most commonly used method for the production of pure Scandium metal. Also, albert, if you have a complete question, post the complete question. Holding back information does nothing but allow room for misinterpretation and confusion, and it could end up wasting the precious time put in by the responders, if an important piece of data were omitted. In general, not posting all the available details is extremely bad form. You are asking the question and others are doing you a favor by answering. The burden is on you to make the job easier for them, lest you tick them off for good. Jdurg, Borek,.... where are you ?

I'm new here, so I thought I'll say 'Hi'. I hope to clear up misconceptions and answers questions in physics, materials science/engg and physical/theoretical/quantum chemistry.

I don't understand the relevance of this part of the post to the OP's query (which, I must say is too vague to answer specifically). The question was about micrometer (screw) gauges, not thread gauges or screw threads. Don't machinists refer to micrometers as screw gauges anymore ? Or you can halve it and subtract it from the radius. But either way, you will end up with a wrong answer - your number will be an underestimate because the threads are not sharp on the major dia (ie : the profiles are not complete equilateral triangles; the tops are chopped off), and without a knowledge of the exact profile (or the amount of flattening on the major dia) you can not calculate the minor diameter. So instead, you look up a table, like this one. To the OP : Coquina's second link tells you how to understand what a traditional vernier reads at a certain position. A screw guage (or micrometer) is easier to understand than a vernier caliper. Both are explained here : http://www.phy.uct.ac.za/courses/c1lab/vernier1.html

No, that's not right. You would be in DC earlier than you left New York, according to an observer at rest on earth. But of course, you haven't specified the rate at which the person slows down to a stop and then chenges direction, so the time interval can be tuned. If it did take a nano-second, that would make it a billion times a second. You know at an average speed of 1 m/s I can shuttle back and forth between two points a billion times a second, if the points are a nanometer apart. To an outside observer, it would seem like .... Yes. I understand that your head hurts ! Give it a rest.

Phew ! At least someone got the answer right. But why are folks providing complete (at least one person has) solutions, when the OP has shown no original effort ? To the OP : Please show anything that you have tried or any ideas you have. You won't gain much by having others do your homework for you. Fortunately, there are enough wrong answers here that the correct solution is not yet revealed. What do you think are the steps you must take; and what important properties must you take advantage of ? To Dave/matt : Is this kind of thing the norm here ?

This argument is backwards. It is because there are 360 degrees in a complete revolution that each degree takes 15 minutes to traverse. There really is no further need for "here's what I think is the reason..." posts. Matt, Lyssia and Dave have essentially revealed the likely historical reasons for the choice : (i) 360 is very divisible; (ii) The Sumerians worked with base 60 and the Egyptians sometimes used base 12. One or the other of these folks likely came up with the 360 degree angle for a complete revolution; (iii) The solar year may have thought to have had 360 days.

I don't understand what you mean by that, so it might take a picture to make your idea more clear; but here's what I have to say, nevertheless : 1. Why are you so hooked on Bi (yes it has a fairly high diamagnetic susceptibility compared to most elemental diamagnets, but it is still 4 orders of magnitude smaller than that of a superconductor) ? 2. Using even a "real monopole" (which will have a pole strength that's 4 orders of magnitude higher than anything that can be got from Bi shielding) from the best permanent magnets in existence (like an NdFeB magnet), the interaction energy with the terrestrial field (which is incredibly weak) is about 3 mJ/kg. U(magnetic) = 0.003M J U(grav) = Mgh = 9.8Mh J Comparing the two, it looks like you can achieve a launch height of about 0.3 millimeters. This is 10,000 times higher than you can get with Bi, even if your shielding did create a mononpole effect. So the idea is just not feasible.

More links : "The Search for the Top Quark", from Fermilab http://www-ed.fnal.gov/samplers/hsphys/activities/student/index.html http://www-ed.fnal.gov/samplers/hsphys/activities/student/resources.shtml

Neither is the bottom one (even filling in the open square) ! Simply put [imath]2/5 \neq 3/8[/imath]

I think you mean [imath]a = b = 1/\sqrt{2} [/imath] and [imath]\sqrt{i} = 1/\sqrt{2} + i/\sqrt{2}[/imath]

Often, you could use a binomial approximation (as suggested previously) : choose the nearest perfect square to x; let it be n2, where n is some convenient rational or known square root. Let x = n2 + d, where |d| << n2 Then [math]\sqrt{x} = \sqrt{n^2 + d} = n*\sqrt{1 + \frac{d}{n^2}} \approx n*(1+ \frac{d}{2n^2}) [/math]