studiot

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

Here are a series of lectures you can donwload in pdf. Be warned it's the full monty - pretty advanced stuff www.umsl.edu/~chickosj/c365/lectureNM2.pdf just change the NM2 to NM3 , 4 etc up to 7.

You have posted in the chemistry section and also asked about the implications for drug molecules. So physical properties such as optical rotation of polarisation are not important here. We are looking at chemical properties. This is important because we are no longer talking about one molecule here but two or more molecules and the effect on their (chemical) interaction. This is the significance you were seeking. Enantiomers arise when the configuration of a molecule is such that it is chiral or posseses 'handedness'. The left and right handed versions are called enantiomers. One is the enantiomer of the other. Since we are talking about at least two different molecules for a chemical reaction, we must recognise that either or both can be chiral and possess two enantiomers. I will call the first molecule the reagent molecule and the second the environment molecule. So with a chiral reagent we have two situations: A chiral reagent and a non chiral environment : Fig1 A chiral reagent and a chiral environment : Fig2 I hope you understand the 3D notation for the configuration of the molecules ask if you do not. I suggest you use sensei's models if you have access to them or make your own with potatoes and cocktail sticks. You will see that the functional groups on the enantiomers of the different molecules line up differently for a chiral environment, so will react differently. but for a non chiral environment both reagent enantiomers line up the same so will react the same.

I would be very grateful if you would review / explain this sentence.

Then you will have to have another one. It doesn't hurt. Hundreds of millions now have the ordinary flu vaccine annually without problem, but to general benefit.

Respectfully, I think you have misremembered this one. Coancave mirrors have the capability of focusing incident light. https://en.wikipedia.org/wiki/Curved_mirror

Firstly further observation would be useful. A fuller description of the wobble for instance. Does the fan still go round smoothly, even if it wobbles ? Or does it clunk and bump and hesitate at some point in its travel? If the blades hesitate or bump against something , perhaps a dead fly or grit has got into the mechanism and is causing this. Alternatively if there are too few poles on the motor the drive may actually be a series of pulses driving it round and if there is too long a time gap between pulses the rotational inertia will not be enough to keep the blade speed even at low speed. If however the blades just wobble then perhaps this is a similar effect to the reason you cannot stay upright on a stationary bicycle: in fact the faster you go the more stable you are. This effect is due to the increase of rotational inertia (the flywheel effect) stabilising above a certain speed.. As to your question of air disturbance, yes this is a fair one. I assume the fan in inside a room. Inside the room the distance to the walls, corners, openings etc will vary as the blade goes round. You say that air is still directed down from the centre of the fan. For this to happen, air must be drawn in sideways (horizontally) and, as just noted, the air path for this air will be different as the blade rotates. So the blade will encounter a varying air resistance as it goes round. Again this may be stabilised by rotational inertia. Finally, as others have said, the bearings may have worn sloppy, permitting the wobble which again will tend to centre itself at higher speed due to rotational inertia.

I presume this was an answer to my question Well here is what I think about this : [math]\begin{array}{*{20}{c}} 1 \hfill & 2 \hfill & 3 \hfill & 4 \hfill & 5 \hfill \\ 1 \hfill & 4 \hfill & 9 \hfill & {16} \hfill & {25} \hfill \\ \end{array}[/math] The top row is made up of the natural counting numbers. So the count of these numbers is the same as the largest number. In my example there are 5 numbers in the top row and the count of numbers is also 5. In the second row which are simply the squares of these numbers, there are also 5 numbers But the they are all larger than the corresponding number in the top row (except for the 1). So whatever might be the largest number in the top row as it is extended, there is always a larger number in the bottom row. This larger number is also a simple integer and so whatever number you propose as the 'end' number of of the top row is not the largest integer and not the end of the row. That is the process of counting has no end. This is called a non terminating infinity. It is also interesting to note that the bottom row does not include all the numbers in the top row; it does not contain 2,3 or 5 or other top row numbers if it is extended. Yet for every top row number there is an entry in the bottom row so the count is the same in both top and bottom rows. There is the same count of numbers of the bottom row as for the top row. This property is called the cardinality. Cardinality is very important in comparing infinities. This is a truly remarkable property of infinities. It is important to stay focused with this stuff and not mind-hop to many disparate subjects.

Well I think this is a perfectly reasonable question and a good one to discuss. Also I think this is much better put than recent posts (though I would have liked the picture the right way round). +1 for encouragement to do more of this and start wiping out those red ones. Perhaps you will notice that there are actually two (or is it three with the negatives) infinities going one here. There are the numbers being suqred, which are increasing one at a time 0,1,2,3... and there are the squares themselves 0,1,4,9... Which are increasing much quickly. What do you think about this ?

Just you ? No way. I claim first dibs on that.

Now you are in a better frame of mind, perhaps you are ready to return to one of your many Science questions and view the updates. Perhaps the infinity one ?

I think his point is "What two locations ?"

That would indeed be a correct common use (in Thermodynamics and Physical Chemistry) use for co-exist. Nice example +1 Another might be the co-existence of isotopes which account for the observation that measured atomic weights are often not whole numbers.

Nicely put. +1 Since you didn't follow the above I will try to put it another way. There is more than one infinity, in fact there are many infinities. And every infinity has its own unique properties as well as those it might share with (some) other infinities The word infinity is like the word sheep. It is used to refer to either a whole flock of sheep and also a particular member of that flock. If you need to be specific, you need extra words to identify which particular sheep you mean. It is the same for infinities. Many so called paradoxes arise because of failure to add these extra distinguishing words.

This issue, in Relativity, is complicated by the nature of the the subject. Here is a short extract from Professor Schrodinger's explanation of 'the metric' in his book on the subject. The book is not a textbook of Relativity, more of a commentary which contains some definite insights as might be expected from a Professor of Applied maths. I have marked just such an insight.

Since you have given us no idea of the level of you understanding of Mathematics I will have to give a general answer. Mathematically, evolution is a dynamical system. There is substantial math for dynamical systems of all sorts. Probably the best place to start would be the so callled predator - prey equations, which can include chaotic solutions. https://mathworld.wolfram.com/Lotka-VolterraEquations.html

So within the stated operating distance range of your thermometer it reads 36.7o ± 0.1o. Is the resolution of your instrument 0.1o ? Then your readings would be within calibration.

There will be an optimal range of distances for which a given instrument is designed. Outside of this erroneous readings may be expected. Have you read the manufacturer's instructions for your particular instrument ?

Yes they do compensate for distance . Read here how. https://www.grainger.com/know-how/equipment-information/kh-370-infrared-thermometers-qt Scroll down to the paragraph headed Using an Infrared Thermometer: Understanding Field of View and D:S Ratio

So how about attempting my question What happens if you (repeatedly) square something less than 1 ? What happens if you square (repeatedly) something greater than 1 ? What happens if you square (repeatedly) something equal to 1 ?

Edit my apologies the cut, paste and edit gremlin strikes again. This should be A repeated square root is convergent (for initial numbers greater than 1) as each time you take a square root the result is smaller than before. A repeated square root is also convergent (for initial numbers less than 1) although each time you take a square root the result is greater than before, the final result (1) is bounded as Ahmet said. A repeated square root is neither convergent nor divergent (for initial number is equal to 1) as each time you take a square root the result is the same as before.

Heretic

No one with any sense will make no attempt to test a model. It may not be possible to match the model against the actual thing being modelled (perhaps like my dam because it does not yet exist) or perhaps because it pertains to conditions we cannot achieve on Earth such as processes with a star. But, it makes sense to 'test' the model under simpler known conditions and hope that the extrapolation will hold true. We try to (or should ?) recognise when we do this that extrapolation is more likely to be in error than interpolation. A model may be physical (hydraulic ones often are) or theoretical as you describe. Is that a problem ?

I think I understand your question. Unfortunately you have confused everyone else and probably yourself with your additional remarks which are totally irrelevent. So please start another thread inquiring about units and dimensions. You are asking about what I call continued or repeated exponentiation and the American Mathematical Society calls infinite exponentials see here. https://www.math.usm.edu/lee/BarrowInfiniteExponentials.pdf This is following on from the idea of repeated addition (the sigma symbol) repeated product (the Pi symbol) Continuous division Continuous square rooting and so on. Now further information A repeated process can be convergent (the result of each repeat is smaller and smaller) or divergent (the result of each repeat is larger and large) or neither. A repeated square root is convergent (for initial numbers greater than 1) as each time you take a square root the result is smaller than before. A repeated square root is convergent (for initial numbers less than 1) as each time you take a square root the result is greater than before. A repeated square root is neither convergent nor divergent (for initial number is equal to 1) as each time you take a square root the result is the same as before. Can you look at your squaring process and make the same sort of analysis - it is a worthwhile exercise for you . All these processes involve infinity in some way since they could involve an infinite count of repetitions. But only some (divergent processes) involve an infinite result. For most processes it is possible to devise conditions where one of the three alternatives (for the results) holds sway for an infinite count of repetitions. Does this help ?