studiot

From this paper A flow reactor setup for photochemistry of biphasic gas/liquid reactions Article in Beilstein Journal of Organic Chemistry · August 2016 DOI: 10.3762/bjoc.12.170 3 authors, including: Axel Jacobi von Wangelin University of Hamburg

Adding some figures Visible light lies within the range 400 THz to 800 THz A typical red LED has a (peak) frequency of 474 THz and blue has 669 THz This makes the sum frequency 1183 THz ie > 800THz and the difference frequency 195 THz ie < 400 THz.

This is a key statement. Neither the sum nor the difference frequencies/wavelengths resulting from a heterodyining process will be anywhere near the visible spectrum. This is unlike radio waves where the results may still be in the radio spectrum. Although even there we can get audible 'heterodyne whistles'.

There is no problem with defining 'square roots'. Problems do arise when failing to distinguish between the square root function and a specific square root, just as with any function it is necessary to distinguish between the function itself and the value of that function at a particular point, often called 'the square root of ...' I have already defined a square root - and this applies equally well to negative as to positive numbers and to zero, which is neither positive nor negative. Now consider the number 4. My definition is satisfied by two different numbers +2 & -2. I hope we can agree that these are different. so multiply (+2) x (+2) or (-2) x (-2) Both of these products yield the initial value of 4, as per definition. So both are square roots. But what happens if you multiply one by the other ? (-2) x (+2) or (+2) x (-2) Neither are equal to the initial value of +4 ! You cannot take the negative sign inside the square root sign, like you do with brackets, which is what you appear to be trying to do. [math] - \sqrt 4 = \sqrt { - 4} [/math] is just plain wrong - it is never right. Many problems with functions arise because people only consider the rule and forget to consider the Domain and/or the CoDomain as well. This consideration is necessary when considering the whole function.

Oh dear, Oh dear, Oh dear. You should have believed me when I strongly suggested you took notice of what uncool says. Right at the beginning. The square root of something is defined as that which which when multiplied by itself yields that very something. But multiplying the suqare root of minus one by the square root of plus one is not multiplying something by itself, since the square root of mius one is not the same as the square root of plus one.

I really don't see where you are trying to get to. A function has three parts so you are right in saying that a function is a map from one set to another (which may be the same set). The base set or set mapped from is called the Domain and the target set or set mapped to is called the CoDomain. A function comprises the Domain, the CoDomain and a rule that links members of the Domain to members of the CoDomain. Many (or even all) members of the Domain may be linked to some particular member of the CoDomain, this is called many-to-one. But no member of the Domain may be linked to more than one member of the Codomain. This would called one-to-many and is not allowed. A function that links all the members of the domain to one single member of the CoDomain is called a constant function. Getting your head around all this is probabaly not worth the effort as it will not help you much, if at all. It is better to think of the three components as being two variables (say x and y since we are discussing numbers) and a rule or formula connecting them. The Domain is called the independant variable (x) and the CoDomain is called the dependant variable (y). For most purposes the Domain will be the set of real numbers or the real number line. The constant function has the rule y = a constant, say y = 5. This means that for each and every value of x the value of y is 5. This function can indeed be differentiated and the value of its derivaitve for all values of x is zero. I hope you will find this little exposition helpful and will listen to it.

When I first read this thread I thought dendrites ? But you say these are organic. Dendrites are similar inorganic structures. Here is a paper on decimetre scale ones. https://www.researchgate.net/publication/319654805_Pyrite-walled_tube_structures_in_a_Mesoproterozoic_sediment-hosted_metal_sulfide_deposit/link/59d5ac1a0f7e9b7a7e4677a8/download

Have you done an energy balance for the project or a cash flow plan ?

Consider the following NaOH Ca(OH)2 HCl H2SO4 One molecule of sodium hydroxide will neutralise one molecule of hydrochloric acid in an acid - base reaction. But it takes two molecules of sodium hydroxide to neutralise one molecule of sulphuric acid. So in some sense the sulphuric acid has twice the neutralising power of hydrochloric acid. The equivalent mass or equivalent weight is an old fashioned method of recognising this fact and we say that the equivalent weight of sulphuric acid is half its molecular weight. By the same token we say that the equivalent weight of hydrochloric acid is equal to its molecular weight. Or we say that the molecular weight of hydrochloric acid contains one 'equivalent' and the molecular weight of sulphuric acid contains two 'equivalents'. This method of 'equivalents' tells us how much of a given acid we need to neutralise a given quantity of sodium hydroxide. The same thing goes the other way when we consider calcium hydroxide, as compared to sodium hydroxide. It takes twice as much acid to neutralise the calcium hydroxide as for the sodium hydroxide. So the molecular weight of sodium hydroxide contains one equivalent and the molecular weight of calcium hydroxide contains two equivalents. Does this help ?

I understand derivation to mean a series of steps leading to a statement or conclusion. I think you mean 'differentiation' which means calculating the derivative as per the differential calculus. I know that in some other disciplines differentiation means distinguishing between alternatives. You differentiate a function and the result is known as the derived function or the derivative. Spooky. Life is made more difficult because you can't 'differentiate' a point or single member of a set or a set itself. This is my objection to your lines derivation produces produces: since you have already defined i' as a set. Does this help ?

Yeah definitely +1 Here is a simple dilution / mixtures formula that always works so long as you use consistent units, eg gms, w/w/, v/v, w/v, % molarity normality etc.

Yes you have definitely got the idea. +1 F = k1m and F = k2a are simultaneous equations so we combine them as I indicated to form one equation F=k3ma Having got that out of the way a couple of small points It is not quite right to say that k1 'contains' a or that k2 'contains' m which brings us neatly to the subject of units. Nearly always in Physics, the constant of proportionality also 'contains' the tranformation of units. It is not just a number (as it is in pure maths) it has units of its own that are very important. F, a and m all have different units so k1 converts acceleration units to force units and k2 converts mass units to force units. Can you see why it is this way round ? Furthermore in SI units the constants are arranged so that k3 = 1 This is the basis for physicists saying that the force is proportional to the acceleration and the 'constant of proportionality' is mass. This is true for a particular body when mass is not changing. (again as MigL has already noted) and is the usual form of presenting Newton's second law (N2) This is combining the two constants k1 and k2 to form a new constant k3 . Factoring would be splitting a single constant k3 into factors (two factors k1 and k2 in this case)

As MigL (+1) has noted, direct proportionality between two variables is the starting point for this. But a variable (force, F in this case) can be proportional to more than one variable at the ame time. In with your example, Force, F, is directly proportional to the mass of a body all other influences be held constant. It is also proportional to acceleratio, again all other influences be held constant. When this happens, the dependent variable (F) is given by the product of the two influencing variables as in F = ma. (Sometimes there will be three or more variables then we have a triple product. This happens in fluid mechanics and electronic signal theory) This is very good and very important mathematically because the variables are 'separated', which means we can deal with them separately or independently. Separation of variables is the method of solution for some of the most important equations in Physics. Going back to two variables, one directly proportional to the other I would add to MigL's description that a graph or plot of one variable against the other is a straight line graph through the origin. Straight lines not through the origin, are not representative of direct proportionality.

Hi Moon, I hope the recovery is going well. I wonder if your question is a bit short and general ? Why metal alloys ? Do you mean all metal since a carbon -iron alloy is not? Then again predict the properties is a very big ask. All of them ? and how accurately ? The short answer is yes. The longer answer is we can predict some of the properties some of the time and sometimes very accurately indeed. For instance the alloying process to make the earliest transistors with metallic germanium literally counted atoms of alloying element to achive the desired electrical properties. There are not that many possible crystal structures or arrangements and alloying means combining two elements into one structure so their respective crystal structures must be compatible, other wise a mixture is produced instead. Physical properties such as melting point can be estimated quite well, though some systems are more complicated than others. The Iron - Carbon system is particularly complicated by itself. Start to add further alloying elements such as manganese, chromium, nickel, vanadium, ... and it gets real complicated. We know from experience, rather than theory, what constituents produce desirable properties such as corrosion resistance (stainless steel). So give us some more detail to work with please.

Thank you for the clarification. When speaking to wooden planks like myself it helps to say exactly what you mean. 😉

Bayko dates from the 1930s. Like Meccano it had the characteristic of being dissassemblable. Another type of constructional toy, not yet mentioned would be the type where the result of construction was permanent. such as the 'Airfix' kits, mostly model aircraft. These followed on from earlier hobbies such as 'matchstick modelling' carried over from the previous century into the early part of the 20th. If you visit western Europe there are lots of toy museums scattered around, with some really fascinating toys and games. The one in Perth (Scotland) and the one downstream of Duisburg and Dusseldorf particularly spring to mind.

The answer to what ? I didn't ask a question, nor did you.

Thanks beecee, nice one. +1 Do you know if the 'waterfall' is the result of a step in the bed or is just in the water, looks like a bit like hydraulic jump to me. In fact it seems to be more like the effect you get pouring a bucket of water into a bath of water. https://parks.dpaw.wa.gov.au/park/lalang-garram-horizontal-falls

Looks very similar to the description by Alan Turing in his essay "Can a Machine think ?"

Perhaps the organic parts come from decayed fossils from this process http://preparation.paleo.amnh.org/56/pyrite-disease https://www.zoicpalaeotech.co.uk/pages/pyritefossils

A good place to start looking for information is this book - 700 + pages of wisdom. Chapter 2 is dedicated to your tidal question.

If you are not going to take the discussion seriously, you will need to find another to continue the discussion with.

Please elaborate on what you mean by these statements, since they are not mathematical ones I recognise. Note mathematical statements need not be symbolic, English is perfectly good. Please pay particular attention to what you mean by 'derivation' and 'set'. I seen no point worrying about the rest of the material in your post until the basics are cleared up.

I've not seen that method of mass accounting before, well done for spotting the issue and presenting it. +1 However perhaps you should explain the meaning of your square brackets, some may have difficulty working it out for themselves.

Of course they are, that is how the water body moves up and down to support the vertical movement of the water/air interface. Of course they are not the only source of water movement.